Alignment: Overall Summary

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Alignment to the CCSSM. The materials meet expectations for all of the indicators in Focus and Coherence (Gateway 1), and the materials meet expectations for all indicators in Rigor and Mathematical Practices (Gateway 2).

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
18
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
9
14
16
16
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Usability

|

Meets Expectations

Not Rated

Gateway 3:

Usability

0
17
24
27
25
24-27
Meets Expectations
18-23
Partially Meets Expectations
0-17
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; attending to the full intent of the modeling process; spending the majority of time on content widely applicable as prerequisites; allowing students to fully learn each standard; engaging students in mathematics at a level of sophistication appropriate to high school; making meaningful connections in a single course and throughout the series; and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards.

Criterion 1a - 1f

Materials are coherent and consistent with “the high school standards that specify the mathematics which all students should study in order to be college and career ready”.

18/18
+
-
Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; attending to the full intent of the modeling process; spending the majority of time on content widely applicable as prerequisites; allowing students to fully learn each standard; engaging students in mathematics at a level of sophistication appropriate to high school; making meaningful connections in a single course and throughout the series; and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards.

Indicator 1a

Materials focus on the high school standards.

Indicator 1a.i

Materials attend to the full intent of the mathematical content in the high school standards for all students.

4/4
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. Examples of the materials attending to the full intent of the standards include: 

  • N-CN.1,2,7: The introduction of rational exponents is done in Algebra 1, Lesson 2.4 as students analyze conjectures about how rational numbers between whole number data points are approximated to develop a continuous exponential function from a discrete geometric sequence. In Algebra 2, Lesson 3.5, students are formally introduced to complex numbers and operations with complex numbers as they relate to solutions to quadratic equations. 

  • A-SSE.3: In Algebra 2, Lesson 3.7, students verify different forms of a quadratic expression to solve a given equation. Students explain how the factored form helps to reveal the zeros and what that means in the context of the question. In Algebra 1, Lesson 2.6, students are guided through an exploration of how expressions with different rational exponents are equivalent yet highlight different mathematical properties.

  • A-APR.1-3: These standards are addressed in Algebra 2, Units 3 and 4. In Lesson 3.1, students add and subtract polynomials algebraically and graphically while also making and testing conjectures about the sum and difference of polynomials. In Lesson 3.2, students multiply polynomials using area models and traditional algebraic methods. Students divide polynomials using long division in Lesson 3.3 and use the Remainder Theorem to determine if a divisor is a factor of a polynomial. In Lesson 4.3, students investigate the relationship between roots, zeros, and x-intercepts using cubic functions. Students write cubic functions in factored form in order to identify the roots. In Lesson 4.4, students find real and complex imaginary roots of polynomials and write the polynomials in factored form.

  • F-IF.3: In Algebra 1, Lesson 2.1, students work with arithmetic and geometric sequences including discrete and continuous linear and exponential situations. In Algebra 1, Lesson 2.2, students connect context with domain and use the domain to distinguish between discrete and continuous functions. In Algebra 1, Lesson 2.3, students name functions based on identifying the change over equal intervals to prove that the function is either linear or exponential.

  • G-MG.1: In Geometry, Lesson 8.3, Retrieval, Ready, Set, Go, problems 10-11, students use a model to find the total surface area and volume of the Washington Monument. In Geometry, Lesson 8.4, students model how they would determine the volume of a nail.

  • S-CP.A: In Geometry, Lesson 9.3 students use samples to estimate probabilities. In Geometry, Lesson 9.5, students examine independence of events using two-way tables; and in Geometry, Lesson 9.6 students use data in various representations to determine independence.

Indicator 1a.ii

Materials attend to the full intent of the modeling process when applied to the modeling standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The materials provide opportunities for students to engage in the modeling process. Tasks that involve modeling include a graphic of the modeling process in the teacher notes. Additionally, the modeling standards are addressed in the materials.

Examples where students engage in some, or all, aspects of the modeling process with prompts or scaffolding from the materials include, but are not limited to:

  • In Algebra 1, Lesson 3.1, students sketch a graph given steps that Sylvia used to clean and refill her pool. Students complete the problem by responding to provided questions (F-IF.4). 

  • In Algebra 1, Lesson 8.3, students interpret a graph detailing Michelle’s bike ride to and from a lake. Students create a function to model the situation and identify key characteristics of the function (F-IF.4, F-IF.7b). 

  • In Geometry, Lessons 4.10 and 4.11, students solve real-world problems that include angles of elevation, angles of depression, and right angles (G-SRT.8).

  • In Geometry, Lesson 6.8, students “deepen their understanding of volume formulas.” Students discuss why the formula for the volume of a cone is one-third the volume of a prism and compare the two volumes (G-GMD.3). 

  • In Algebra 2, Lesson 1.2, students solidify their understanding of an inverse function. Students engage with mathematical models that represent relationships amongst car length, speed, and braking distance (F-BF.4). 

  • In Algebra 2, Lesson 9.2, students analyze and determine a “good” score on the ACT given information about the mean and standard deviation. Students answer analysis questions that are provided (S-ID.A).

Indicator 1b

Materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.

Indicator 1b.i

Materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs, and careers. Examples of the ways the materials allow students to spend the majority of their time on the WAPs include:

  • A-SSE: Throughout the AGA series, students engage with content related to the widely applicable prerequisites in A-SSE. Work related to the content standards found in this domain can be found in each course as both focus standards and supporting standards. For example, in Algebra 1, Lessons 7.3-7.6, students factor and rewrite expressions as directed in A-SSE.2. In Geometry, Lessons 7.5, students complete the square to reveal its center and radius (A-SSE.3b). In Algebra 2, Lesson 2.6, students interpret complicated expressions by viewing one or more of their parts as a single entity (A-SSE.1b). Students routinely factor polynomials of different powers in order to highlight different aspects of the function both algebraically and graphically.

  • G-CO.9: In the Geometry course, students work with content related to standard G-CO.9. In Geometry Lesson 3.3, students develop proofs that show that points on the perpendicular bisector of a segment are equidistant from the endpoints of the segment. In Geometry, Lesson 3.7, students prove that vertical angles are equal. In Geometry, Lessons 3.4-3.7, 5.1, and 7.3, students have additional opportunities to engage with the content of this standard.

  • G-SRT: In Geometry, Lessons 4.1 and 4.2 students build upon their understanding of dilations developed in Grades 7 and 8 to solidify their understanding of dilations and how triangles are similar. In Geometry, Lesson 4.3 students use the AA, SSS, and SAS Similarity Theorems to prove that triangles are similar. In Geometry, Lesson 4.5 students practice applying theorems about lines, angles and proportional relationships. In Geometry, Lesson 4.7 students develop a new proof of the Pythagorean theorem based on similar triangles. In Geometry, Lesson 4.8 students apply prior understandings about similar triangles to develop the definitions of the trigonometric ratios. In Geometry, Lessons 4.10 and 4.11 students continue to work with right triangles, trigonometric relationships and methods for finding missing angles and sides in right triangles and applied problems. 

  • S-ID.7: Students work with standard S-ID.7 in the Algebra I course. In Algebra I, Lesson 9.2, students use data sets to create scatterplots and determine the line of best fit. They examine different attributes of the graph of the line of best fit and determine if a linear model is appropriate. In Algebra I, Lesson 9.3, students interpret data based on the line of best fit, compare data sets, and make conjectures based on graphs of data sets and lines of best fit.

  • S-IC.1: In Algebra 2, Lessons 9.5 and 9.8-9.12, students compare different sampling methods and types of studies and address what kinds of conclusions can be reached when using the different types of studies. Students form conclusions given specific sets of data. This standard serves as a supporting standard for Lessons 9.6 and 9.8-12 as students work with confidence intervals and determine whether their results are statistically significant.

Indicator 1b.ii

Materials when used as designed allow students to fully learn each standard.

4/4
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for, when used as designed, letting students fully learn each non-plus standard. In general, students would fully learn most of the non-plus standards when using the materials as designed.

The non-plus standards that would not be fully learned by students across the series include:

  • A-APR.4: In Algebra 1, Lesson 7.4, students find the square of a binomial expression, recognize perfect square trinomials, and create perfect squares from partial areas. In Algebra 1, Lesson 7.7, Problems 9-11, students engage with the difference of squares. In Geometry, Lesson 6.6, Retrieval, Ready, Set, Go, problems 1-5, students apply the Pythagorean Theorem to find the unknown lengths in figures. In Algebra 2, Lesson 4.5, Retrieval, Ready, Set, Go, Problems 9-12, students engage with the sums and differences of cubes. Students do not use proven polynomial identities to describe numerical relationships.

  • F-IF.6: In Algebra 1, Lesson 2.9, Retrieval, Ready, Set, Go, problem 7, students calculate the average rate of change given two tables. In Algebra 1, Lesson 2.9, problems 3-7, students use both linear and exponential functions to calculate the average rate of change and, in Problems 10-17, students use a given exponential graph and student-generated equations to calculate the average rate of change. The materials have limited opportunities for students to estimate the average rate of change from a graph.

  • F-IF.7b: In Algebra 1, Lesson 8.7, students sketch graphs of piecewise-defined and absolute value functions. In Algebra 1, Lesson 8.7, Retrieval, Ready, Set, Go, problems 19-20, students graph cube root functions. The materials provide a limited number of problems for students to graph cube root functions.

  • F-TF.8: In Geometry, Lesson 4.9, Problem 14, students reason about the Pythagorean identity. In Algebra 2, Lesson 7.5, problem 3, students use a right triangle to show that the same Pythagorean identity is true for all acute angles. Students have a limited number of opportunities to learn how to find the trigonometric value of angles in all of the four quadrants using the Pythagorean identity.

Indicator 1c

Materials require students to engage in mathematics at a level of sophistication appropriate to high school.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age appropriate contexts, apply key takeaways from Grades 6-8, and vary the types of real numbers being used. 

Examples of the materials using age-appropriate contexts include:

  • In Geometry, Lesson 8.3, students find the volume of a frustum (created by rotating a trapezoid around the y-axis) and approximate the volume of a vase by replacing the curved edges of the vase diagram with segments. Teachers have students share several different strategies for approximating the volume (G-GMD.1,4).

  • In Algebra 2, Lesson 7.1, students use the information from Ferris Wheel tasks in the previous unit to develop strategies for transforming the functions to represent different initial starting positions for the rider. Students focus on horizontal translations and may recognize that either sine or cosine functions can be used with an appropriate horizontal shift (F-BF.3, F-TF.5).

  • In Algebra 2, Lesson 8.2, students sketch the shape of given graphs and justify their sketches. These functions combine linear, quadratic, absolute value, and trigonometric functions. While doing this, students design plans for a new amusement park ride (F-BF.1b).

Examples of the materials applying the key takeaways from Grades 6-8 include:

  • In Algebra 1, Lesson 3.4, students use a given graph of two functions to answer questions regarding key features of the graph, and students interpret some of the key features. This is an application of a key takeaway from Grades 6-8 in applying basic function concepts to develop/solidify new understanding in this unit (A-APR.1, A-CED.3, A-REI.11, F-IF.7).

  • In Geometry, Lesson 4.1, students consider a scenario where an employee at a copy center is enlarging a photo for a customer and makes a mistake. Students answer questions to determine what the mistake was and how the employee should have enlarged the photo. Students apply a key takeaway from Grades 6-8 regarding similar figures (G-SRT.1).

Examples of the materials using various types of real numbers include:

  • In Algebra 1, Lesson 2.6, students verify that the properties of integer exponents also apply to rational exponents. Students use exponent rules to write equivalent forms of expressions involving rational exponents and rational bases. Expressions include rational numbers in the base as well as in exponents (N-RN.1,2, A-SSE.3).

  • In Algebra 2, Lesson 3.4, students write the equation of given graphs of parabolas in vertex, standard, and factored forms. Students use irrational numbers and the radical form of i to write the factored form of equations (A-REI.4a,b). In Algebra 2, Lesson 3.5, students learn about i and calculate solutions for given quadratic equations that have both real and imaginary roots (N-CN.1,7).

Indicator 1d

Materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. Overall, the materials provide tasks in similar contexts throughout the series, so students can make connections to previous and future learning. The practice problems in Retrieval, Ready, Set, Go revisit topics in a spiral manner for students to maintain skills throughout the series. 

Examples of the materials fostering coherence through meaningful mathematical connections within a single course include:

  • In Algebra 1, Lesson 6.1, students describe a growing pattern that represents a quadratic function. They build upon interpreting expressions and writing recursive and explicit equations from Unit 1 (A-SSE.1, F-BF.1) to develop the idea that quadratic functions show linear rates of change. In Unit 6, students write equations to represent quadratic relationships (A-CED.2). 

  • In Geometry, Lesson 4.9, students develop relationships between the sine and cosine of complementary angles and justify whether given conjectures are true or false; and, in Problems 8-16, students use right triangles to justify if certain conjectures related to trigonometric identities are true (F-TF.8). In Geometry, Lesson 4.10, students solve for unknown angles and side measurements in a right triangle. In Geometry, Lesson 4.11, students solve applied and mathematical problems using all the concepts and skills developed by the previous tasks. 

Examples of the materials fostering coherence through meaningful mathematical connections between courses include:

  • In Algebra 1, Lessons 1.4 and 6.3, students analyze the pattern of push-ups that Scott will include in his workout. Students examine tables, graphs, and recursive and explicit formulas that show how the constant difference is represented in different ways, define the function as an arithmetic sequence, and recognize that a quadratic function is a model for the sum of the linear function. In Algebra 2, Lesson 4.1, students revisit Scott’s workout and develop understanding related to the degree of a polynomial function and the overall rate of change. Students use multiple representations to arrive at this understanding (A-CED.1,2, F-IF.4,5, F-BF.1, F-LE.1,2,3,5).

  • In Geometry, Lessons 7.7 and 7.8, students define a parabola geometrically using the focus and directrix. In Lesson 7.8, students connect this to quadratic functions and parabolas, which were addressed in Algebra 1, Units 6 and 7 (Functions and Algebra conceptual categories) (G-GPE.2). The concepts are further connected in Algebra 2, Lessons 3.4 and 3.5, where students discover a need for complex solutions to quadratic equations and define the imaginary unit (A-REI.4, N-RN.3, N-CN.A).

Indicator 1e

Materials explicitly identify and build on knowledge from Grades 6-8 to the High School Standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The materials explicitly identify the standards from Grades 6-8 in the Progression of Learning section of the teacher materials. This information appears routinely in the design of the teacher materials but not in the student materials.

Examples where the teacher materials explicitly identify standards from Grades 6-8 and build on them include, but are not limited to:

  • In Algebra 1, Lesson 2.6, students build on 8.EE.1, where they applied the properties of integer exponents, and their beginning work with fractional exponents from Lesson 2.4. Students rewrite expressions using the properties of exponents.

  • In Algebra 1, Lesson 9.1, students extend their prior learning from 8.SP.1 and 8.SP.2, constructing scatter plots and informally fitting lines to data. Students plot data sets, calculate the correlation coefficient, and learn to use it as a measure of the strength and direction of a linear relationship.

  • In Geometry, Lesson 4.3, students build on their experience with 8.G.4, where they applied a sequence of transformations to determine the similarity of two figures, and with 7.G.1, where they solved problems involving scale drawings of geometric figures. Students extend this understanding to develop a new definition of similarity for polygons. 

  • In Geometry, Lesson 4.7, students extend their prior learning from 8.G.6 and 8.G.7, where they engaged with the Pythagorean Theorem and used it to determine unknown side lengths of right triangles, and from 7.RP.2c and 7.RP.3, where they wrote proportionality statements based on similar triangles. In Lesson 4.7, students prove the Pythagorean Theorem in two different ways algebraically and use similar right triangles and the Pythagorean Theorem to develop right triangle trigonometric ratios.

  • In Algebra 2, Lesson 3.3, students build on their experience with factoring and dividing whole numbers (6.NS.1) as they learn the long division process for polynomials and use the quotient and remainder to write multiplication statements that are equivalent to the dividend.

  • In Algebra 2, Lesson 3.5, students extend their prior learning from 8.NS.1 and 8.NS.2, where they were introduced to the irrational numbers and approximated their values. Students revisit irrational numbers and the entire set of real numbers to contrast with imaginary numbers.

Indicator 1f

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series do explicitly identify the plus standards and do use the plus standards to coherently support the mathematics which all students should study in order to be college and career ready. 

Throughout the series the plus standards are included in such a manner that they can be studied simultaneously with the non-plus standards. In the Course Materials Guidance document, the following statement addresses the inclusion of plus standards in lessons primarily aligned to non-plus standards: “Some non-enrichment lessons may include (+) standards and /or (^) [mathematics that goes beyond the expectations of the standards] if the content is related to the mathematics of the lesson and can be explored simultaneously with the non-plus standards of the lesson. Enrichment lessons are distributed throughout the curriculum as natural extensions of the mathematics of the units. Consequently, the mathematical ideas of the Enrichment lessons are accessible to all students.” Lessons which are identified as enrichment (E) which are primarily aligned to plus standards can be easily omitted if necessary. Plus standard activities included in non-enrichment lessons, however, may not be as easily omitted.

Examples of components of the materials that address the plus standards include:

  • N-CN.8: In Algebra 2, Lesson 3.4, students use the quadratic formula to find non-real roots and write the equation of the parabola in factored form. In Lesson 4.6, students find suitable factorizations of quadratic, cubic, and quartic polynomials; some of these have imaginary roots and develop understanding that imaginary roots occur in conjugate pairs.

  • N-CN.9: In Algebra 2, Lesson 3.4, students engage with the complex solutions, the Fundamental Theorem of Algebra, and the relationship between roots and factors. These themes are extended throughout Unit 4. The materials include problems that are tagged with “(+)” to indicate alignment to the plus standard.

  • A-APR.5: In Algebra 2, Lesson 3.2, students begin by reviewing how to multiply polynomials and end with by applying Pascal’s Triangle to expand binomials.

  • A-APR.7: In Algebra 2, Lessons 5.4 and 5.5, students perform operations with rational expressions.

  • A-REI.9: In Algebra 2, Lessons 10.5 and 10.6, students use the inverse of the coefficient matrix to solve systems of linear equations.

  • F-IF.7d: In Algebra 2, Unit 5, students graph rational functions, identify zeros and asymptotes, and show end behavior.

  • F-BF.1c: In Algebra 2, Lessons 8.4, 8.5, and 8.6, Retrieval, Ready, Set, Go, students compose functions.

  • F-BF.4b: In Algebra 2, Lesson 1.4, students find the inverse of linear, quadratic, and exponential functions, apply verbal descriptions to the inverse operations, and generalize an algebraic process for finding inverses. In Lesson 1.5, students continue to find inverse functions and verify the inverse functions with an alternate use of composition (“The function g is the inverse of function f if and only if f(a) = b and g(b) = a”). In Algebra 2, Lesson 1.5, Retrieval, Ready, Set, Go, students use composition to verify that functions are inverses of each other. 

  • F-BF.4c: In Algebra 1, Lessons 8.5 and 8.6, students create multiple representations, including graphs and tables, of given functions and determine if there is a relationship between the functions, which develops into recognizing inverse functions. In Algebra 2, Lesson 1.2, students find inverse functions to quadratic and square root functions, and, in Lesson 1.3 find inverse functions for exponential functions. Lesson 1.5 provides students additional practice with finding inverses. 

  • F-BF.4d: In Algebra 2, Lesson 1.2, students produce an invertible function from a non-invertible function by restricting the domain. 

  • F-BF.5: In Algebra 2, Lesson 1.3, students learn that the inverse of an exponential function is a logarithmic function. In Algebra 2, Lesson 2.5, students solve base 10 exponential equations using logarithms graphically and algebraically. 

  • F-TF.3,4: In Algebra 2, Lessons 7.4, students use the unit circle diagram to find tangent values for angles that are multiples of the angles found in the special right triangles. Later in Unit 7, students explain why the sine, cosine, and tangent functions are even or odd using reasoning based on the unit circle, graphs of the functions, and prior knowledge of the trigonometric even and odd identities.

  • F-TF.7: In Algebra 2, Lesson 7.6, students use trigonometric identities and inverse functions to solve trigonometric equations.

  • G-SRT.9-11: In Geometry, Lessons 8.6-8.7, students find missing sides and angles of non-right triangles using a variety of strategies leading to the development of the Law of Sines and the Law of Cosines. In Geometry, Lesson 8.8, students derive an alternate formula for the area of a triangle in terms of trigonometric functions.

  • G-C.4: In Geometry, Lesson 5.4, students describe a procedure for constructing a tangent line through a point outside the circle and then prove the procedure works.

  • G-GMD.2: In Geometry, Lesson 6.8, students make an informal argument using Cavalieri’s principle for the formulas for the volumes of solid figures.

  • S-MD.7: In Geometry, Lesson 9.1, students analyze and make sense of tuberculosis skin test data using conditional probability.

The following plus standards are not addressed in the series:

  • N-VM.4b,4c,5a,5b

  • S-CP.8,9

  • S-MD.1-6

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

Criterion 2a - 2d

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

8/8
+
-
Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Rigor and Balance. The materials meet expectations for providing students opportunities in developing conceptual understanding, procedural skills, and application, and the materials also meet expectations for balancing the three aspects of Rigor.

Indicator 2a

Materials support the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Every unit attends to the learning cycle, interweaving aspects of mathematical proficiency. “Some lessons are devoted to developing a concept, others to solidifying understanding, yet others to practicing mathematics.” For example, in Algebra 1, Unit 4, each lesson builds upon the previous to reinforce concepts:

  • In Algebra 1, Lesson 4.1, students develop conceptual understanding by explaining each step in the process of solving an equation (A-REI.1).

  • In Algebra 1, Lesson 4.2, students solidify their understanding by rearranging formulas to solve for a variable (N-Q.1, N-Q.2, A-REI.3, A-CED.4).

  • In Algebra 1, Lesson 4.3, students practice solving literal equations (A-REI.1, A-REI.3, A-CED.4). 

The materials systematically support the development of conceptual understanding as students build on the previous day’s learning with each new lesson.

  • N-RN.3: In Algebra 2, Lessons 3.5 and 3.6 develop the concept of irrational numbers. The students begin by plotting rational numbers on a number line and then move on to plotting irrational numbers on the number line. This activity helps students understand the similarities and differences between irrational and rational numbers. Once students establish this understanding in Lesson 3.5, the students develop their understanding of the properties of irrational numbers in Lesson 3.6. The materials address irrational numbers and their properties over two lessons, so students have the opportunity to develop a more thorough understanding of the mathematical concept.

  • F-IF.7: In Algebra 1, Lesson 7.1, students develop an understanding of transformations on a graph and how a graph relates to a corresponding equation. Students explore the changes of a graph in relationship to the area of a square. By the end of this lesson, students identify the key features of the graph and how changes to a corresponding equation will change the graph. This development is continued in Algebra 1, Lesson 7.2, where “students write and graph quadratics with multiple transformations.”

  • G-CO.10: In Geometry, Lessons 3.1, as students explore ways of knowing the triangle interior angles sum theorem - one based on experiments with specific triangles and the other based on a transformational argument - they consider the difference between making a conjecture based on experimentation versus reasoning about the validity of the conjecture using diagrams. In Lesson 3.2, students generate proofs for specific cases showing that the base angles of isosceles triangles are congruent; and in Lesson 3.3, students prove that the base angles of isosceles triangles are congruent for all cases.

  • G-GPE.B: In Geometry, Lessons 7.1-7.3, students engage in a complete learning cycle. In Lesson 7.1, students find the distance between two points; and in Lesson 7.2, students prove that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals. In Lesson 7.3, students apply coordinate geometry to quadrilaterals to prove that a given quadrilateral is a parallelogram, a rectangle, a rhombus, or a square.

Indicator 2b

Materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.

2/2
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-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. Examples in the materials where students independently demonstrate procedural skills include, but are not limited to:

  • N-CN.7: In Algebra 2, Lesson 3.5, Retrieval, Ready, Set, Go, students solve six quadratic equations, three of which have complex solutions (problems 28, 31, and 32). In Algebra 2, Lessons 3.6-3.8 and Lesson 4.5, students solve additional problems that have complex solutions.

  • A-SSE.2: In Algebra 2, Lesson 2.3, students derive the product, quotient, and power rules for logarithms by graphing various logarithmic functions and generalizing the patterns found in corresponding equations. In Retrieval, Ready, Set, Go, problems 1-12, students practice rewriting radical expressions with fractional exponents and logarithmic expressions with radical exponents. In problems 15-16, students practice applying the rules of logarithms by identifying which of the given expressions are, in fact, equivalent, and showing why. In problems 17-22, students practice converting exponential equations into their logarithmic equivalents, and vice versa. In Algebra 2, Lesson 4.6, students use the given features of a polynomial to find other features, such as writing the function in factored form when given the graph of the function or its roots. Because only some information about the function is provided, students write the equation of the polynomial from scratch or write the equation in a different form than is given in order to find the other missing information. Students continue practicing these types of problems on their own in Retrieval, Ready, Set, Go, problems 10-15. In problems 1-8, students also practice rewriting rational expressions by dividing out common factors from the numerator and denominator. 

  • F-BF.3: In Algebra 1, Lesson 7.1, students complete scaffolded questions about the effect on the graph of f(x) by replacing it with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). In Retrieval, Ready, Set, Go, students complete problems to develop and demonstrate their procedural skill. In Lessons 7.2 and 8.3-8.4, students write equations and graph functions that have multiple transformations for quadratic and absolute value functions, respectively. Students continue to write equations and graph functions that have multiple transformations for cubic, rational, logarithmic, and trigonometric functions in Algebra 2, Units 2-8.

  • G-GPE.7: In Geometry, Lesson 7.1, students determine the distance between two points on the coordinate plane. At times they are only required to calculate the distance vertically or horizontally. Other times, students are asked to determine the distance between two points on a diagonal. Students use the Pythagorean Theorem to determine the distance and then formalize that understanding into the distance formula. Students practice with the procedure and formalize their thinking (strategies) conceptually. The procedural use of the distance formula is reinforced in Geometry, Lesson 7.3, where students prove that figures are parallelograms by comparing the lengths of opposite sides.

  • S-CP.3: In Geometry, Lessons 9.4-9.6, students connect conditional probability and general probability and come to understand the meaning of independence, using tests to determine if two events are independent, and using the Multiplication Rule to find probabilities for independent events. In Lesson 9.4, Retrieval, Ready, Set, Go, problems 9-14, students find the conditional probability in contextual situations. In Lesson 9.5, Retrieval, Ready, Set, Go, problems 7-10, students use formulas for P(A and B) and P(A|B) to determine independence; in problems 11-22, students find general and conditional probabilities. In Lesson 9.5, Retrieval, Ready, Set, Go, problems 5-15, students find general and conditional probabilities and determine independence within a range of contexts.

Indicator 2c

Materials support the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for supporting the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters. 

Lessons often begin with an engaging scenario that is either a direct, real-world application of the content for that day or a unique, novel problem for the students to solve. The applications within the series support students as they develop their conceptual understanding of the mathematics and subsequent acquisition of abstract notation and procedural skills. There are also scenarios that recur throughout the series. As a result, students contextualize many different mathematical ideas to the same scenario.

The series includes numerous applications across the series, and examples of select standard(s) that specifically relate to applications include, but are not limited to:

  • A-CED.3: In Algebra 1, Lessons 5.1, 5.2, 5.4, and 5.5, and within a pet-sitting context, students use systems of equations and inequalities to build a business model, minimize cost, and maximize profit. 

  • A.REI.3: In Algebra 1, Lesson 4.1, students “develop insights into how to extend the process of solving equations to multistep equations” associated with the actions of Elvira, a cafeteria manager. This storyline continues in Lesson 4.2, where students “apply the equation solving process developed in the previous task to solving literal equations and formulas” as Elvira continues to work to improve the efficiency of the cafeteria.

  • F-IF.4,5: In Algebra 1, Lesson 3.2, students use tables and graphs to interpret key features of functions (domain and range, increasing and decreasing intervals, intercepts, rates of change, discrete vs. continuous) while analyzing the characteristics of a float moving down a river. Students interpret water depth, river speed, and distance traveled.

  • F-IF.7: In Algebra 2, Lesson 5.1, students write, graph, and solve rational equations in the context of winning the lottery. Students compare different points on the equation and graph based on different ways of splitting the prize money. In Retrieval, Ready, Set, Go, problems 7-10, students interpret an equation and a graph to determine different ways of paying for a gift among friends.

  • F-TF.5: In Algebra 2, Lesson 6.1, students will use right triangle trigonometry to develop a function for finding the height of a rider at any position on a stationary Ferris wheel with specified midline (center) and radius (amplitude). In Algebra 2, Lesson 6.2, students model the circular motion of a rider as the angle measures the amount of rotation around a moving Ferris wheel, creating a function that models the amplitude, period, and average height (or midline) of the rider.

  • G-SRT.8: In Geometry, Lesson 4.10, students determine the height of a tree using angle of elevation and shadows. Students work within the same scenario to determine unknown angles of depression and elevation. In the Retrieval, Ready, Set, Go problem set, students work multiple real-world problems using trigonometric ratios to determine missing lengths and angles.

  • S-ID.2: In Algebra 1, Lesson 9.7, students select the bridge design that will support the most weight upon calculating and comparing the mean and standard deviation of their weight-bearing data. In Algebra 1, Lesson 9.8, students calculate measures of center (mean and median) and spread (interquartile range and standard deviation) of test results of six classes; by analyzing these results, students determine which class performed the best on the test and wins free pizza. 

Indicator 2d

The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Overall, the three aspects are balanced with respect to the standards being addressed.

Throughout the materials students engage in each of the aspects of rigor in a cycle: each unit contains at least one Developing Understanding lesson to build conceptual understanding in students, at least one Solidifying Understanding lesson to build on that conceptual knowledge, and at least one Practicing Understanding lesson. Real-world applications are often incorporated in these cycles. Within each lesson there are Retrieval, Ready, Set, Go problems that spiral procedural skills for students. Examples include:

  • In Algebra 1, Lesson 2.1 (a Developing Understanding lesson), students build upon their experiences with arithmetic and geometric sequences and extend to the broader class of linear and exponential functions with continuous domains. Students compare these types of functions using multiple representations. In Algebra 1, Lesson 2.2 (a Solidifying Understanding lesson), students discern when it is appropriate to represent a situation with a discrete or continuous model, thus deepening their conceptual understanding. Within this lesson, students also practice modeling with mathematics by connecting the type of change (linear or exponential) with the nature of that change (discrete or continuous), thus supporting student development of procedural skill and fluency. Throughout both of these lessons, students learn the concepts and procedures through their application to real-world contexts (e.g., medicine metabolized within a dog’s bloodstream and pool filling/draining). (F-IF.3, F-IF.5, F-BF.1, F.LE.1, F.LE.2)

  • In Algebra 1, Lessons 8.5-8.7, students work with inverse functions and engage in all three aspects of rigor. The emphasis of this learning cycle, students work with inverse functions. In Lesson 8.5 (a Developing Understanding lesson), students compare the two different ways of modeling the same real-world context (two friends who ride bikes for exercise) to see characteristics of inverse functions, such as: the graphs are reflections over y = x, the inputs and outputs in the tables are reversed, and the equations have reciprocal slopes with the variables reversed. In Lesson 8.6 (a Solidifying Understanding lesson), students find inverse functions from equations and graphs. In the culminating lesson of the unit, Lesson 8.7 (a Practice Understanding lesson), students combine the work of piecewise functions, inverse functions, and absolute value functions using tables, graphs, and equations. (F-LE.2, F-LE.3, F-LE.5, F.BF.2, F-IF.5, F-IF.7, F-IF.9, A-REI.10)

  • In Geometry, Lesson 6.4 (a Develop Understanding lesson), students use the formulas for arc length and area of a sector, developed in Lesson 6.3, and proportional reasoning to calculate the ratio of arc length to radius. Students use this ratio to define a constant of proportionality for any given central angle that intercepts arcs of concentric circles and develop radians as a way to measure an angle. Students conduct this work as they help Madison design her circular garden. In the Retrieval, Ready, Set, Go problem set, students practice the procedures by answering problems related to area, circumference, and the arc length of circles. (G.C.5)

  • In Geometry, Lesson 7.2 (a Solidifying Understanding lesson), students use the slope formula and determine the relationship between parallel and perpendicular lines. Students engage with procedures by finding the slope between two points. Students then think conceptually when comparing the slopes of two lines to determine if the lines are parallel, perpendicular, or neither. Students also use rotations and transformations to hypothesize about the relationships between the slopes of lines that have undergone a transformation. (G.GPE.B, G.GPE.5)

  • In Algebra 2, Lesson 5.2 (a Solidifying Understanding lesson), students engage with the same function f(x) = 1/x, but with a primary focus on the procedures of graph transformations and writing equations from graphs, without incorporating application problems. The lesson begins with practice problems that activate students’ prior knowledge about transformations of functions addressed in earlier lessons in the course. The lesson then revisits a graph of the function f(x) = 1/x and students name the asymptotes and anchor points. Later, given a set of problems containing either a graph or a description of a function that is a transformation of f(x) = 1/x, students write the equation for each. In yet another problem set in the lesson, students match a given equation to one of the given phrases that describes a transformation from y = 1/x. (F-IF.7d+, A-CED.2) 

Criterion 2e - 2h

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

8/8
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Practice-Content Connections. The materials intentionally develop all of the mathematical practices to their full intent: make sense of problems and persevere in solving them (MP1), reason abstractly and quantitatively (MP2), construct viable arguments and critique the reasoning of others (MP3), model with mathematics (MP4), use appropriate tools strategically (MP5), attend to precision (MP6), look for and make use of structure (MP7), and look for and express regularity in repeated reasoning (MP8).

Indicator 2e

Materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional  series meet expectations for supporting the intentional development of overarching, mathematical practices (MPs 1 and 6) in connection to the high school content standards.

Examples of where students make sense of problems and persevere in solving them include, but are not limited to:

  • In Algebra 1, Lesson 3.1, students make sense of a story context to make a graph of a function without any knowledge of shape or scale. Working within the context of a pool’s water level over time, students persevere in making sense of increasing and decreasing intervals, minimum and maximum values, and domain and range. 

  • In Geometry, Lesson 2.1, students construct two shapes: a rhombus and a square. Within the materials, teachers are prompted to provide students with enough time to explore the constructions fully. Within this lesson, students make sense of the constructions and persevere through the process of making the construction.

  • In Algebra 2, Lesson 1.1, students make sense of two different views of a problem situation, each using a different dependent and independent variable. Because students who attempt to model the problem using the same variables in both cases will likely encounter confusion, students have an opportunity to persevere and in doing so see the importance of defining and making consistent use of variables as well as highlighting features of a relationship between a function and its inverse.

Examples of where students attend to precision include, but are not limited to:

  • In Algebra 1, Lesson 2.2, students identify the domains of two sequences. As students “connect the type of change---either linear with a constant rate of change or exponential with a constant change factor, with the nature of the change, either discrete or continuous”---they further conceptualize that an arithmetic sequence is a linear function with a domain that is limited to the natural numbers and that a geometric sequence is an exponential function with a domain of the natural numbers. In Lesson 2.2, problems 6-11, students discuss a situation that is not clearly discrete or continuous and attend to precision as they make mathematical arguments about modeling choices.

  • In Geometry, Lesson 1.1, students attend to precision in their language for transformations. Students use precise definitions for each of the transformations so the final image is a “unique figure, rather than an ill-defined sketch.” The materials prompt students to see how precision is needed when defining geometric relationships to make sure that images are well defined. 

  • In Algebra 2, Lesson 8.3, “students naturally attend to precision as they attempt to refine the parameters of the equations they write to model the data given in graphs and tables.” Students become aware of how small changes in some parameters of certain equations result in large differences in results, while other parameters may be less sensitive to small changes. 

Indicator 2f

Materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for supporting the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. Throughout the materials, there are many opportunities for students to critique the reasoning of others and to reason abstractly.

Examples where students reason abstractly and quantitatively include, but are not limited to:

  • In Algebra 1, Lesson 4.4, students are given a statement and determine which of the two expressions represent a larger value. In addition, students reason abstractly about an expression, compare it to another expression, and explain their reasoning.

  • In Algebra 1, Lesson 7.1, students reason abstractly by relating the numeric results in a table to the graphs and explaining how the graph is transformed. Students examine the abstract relationships between the different representations (table, graph, and function) and how a change in one form impacts a change in the other.

  • In Geometry, Lesson 6.2, students reason about how an infinite process might converge on a unique value and examine the case of how an inscribed regular polygon with more and more sides converges on the shape of a circle. This limiting process provides an informal proof for the circumference and area of a circle.

  • In Algebra 2, Lesson 4.2, students identify the characteristics of and graph the basic cubic function. Students come to understand that the same transformations they used to graph quadratic functions can be applied to cubic functions. Students reason abstractly and quantitatively as they compare the rates of change and end behavior of quadratic and cubic functions. In the Retrieval, Ready, Set, Go problem set, students reason quantitatively by substituting in values to compare different power functions. Students reason abstractly by making generalizations based on their knowledge of exponents.

Examples where students construct viable arguments and critique the reasoning of others include, but are not limited to:

  • In Algebra 1, Lesson 3.2, students interpret two representations (a table and a graph) and determine if Sierra’s statements are correct. Within the lesson, students analyze the situations, justify their reasoning, and communicate their conclusions to others. Students listen to the reasoning of others and decide if they make sense.

  • In Geometry, Lesson 4.8, students consider examples of right triangles and explain why their specified ratios are the same, or nearly the same. Students identify and justify that having one acute angle congruent in all of the triangles creates a set of similar right triangles. Students use this observation to hypothesize the trigonometric relationships for all right triangles. Students determine how the ratios are related and construct an argument for what they believe about the trigonometric ratios.

  • In Algebra 2, Lesson 6.4, students work in partners to apply their understanding about sinusoidal functions to the construction of their own Ferris wheel in terms of radius, height, period, and direction of rotation, along with its graph and equation. Students then share their responses with another pair and decide if they agree with the connections they each have made between the three representations of each of their Ferris wheels: the description, the graph, and the function equation. Students are given sentence frames to provide support for constructing viable arguments and critique the reasoning of others; the sentence frames allow students to explain the connections in the representations of their Ferris wheel and provide supporting evidence for their claims.

Indicator 2g

Materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for supporting the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. 

Examples where students engage in modeling include, but are not limited to:

  • In Algebra 1, Lesson 5.3, students manipulate a system of equations to model the constraints of setting up a cat and dog boarding business. They determine the best use of space to provide maximum profit. Students also have to understand what terms in their expressions are related to the different constraints. From this, they derive various forms of the equations to determine maximum profit.

  • In Geometry, Lesson 6.1, students analyze a plan to build a regular, hexagonal gazebo. In the plan, there are several statements with which students must agree or disagree and then design their own gazebo.

  • In Algebra 2, Lesson 8.3, students model two real-world behaviors: a dampened oscillation (the up and down motion of the bungee jumper) and Newton’s Law of Heating. To do so, students draw on mathematics they know well, such as how to model periodic behavior and exponential growth and decay, along with their emerging understanding of combining functions to model more complex behavior. Students use the graphing calculator to test and refine their assumptions until they have an accurate model that fits the data given in the tables and graphs provided in the lesson.

Examples where students choose appropriate tools strategically include, but are not limited to:

  • In Algebra 1, Lesson 2.8, students compare linear and exponential growth related to two small companies. They are encouraged to use a calculator or spreadsheet to determine if this growth is continuous or discrete.

  • In Geometry, Lesson 2.2, students use the circle as a tool to create congruent line segments. Students also consider transformations as tools to think about congruence when creating mappings.

  • In Algebra 2, Lesson 2.5, students use various tools, such as tables, graphs, and technology, to find missing values for exponential functions. Because some problems require the use of a calculator whereas others do not, students make appropriate decisions about using technology, like finding exact values for log expressions without relying on a calculator when they can.

Indicator 2h

Materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for supporting the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards.

Examples where students look for and make use of structure include, but are not limited to:

  • In Algebra 1, Lesson 8.3, students recognize that the operation of absolute value leads to a graph with two distinct sections. They relate the two sections of the graph to their experiences with piecewise functions and write equations in both piecewise and absolute value forms. Students use the structure of the graph to write piecewise functions and relate the structure of piecewise function rules to equivalent absolute value functions. 

  • In Geometry, Lesson 1.6, students uncover the structure of regular polygons through experimenting with rotational symmetry and line symmetry. They notice that different types of line segments serve as lines of symmetry in regular polygons with an even number of sides versus those with an odd number of sides. 

  • In Algebra 2, Lesson 3.4, students gain insight into the different types of roots for quadratic functions by making connections across multiple representations. Students connect information included in a table with the vertex and factored forms of a quadratic equation. Students use graphs to explain why roots of a quadratic function might be integers, non-integer rational numbers, irrational numbers, or non-real numbers.

Examples where students look for and make use of repeated reasoning include, but are not limited to:

  • In Algebra 1, Lesson 8.6, students use the reasoning of how a function and its inverse are related to observe how they can write the inverse function by paying attention to the operations in the original function and the order in which they are performed. Students become familiar with characteristics of an inverse function and how to restrict are prompted to see that when finding an inverse you can sometimes just “undo” the operations in the opposite order of the original function.

  • In Geometry, Lesson 1.2, students make a conjecture about the relationship between the slopes of perpendicular lines based on the collection of data obtained in four experiments. They also provide an informal justification as to why the conjecture is true by examining the rotation of the legs of a right triangle and relating this to the rise and run that determines slopes of the hypotenuse of a right triangle before and after rotation.

  • In Algebra 2, Lesson 4.1, students apply previous experiences with functions and their representations to reason throughout this lesson. Students reason about the different rates of change and create recursive forms of equations as they seek generalizations. For example, students understand that a cubic function has a first difference that is quadratic, a second difference that is linear, and a third difference that is constant. Students generalize this pattern for all polynomial functions.

Gateway Three

Usability

Meets Expectations

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Gateway Three Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Usability. The materials meet expectations for Criterion 1 (Teacher Supports), partially meet expectations for Criterion 2 (Assessment), and meet expectations for Criterion 3 (Student Supports).

Criterion 3a - 3h

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

9/9
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials; contain adult-level explanations and examples of the more complex course-level concepts and concepts beyond the current courses so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

Indicator 3a

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Each lesson uses a consistent format to provide teacher guidance on how to present the student and/or ancillary materials in a way that engages students and guides their mathematical development. For example, the instructional materials, which are divided by section (e.g., Jump Start, Launch, Explore, Discuss, Exit Ticket), include Groupings; Routines; and Narratives. Examples of how the instructional materials provide teacher guidance on how to present the student and/or ancillary materials include:

  • In Geometry, Lesson 2.4, where students justify triangle congruence criteria using rigid transformations, the materials for the Jump Start indicates a duration of 10 minutes and Individual and Whole Class groupings. Annotations about possible student misconceptions are also included. Specifically, the materials indicate “Students may rely upon it 'looks like they are congruent' as their justification. If so, draw a second triangle, ∆ABD, by sliding point A slightly left or right. Such a triangle may appear to be congruent, but only measuring sides and angles to verify they are the same length would verify that they are so.” The Launch Narrative suggests that teachers introduce Proof by Contradiction as a way to help students think about how their arguments support their claims. 

  • In Algebra 2, Lesson 7.8 the instructional materials include Unit Circle and game cards Black Line Masters (BLMs) to support student engagement with the learning objectives as well as students’ understanding of the mathematical concepts through visual representations. Related annotations provide guidance for questions that prompt student thinking, narrative remarks to connect one student’s process to another student’s process, and tips for transitioning from the game card activity to the whole class discussion. For example, the Launch Narrative includes the note: “Some equations require students to use trigonometric identities as part of the solution process. This work is the ‘practice’ part of the task, so watch how adept students are at this work, and select particularly difficult work for the whole class discussion.” The Explore Narrative includes Think-Pair-Share Teacher Notes and suggestions for Selecting and Sequencing Student Thinking while making connections to the Whole Class discussion.

Each lesson uses a consistent format to provide teacher guidance on how to plan for instruction in a way that engages students and guides their mathematical development. For example, at the beginning of each lesson, teacher guidance includes Learning Goals (Teacher), Learning Focus (Student), Standards for the Lesson, Materials (when necessary), Required Preparation (which includes Anticipate Student Thinking), BLMs, Progression of Learning, and Purpose. In the course of the lesson, the materials also include Anticipate & Monitor and Selecting, Sequencing, & Connecting charts. Examples of how the instructional materials provide teacher guidance on how to plan for instruction include:

  • In Algebra I, Lesson 5.8, which addresses A-REI.5, the materials include Anticipate & Monitor as well as Selecting, Sequencing, & Connecting charts so that teachers can plan to guide students’ understanding of the mathematical concepts both individually and as a whole class. The materials prompt teachers to listen for students making arguments in Monitoring Student Thinking. One example for teachers to listen for is: “For problem 1, since Carlos bought the same number of bags of Tabitha Tidbits, the difference in the total cost must be due to the two extra bags of Figaro Flakes.” In Connect Student Thinking, students generate a list of key points to demonstrate their understanding of underlying processes that helped them to solve each scenario. One possible key idea is: “If the number of one type of item is the same in both purchases, then the difference in total cost is due to the difference in the number of the second item purchased.”

  • In Geometry, Lesson 8.5, the instructional materials include Required Preparation notes that suggest using a quick quiz to assess student understanding of the previous lessons and to forego the exit ticket. The materials also remind the teacher to make copies of the quick quiz prior to class. In addition, the instructional materials include timing guidance.

Indicator 3b

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for containing adult-level explanations and examples of the more complex course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. 

The teacher edition contains thorough adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge. Each unit includes an overview of the content addressed in each lesson. The narrative is presented in adult language with a quick table reference of math concepts presented per lesson. In addition, each lesson’s Progression of Learning and Purpose sections describe specifically how lessons connect content throughout the learning cycles of multiple lessons. As a quick reference point, Open Up High School Math Dependency, a chart provided with the series, gives teachers the opportunity to see where a given lesson connects to another course in the series but not outside the scope of the current materials. Examples of how the materials support teachers to develop their own knowledge of more complex, course-level concepts include:

  • At the end of the Algebra 1, Unit 3 Overview, teachers learn how to write features of functions using interval notation. In addition, there is an explanation about how interval notation connects to set notation, which is the notation that students have been using in previous lessons. 

  • In the Teacher Notes, there is an Anticipate & Monitor Chart that gives explanations to guide student thinking. Within these explanations, teachers are able to improve their own knowledge of the subject. In Geometry, Lesson 2.4, teachers are given an explanation in the Teacher Notes with the transformations that can prove two triangles congruent using SSS criteria, including a diagram. 

  • In Algebra 2, Lesson 5.3, the Selecting, Sequencing, & Connecting chart offers multiple possibilities for how students might respond to Explore question 9, which asks them to draw conclusions about the degree of the numerator and denominator in a rational function, the location of asymptotes for the rational function, and the function’s intercepts. In unpacking a solution in which a student claims that the x-intercept can be found by setting the function equal to 0, the teacher notes offer sample follow-up questions that would allow students to test that proposed solution, then offers additional clarification about why those questions are relevant in the context of that solution. Using adult language, the teacher note explains that although the student’s solution is correct, setting just the numerator equal to zero would be a more efficient approach to the problem.

For each course, the materials also provide adult-level explanations and examples for teachers to improve their own knowledge of concepts beyond the current course through a collection of essays titled Connections to Mathematics Beyond the Course. These essays are also directly connected to the lessons with which they are relevant, and examples include:

  • In Algebra 1, Lesson 2.9 is connected to Rate of Change.

  • In Geometry, Lessons 6.1 and 6.2 are connected to Limits, and Lessons 8.2 and 8.3 are connected to Riemann Sums and the Definite Integral.

  • In Algebra 2, Lessons 6.4, 6.5, and 7.1 are connected to Parametrically-defined curves.

Indicator 3c

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

The teacher materials provide Information to allow coherence across multiple course levels and to allow a teacher to make prior connections and teach for connections to future content. Examples include but are not limited to:

  • In the Course Guide, the Standards Alignment for AGA lessons indicates where the standards can be found within the lessons and Retrieval Ready, Set, Go problem sets. 

  • The Course Overview describes the purposeful design of each course. For example, the Algebra 2 Course Overview explains how the course is designed to build upon student understanding of functions developed in Algebra 1 and how the work in the first three units reviews students’ learning of linear, quadratic, and exponential functions, thus preparing them to engage with other functions throughout the course. The Course Overview highlights that the major purpose of Algebra 2 is for students to use and apply the accumulation of learning they have gained from their previous courses, in that students build on their understanding of right triangle trigonometry from the Geometry course, as well as their knowledge of functions and how to manipulate them from Algebra 1.

  • The Progression of Learning section of the instructional materials situates the intended learning outcomes of the current lesson within the continuum of past and future learning. For example, in Geometry, Lesson 9.1, the materials indicate that the lesson builds on students’ prior experience with using tree diagrams to find probabilities from Grade 7 (7.SP.6; 7.SP.7b; 7.SP.8a-c) to introduce conditional probability (S.CP.5, S.CP.6). The materials also indicate Supporting Standards (S.CP.3, S.CP.4) that will be a focus in ensuing lessons. In addition, Algebra 2, Lesson 1.1 explains how the lesson revisits and builds upon concepts related to inverse functions, which were introduced in Algebra 1, Unit 8. It further explains how the lesson fits into the unit as a whole: how students will later explore the inverse of an exponential function, leading to the concept of logarithms which are explored in more depth in the following unit.

The materials clearly indicate how individual lessons or activities throughout the series are correlated to the CCSSM. Each lesson identifies the mathematical content standards as well as the relevant Standards for Mathematical Practice (SMP). Examples include:

  • In Geometry, Lesson 1.4, the materials identify Focus Standards G.CO.1, G.CO.2, G.CO.4 and Supporting Standards G.CO.5 and G.CO.6 related to the content. The lesson also identifies the MPs 3, 6, and 7. In the Exit ticket, G.CO.4 is identified as the content standard to which the lesson should build.

  • In Algebra 1, Lesson 1.9, the Selecting, Sequencing, and Connecting chart includes a sample solution indicating that a student might determine that there are two possible common ratios when there is an even number or jumps of one possible common ratio when there is an odd number of jumps. The materials include a teacher note to emphasize MP3 by asking the whole class “What do you think about this claim?” and encouraging students to test the claim with a couple of problems.

Indicator 3d

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series provide some strategies for informing all stakeholders, including students, parents, or caregivers, about the program and suggestions for how they can help support student progress and achievement.

Information regarding the mathematics that students will learn is provided in the course and unit overviews for teachers, and the Course Guide provides the following description of the Lesson Summaries, “This section provides the class with a summary of the main mathematical points of a lesson, in student-friendly language. The summary is meant for students to read on their own time, or to help catch them up on a day they were absent. It may also be useful for families who want to understand in more detail what their student is learning. Lesson Summaries are included in the student-facing material.”

Also, the materials include Guidance on School to Home Connections, which provides specific ways educators can share, communicate, and explain the mathematics learned in the lessons at school with parents or caregivers.

Indicator 3e

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The Open Up High School Math Course Guide is replete with information that explains the instructional approaches of the program as well as identifies research-based strategies that are used in the design. Specific examples include, but are not limited to:

  • In “About These Materials,” the materials describe the student engagement, the classroom experience, and teacher role that one can expect when implementing a problem-based mathematics curriculum.

  • In “Design Principles,” the materials highlight the Comprehensive Mathematics Instructional Framework (CMI), which provides access to research-based principles and practices of teaching mathematics through problem solving and inquiry. It also refers to the Teaching Cycle and the Learning Cycle. “By using the Teaching Cycle, teachers guide students through the Learning Cycle in order to help them progress along the Continuum of Mathematical Understanding.”

  • In “The Five Practices,” the materials state “Every lesson follows the framework for organizing task-based instruction as described in The 5 Practices for Orchestrating Productive Mathematics Discussions (Smith M., & Stein M.K., NCTM 2018), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014).”

  • In “Routines,” explanations for the implementation of two routines are highlighted.

  • In “Instructional Routines,” the what? and why? of four routines (e.g., Notice and Wonder) are included.

  • In “Supporting All Students,” the materials state that “Lessons are designed to maximize access for all students, and include additional suggested supports to meet the varying needs of individual students.” The Design Principles and Design Elements for All Students as well as support for English Language Learners are explained in detail.

  • Eight Mathematical Language Routines (MLRs), selected because they are effective and practical for simultaneously learning mathematical practices, content, and language, are explained in detail. Sources are cited.

  • “Supports for Students with Disabilities” offers additional strategies for teachers to meet the individual needs of a diverse group of learners. The supports for students with disabilities were developed using the three principles of Universal Design for Learning (http://udlguidelines.cast.org/): Engagement, Representation, and Action and Expression.

  • In “Assessment and Analysis,” the materials describe the “wide variety of assessment resources are provided as a tool to assist teachers.”

Teacher Edition: 5 Practice Charts, which is separate from the Course Guide, provides guidance particular to the Launch; Explore; Anticipate & Monitor Chart; and Selecting, Sequencing & Connecting chart.

Indicator 3f

Materials provide a comprehensive list of supplies needed to support instructional activities.

1/1
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The “AGA Materials List” specifies the materials list for each course. The document specifies physical materials (e.g., highlighters for Algebra 1, compasses for Geometry, and Dry Spaghetti for Algebra 2) as well as suggests digital tools (e.g., GeoGebra for Algebra 1 and Geometry as well as Desmos activities for Algebra 2).

Indicator 3g

This is not an assessed indicator in Mathematics.

Indicator 3h

This is not an assessed indicator in Mathematics.

Criterion 3i - 3l

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

8/10
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series partially meet expectations for Assessment. The materials include assessment information that indicates which standards are assessed and provide assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices. The materials partially provide multiple opportunities throughout the courses to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Indicator 3i

Assessment information is included in the materials to indicate which standards are assessed.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Explicit assessment resources include Quick Quizzes, Self Assessments, Unit Tests, and Performance Assessments. Lesson-based, formative assessments include Exit Tickets and listening to students as they work on the tasks. The materials identify the content standards for all types of assessments, and the Standards for Mathematical Practice (MPs) are identified for many of the Performance Assessments.

Examples of the materials identifying the MPs include:

  • In Algebra 1, Unit 3, the Performance Assessment is aligned to F-IF.1-5 and MPs 1, 2, 3, 6, and 8.

  • In Geometry, seven of the nine Unit Performance Assessments are aligned to content standards and practices, and in Units 7 and 9, the Performance Assessments are aligned to content standards.

  • In Algebra 2, the Unit 6 Performance Assessment aligns to F-TF.5 and MP4, and the Units 8 and 10 Performance Assessments also align to MP4. The Unit 7 Performance Assessment aligns to MP8.

Throughout the series, the Quick Quizzes, Unit Tests, and Exit Tickets align to the content standards. Examples include:

  • Quick Quizzes, which assess student learning over a cluster of lessons within a unit, indicate a content standard alignment at the problem level. For example, in Algebra 2, Quick Quiz 2.1-2.2, Problem 8, students estimate the value of a logarithmic expression that does not have an integer value. The materials clearly indicate that the question aligns to F-BF.5+, as students show that they understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

  • Unit Tests consistently identify the content standards that are assessed across the courses. For example, in Algebra 1, Unit 9 Test includes the content standard alignment at the problem-level.

  • Exit Tickets are lesson-based assessment opportunities that identify the content standards. The Course Guide indicates that across the series, “every Exit Ticket includes a short narrative that describes it, any focus or supporting standards, and solutions.” For example, in Algebra 2, Lesson 1.1, the Exit Ticket identifies F-BF.4 as the Focus Standard, which aligns to the task in that students are asked to find the inverse of each function given: one each in a table format, an equation, and a graph.

Indicator 3j

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

2/4
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Indicator Rating Details

The materials reviewed for the Open Up High School Mathematics Traditional series partially meet expectations for including an assessment system that provides multiple opportunities throughout the series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. Specifically, the assessment system provides multiple opportunities to determine students’ learning and suggestions to teachers for following-up with students but does not provide sufficient guidance for assessing student performance.

Examples of where the materials provide tools for scoring purposes include:

  • Throughout the series, the Performance Assessments include an Evaluation of Understanding chart that outlines possible student understandings and misconceptions and has a placeholder for teachers to record a “total.” The chart does not provide guidance on what teachers should be totaling or interpreting those totals in terms of student proficiency.

  • In Geometry, Unit 5 includes a Unit Test, a Performance Assessment, and a Quick Quiz. For each of these assessments there is an answer key or solution guidelines for teachers. The assessments provide solution keys and list potential misunderstandings with sample student responses; however, there is no connection made to interpret student performance in terms of an overall score or proficiency level so that students understand his/her own proficiency on the summative assessments.

  • In Algebra 2, the Quick Quizzes, Performance Assessments, and Unit Assessments include an answer key showing full solutions to each problem. The materials do not provide scoring guidelines or examples of open-ended feedback.

The materials provide guidelines that help teachers interpret student understanding, but these guidelines do not include scoring tools to support an evaluation of overall student performance. Examples include:

  • In Algebra 1, Unit 5, Performance Assessment, the materials include guidance for teachers to interpret student understanding: “Look for students who can articulate why points on the boundary lines yield higher profits. Also look for students who have successfully plotted some profit lines, and perhaps have an argument based on the parallel profit lines as to why the maximum profit might occur at a vertex point.” This guidance does not include scoring tools or guidelines.

  • In Algebra 2, each Quick Quiz contains a solution key for each problem. In addition, the materials include narrative descriptions of the typical misconceptions students might display as well as descriptions to help teachers interpret when student responses indicate a more in-depth understanding. In Algebra 2, Quick Quiz 3.1-3.3, problem 4, students write p(x)=(x+3)4 as a polynomial in standard form. The corresponding teacher guidance notes that the teacher should watch for evidence that students apply Pascal’s Triangle and describes two examples of how such evidence might be provided (e.g., creating the triangle or writing out an expanded equation with values substituted for the coefficients). In Algebra 2, Quick Quiz 2.1-2.2, problems 6-8, students evaluate logarithmic expressions that do not result in integer values. Accompanying these problems is guidance for the teacher, noting that “a student who correctly indicates that the value of the log is closer to one of the values than the other is demonstrating a deeper understanding of the concept.” While these resources support interpreting student understanding, the guidance does not include scoring tools or guidelines.

Examples of guidance to respond to student needs elicited by the assessment include:

  • In Algebra 1, Lesson 5.7, the Exit Ticket includes the following statement in the teacher lesson: “Students who cannot describe the boundary line or the half-plane that forms the solution set need to revisit the ideas in the lesson summary.“

  • In Geometry, each problem in the Unit Tests and Quick Quizzes provides information for the teacher indicating which lesson included the content being assessed and suggestions about which tasks students should revisit should they struggle with the problem/task. In Geometry, Unit 7 Test, the teacher notes address possible student errors and misconceptions. Each item included in the Unit 7 Test suggests tasks that the student should revisit if they have difficulty with the item.

  • In Algebra 2, Quick Quiz 2.3-2.5, the guidance indicates that problems 6-8 require an understanding of logarithms and the use of technology, that students who struggle with these questions should revisit task 2.5, and that additional practice is available in Retrieval, Ready, Set, Go, problem 3.3.

Indicator 3k

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

4/4
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices across the series.

The Open Up High School Mathematics Traditional series includes an array of assessment types and opportunities to test learning for each unit. Each lesson includes Exit Tickets and Retrieval Ready, Set, Go problem sets. Each unit includes Self Assessments, Quick Quizzes, a Unit Test, and a Performance Assessment. Examples of different types of modalities used for student assessments include:

  • In Algebra 1, Unit 7, the Performance Assessment assesses students’ ability to identify the key features needed to write a quadratic function in standard, vertex, and factored forms. In this task, students write a step-by-step process. 

  • In Geometry, Unit 1 Test, students graph, express transformations algebraically, and justify their answers. The Unit 1 Performance Assessment provides an example of students playing a game that includes an expectation of precise mathematics (MP6) as well as engagement in math practices by all participants, Specifically, the instructions state, “Following the end of the game, each player needs to write a justification describing how they know each quadrilateral they recorded on their recording sheet is actually a quadrilateral. The recording sheets will be turned in and graded for accuracy and completeness of the justifications. This step needs to be completed by each player, regardless of the number or type of quadrilaterals that were completed during the playing of the game.” 

  • In Algebra 2, the Unit 8 Test includes questions that require responses in a table format, in a graph, and as written (verbal) explanations. In Algebra 2, Unit 8 Performance Assessment, students sketch graphs, write equations to model the frequency of notes being played, and write verbal explanations as to why some notes sound better than others when played together.

Examples of different types of items used for student assessments and how they are used to measure student performance include:

  • In Algebra 1, Unit 3 Performance Assessment, students match functions in various representations using a card sort. Specifically, students work individually or in pairs to organize the cards so that each set of three cards all describe the exact same relationship. The cards contain representations of functions that include tables; descriptions of domain, range, and other defining characteristics; graphs; function notation; sequences; equations; and real-world context.

  • In Geometry, Unit 1, the Quick Quiz, students respond to six problems where one correct answer is anticipated. Students agree or disagree with conjectures and justify their response. In the Performance Assessment for this unit, students justify why certain shapes are quadrilaterals. In the Unit Test, students respond to a variety of problem types (e.g., algebra-based, discussion, constructed response, and justification) from previous work in the unit.

Unit Tests in the materials address complexity through question type as well as the way the question is worded to prompt student thinking. Examples of how assessments address complexity include the following examples from the Algebra 2, Unit 3 Test:

  • Given the equations of functions f(x), g(x), and h(x), students select, from a list, all statements that are true about the closure rules for those functions (A-APR.1). Students engage in MP3 as they analyze the situation and apply examples and counterexamples to generalized statements.

  • Given the graphs of functions f(x) and g(x) (one of which has no real solutions), students write the equations of both functions in standard form and in factored form (N-CN.8+, F-BF.1). Students utilize MP2 as they shift from a graphical to a symbolic representation of the functions, consider the units involved, and attend to the meanings of the root quantities that must be present in the factored form.

  • Provided a statement that (a+bi) and (a-bi) are complex, conjugate pairs, students name at least four things they know about complex, conjugate pairs (N-CN.1, N-CN.2). Although not explicitly stated in the materials, this question requires students to utilize MP2 as they apply quantitative and abstract reasoning when considering how the expressions are related, how they could be manipulated, or what they might result in.

  • Given an expression showing division between two polynomials, students write two equivalent expressions using multiplication statements. (A-APR.6)

Indicator 3l

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

Narrative Evidence Only
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment as no such guidance is provided.

The materials do not provide accommodations (e.g. text to speech, increased font size, etc.) that ensure all students can access the assessment and, thus, do not include guidance for teachers on the use of provided accommodations.

Criterion 3m - 3v

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

8/8
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations to support their regular and active participation in learning course-level mathematics; extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity; strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning course-level mathematics; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Indicator 3m

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning course-level mathematics.

The Open Up HS Math Course Guide provides guidance on strategies and accommodations for special populations outlining best practices to support all students, as well as students with disabilities (SWD), English Language Learners, and students in need of enrichment. The Open Up HS Math Course Guide states “The philosophical stance that guided the creation of these materials is the belief that with proper structures, accommodations, and supports, all children can learn mathematics. Lessons are designed to maximize access for all students, and include additional suggested supports to meet the varying needs of individual students. While the suggested supports are designed for students with disabilities, they are also appropriate for many students who struggle to access rigorous, course-level content. Teachers should use their professional judgment about which supports to use and when, based on their knowledge of the individual needs of students in their classroom.” Examples of where and how the materials provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations include:

  • In Algebra 1, Lesson 9.1, Launch, the materials indicate support for engagement of SWD with an emphasis on Social-Emotional Functioning, Attention, and Organization. Teachers provide access by recruiting interest as students select one of seven data sets. This improves task initiation and encourages student connection to learning, and teachers separate the task into more manageable parts in an attempt to support students with additional processing time. This strategy also occurs in Algebra 2, Lesson 1.4, Explore, as students find the inverse of given functions by selecting 4 or 5 problems.

  • In Algebra 1, Lesson 9.6, Launch, the materials provide the SWD support, Representation: Internalize Comprehension, where teachers encourage students to write ideas shared by other students on top of the corresponding graphs, highlight/circle the important features discussed, and provide specific things within representations for students to look for. The Narrative notes that differentiating instruction in this manner supports accessibility to Visual Spatial Processing and Conceptual Processing.

  • In Geometry, Lesson 2.1, Explore, the materials provide the SWD support, Action and Expression: Conceptual Processing, Fine Motor Skills, which suggests providing access to GeoGebra or Sketchpad and notes that “technology tools can eliminate barriers and allow students to more successfully take part in the learning.” The Narrative indicates that this means of differentiating instruction supports accessibility for Conceptual Processing and Fine Motor Skills.

  • In Geometry, Lesson 3.4, Launch, the materials indicate the SWD support, Engagement: Attention; Organization; Social-emotional functioning, and the Narrative specifies that teachers “invite students to select two or four classmates’ arguments when following the diagram and making the two column proof.”

  • In Algebra 2, Lesson 1.1, Launch, the materials provide the SWD support, Representation: Access for Perception, which suggests presenting the contextual task both visually and auditorily to increase sense-making, improve comprehension, and encourage students to annotate the task.

Indicator 3n

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity. 

The materials provide opportunities for students to investigate course-level content at higher levels of complexity. Each course in the series includes Enrichment lessons identified with an “E.” Based on the information provided in the Open Up HS Math Course Guide, these lessons “align primarily with CCSSM (+) standards and/or engage in mathematics that goes beyond the expectations of the standards (^).” As indicated in the Course Guide, the content of the enrichment lessons is not required for all students, although the mathematical ideas are accessible to all students. The enrichment tasks are available to use for all students at a teacher’s discretion.

Examples of opportunities specific to extending students' learning of the course-level content, include:

  • In Algebra 1, Unit 5, every lesson has at least one Ready for More? that extends the mathematics of the unit: Systems of Equations and Inequalities. Lessons 5.11E and 5.12E are enrichment lessons that extend the work of the unit to N-VM.6(+). In addition, the materials include a Self Assessment that complements the two enrichment lessons.

  • In Geometry, Lesson 7.12 includes guidance for the instructor that relates to the progression of learning. In Ready for More?, the materials provide the teacher with one additional practice problem that is intended to deepen or extend the mathematics of the lesson. The Course Materials Guidance indicates that fast finishers should be encouraged to work on these extensions.

  • The third learning cycle of Algebra 2, Unit 7, is a set of enrichment lessons extending the work of the unit to include additional trigonometric identities and their applications to changing the form of trigonometric expressions and solving trigonometric equations (Lessons 7.7E to 7.10E). The final enrichment lesson introduces students to the polar form of complex numbers and uses polar form to extend the arithmetic of complex numbers to finding roots of complex numbers.

  • All of Algebra 2, Unit 10 is an enrichment unit, with each lesson addressing almost exclusively plus standards (with non-plus supporting standards).

Examples of opportunities for students to engage in course-level content at a higher level of complexity.

  • In Algebra 1, Lesson 8.5, where students engage with F-BF.4a and F-BF.4c(+), Problems 6 and 7 involve quadratic functions whose domains must be restricted so that its inverse will be a function. As the notion of restricted domains and conditions under which functions are invertible is a topic of Algebra 2, teachers are encouraged to amplify the possibility that an inverse of a function may not be a function.

  • In Geometry, Lesson 7.12E, all of the focus standards are plus standards: N-VM.1-5. Appropriately, students represent quantities that have magnitude and direction using vectors, examine the arithmetic of vectors, and sketch vectors in the coordinate plane. The materials provide teachers with a chart that outlines the Selecting, Sequencing, and Connecting Whole Class Questions & Connections for students. Teachers are encouraged to consider the different tasks/skills for which students might be prepared as doing so allows the teacher to extend the task complexity when appropriate. There are examples of real-world applications of vectors that can be introduced when students show readiness.

  • In Algebra 2, Lesson 8.4, students are presented a scenario at an amusement park in which the output of one function becomes the input of another. The task allows students to approach working the problems either by decomposing the scenario into its component functions and working with them individually and in sequence or by composing a single function that accommodates the sequence of computations. Teachers are instructed to monitor student thinking, as the students who create the composition function first (before constructing a table of values) are navigating the task via the plus standard F-BF.1c(+), a higher level of complexity compared to the other standards addressed in the lesson.

Indicator 3o

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

Narrative Evidence Only
+
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials provide varied approaches to learning tasks, in how students are able to share their thinking, and in how students are expected to demonstrate their learning, and the materials provide varied opportunities for students to monitor their learning based on feedback from a few sources. There are opportunities for peer feedback through instructional dialogues, but in many cases, the person monitoring student thinking and providing feedback is the teacher during instruction or in response to an assessment.

Examples of varied approaches for students to share their thinking, ask questions, investigate, make sense of phenomena, and problem-solve using a variety of formats and methods include:

  • In Algebra 1, Lessons 4.1 and 4.7E, students use card sorts to support their learning. In Lesson 4.1, students work with a partner to rearrange the cards to model the sequence of events and use the arrangement to determine the order of inverse operations to be used in solving the equation. In the Lesson 4.7E Launch, students work with a partner to arrange multi-colored Post-it Notes as they consider different ways to organize the information on the notes. Without identifying any structure as correct, the teacher shares some structures with the entire class and encourages pairs of students to consider how their structure might facilitate the mathematics of the problems being asked or if their structure needs to be modified.

  • The Geometry materials consistently allow students to compare their thinking with the thinking of others through different grouping techniques (e.g., individual, pairs, small groups, large groups). When this isn’t possible, students are asked to determine if the reasoning presented in a problem is accurate. In Lesson 3.1, Jump Start, students consider four different arguments about why the sum of two odd numbers is even. Students work with a partner to determine the different characteristics in the explanations. During the ensuing whole class discussion, students debate which explanation is most convincing and what constitutes knowing that a claim is always true.

  • Throughout the Algebra 2 materials, students have opportunities to verbally share their thinking (either with a partner or with the whole class), write about their ideas, and formulate conclusions about phenomena based on evidence presented in tables and graphs. In Algebra 2, Lesson 7.9, teachers are encouraged to support opportunities for peer collaboration by having students share their work with a partner and by displaying sentence frames to support the conversation.

The materials give students opportunities to monitor their own progress and learning through ongoing review, practice, and self-reflection, and feedback is primarily provided by the teacher. Examples include:

  • Exit Tickets, Performance Assessments, and Quick Quizzes present opportunities for students to monitor their learning, and in each instance, the teacher is the primary source of any feedback.

  • Self-Assessments allow students to reflect on their level of proficiency and evaluate themselves with respect to a set of success criteria up to a given point in the unit, then generate an action plan for mastering content they are not yet proficiency in. For example, in Algebra 2, Self Assessment 9.1-9.4 students rate themselves against criteria such as “I can describe the features of a normal distribution” and “I can calculate and interpret a z-score.” Students must also provide evidence of their self-determined rating, which helps to guide them toward steps for mastering content they don’t understand yet.

  • Every lesson includes a Retrieval section within the Retrieval, Ready, Set, Go problem sets that prepares students for practice problems after the lesson. More specifically, the Retrieval provides students with ongoing practice that spirals back to prerequisite concepts that remain relevant for the remainder of the assignment. While students may be able to assess their understanding of the prerequisite learning, the teacher has access to guidance that maps these problems to previous work.

Indicator 3p

Materials provide opportunities for teachers to use a variety of grouping strategies.

Narrative Evidence Only
+
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series provide opportunities for teachers to use a variety of grouping strategies. 

The materials utilize grouping strategies (e.g., individual, small group, whole group) based on the task within the lesson, however the materials do not delineate how they differ based on the needs of particular students. For example, in Algebra 1, Lesson 6.5, the breakdown of grouping strategies includes: Jump Start, individuals / pairs / whole class; Launch, whole group; Explore, individual/pairs or small group; Discuss, whole group; Exit Ticket, individual.

Guidance for the teacher on how and when to use specific grouping strategies is included in the narratives for the relevant phases of a lesson, along with some general guidance in the Course Guide. Examples include:

  • In Geometry, Lesson 7.7, the Jump Start Narrative indicates “After describing how to find the distance between a point and a line and answering any questions, ask students to work individually to complete the problems. Monitor their work and when they are finished, have a student share problem b and another student share problem d with the class. Discuss …”

  • The Individual to Pair or Small Group to Whole Class Progression provides “students with time to think through a situation or question independently before engaging with others allows students to carry the weight of learning, with support arriving just in time from the community of learners. This progression allows students to first activate what they already know, and continue to build from this base with others.”

  • “Suggestions for timing and grouping are part of the Launch description. Typically, students work in small collaborative groups during the explore phase.”

Indicator 3q

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

2/2
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Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials provide general guidance about how to support English Language Learners (ELLs) in the Course Guide and indicate specific Math Language Routines (MLRs) within some phases of some of the lessons. The materials indicate that the curriculum builds on foundational principles for supporting language development for all students. The Supporting English Language Learners section “aims to provide guidance to help teachers recognize and support students’ language development in the context of mathematical sense-making. More specifically, the materials indicate “Embedded within the curriculum are instructional supports and practices to help teachers address the specialized academic language demands in math when planning and delivering lessons, including the demands of reading, writing, speaking, listening, conversing, and representing in math (Aguirre & Bunch, 2012).” The supports and practices “are crucial to meeting the needs of linguistically and culturally diverse students who are learning mathematics while simultaneously acquiring English.”

The materials continue that “the framework for supporting English language learners in this curriculum includes four design principles for promoting mathematical language use and development in curriculum and instruction. The design principles and related routines work to make language development an integral part of planning and delivering instruction while guiding teachers to amplify the most important language that students are expected to bring to bear on the central mathematical ideas of each unit.” The materials identify where both student successes and challenges may be rooted in misconceptions in content versus language demands, through learning and assessment. The Course Guide describes how MLRs have been incorporated throughout the series because they are effective and practical for simultaneously learning mathematical practices, content, and language. The eight MLRs included in the materials are: MLR1 Stronger and Clearer Each Time; MLR2 Collect and Display; MLR3 Clarify, Critique, Correct; MLR4 Information Gap; MLR5 Co-Craft Questions and Problems; MLR6 Three Reads; MLR7 Compare and Connect; and MLR8 Discussion Supports.

Examples of the materials utilizing the MLRs and additional supports for EL students based on the language demands of the lesson and examples of appropriate support and accommodations for EL students that will support their regular and active participation in learning mathematics include:

  • In Algebra 1, Lesson 3.2, the Discuss Narrative provides guidance on how to implement the MLR2 Collect and Display. Teachers are instructed to listen and collect the language students use to describe strategies for finding key features of functions.Teachers create a two-column table with the headings “table” and “graph” to record student language in the appropriate column for strategies identifying range in each representation. Students may then “borrow” language from the display as needed.

  • In Algebra I, Lesson 4.4, Discuss, Problems 2-5, students share their explanations for each of these problems using models from the Jump Start and create arguments as to why the properties of inequalities can be generalized to all real numbers. Students speak to the entire group and engage in question and answer with the teacher and their peers. In addition, students paraphrase the properties of inequalities.

  • In Geometry, Lesson 3.3, the Jump Start Narrative includes general guidance about MLR2 Collect and Display. The Launch Narrative includes general guidance about implementing MLR6 Three Reads and indicates that “students who would benefit from additional support may follow along as the teacher or a single student reads these paragraphs.”

  • In Geometry, Lesson 5.3, students engage in content related to inscribed angles and polygons as well as circumscribed polygons. Using MLR7 Compare and Connect, students consider individually the work of other students before verbally describing not only their visual representations of different inscribed and circumscribed polygons but also the visual representation of others work.

  • In Algebra 2, Lesson 6.1, Discuss, the MLR3 Clarify, Critique, Correct routine provides students with a structured opportunity to analyze, reflect on, and improve their written work by correcting errors and clarifying meaning. The teacher selects one of the student’s descriptions of the procedure for finding the distance a point on a circle is above or below the center of a circle from problem 5, then asks a series of Revise and Refine prompts one at a time so that students have an opportunity to offer suggestions following each prompt. This revision process continues until students have a shared statement that can be recorded in the takeaways chart in their lesson materials.

  • In Algebra 2, Lesson 8.2, Launch, students engage in MLR6 Three Reads, which supports reading comprehension of the context in a word problem. Students sketch a graph of the path of a rider on proposed thrill rides at a local theme park. Three Reads enables students to focus on comprehending the situation by reading only about the context in the first read, then adding the proposals in the second read, then identifying key mathematical features of the story and reading for those in the third read, with the goal of devising a strategy for starting on the problems. Students also engage in several writing exercises because the task has them explain their reasoning about the shape of each graph.

  • In Algebra 2, Lesson 8.6, Explore, students engage in MLR8 Discussion Supports. Students use sentence frames to prompt their thinking or to provide support for explaining their thinking. To prompt students to reason abstractly and quantitatively (MP2), students are provided sentence frames such as: “I had to think about __ in order to ...”, “It made sense to me to __ when I ....” Students share their answers with a partner and are encouraged to rehearse what they will say when they share with the full group. Teachers are provided a note that rehearsing provides opportunities for students to clarify their thinking.

  • In Algebra 2, Lesson 9.11, Launch, students engage in MLR1 Stronger and Clearer Each Time. Students formulate a written response, share verbally, then revise their written response helps students to synthesize their understanding of the data and supports sense-making.

Indicator 3r

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series provide a balance of images or information about people, representing various demographic and physical characteristics. The materials offer limited depictions of different individuals of different genders, races, ethnicities, and other physical characteristics.

  • Throughout the Algebra I materials, there is no reference to physical characteristics of the characters, such as race or ethnicity. 

  • Many of the student-facing lessons/tasks in Geometry have no images. Lesson 8.2 includes pictures of a bell, a vase, and a rocket. Most other lessons include images such as graphs, diagrams, and area representations. The materials routinely use names depicting different genders and ethnicities. In Geometry, Lesson 3.4, the names Travis, Tehani, Clarita, and Carlos are used in the student-facing materials.

When the materials include names, they balance positive portrayals of demographics or physical characteristics. Examples include:

  • In Algebra 1, Unit 2 includes the following names: Savannah, Travis and Tehani, Carlos and Clarita (the Martinez twins), Tia, Kwan, Grandma Billings, Zac, Sione, Marcus, Joe, and LaTisha.

  • Most Unit Tests and Performance Assessments in Geometry do not include student names or references to different genders, races, ethnicities, or other physical characteristics.

  • In Algebra 2, the Unit 6 Performance Assessment names Kwan and his sister Dhyanna, who go to ride the merry-go-round at the county fair.

Indicator 3s

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series do not provide guidance to encourage teachers to draw upon student home language to facilitate learning. Although the Course Guide notes that one of the core values inherent in the design of the materials is “the central role of student agency in the learning process,” the materials provide limited guidance for how teachers could incorporate the student’s home language.

Indicator 3t

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. No references to cultural or social supports to facilitate learning were found.

Indicator 3u

Materials provide supports for different reading levels to ensure accessibility for students.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series provide some supports for different reading levels to ensure accessibility for students.

Examples of strategies to engage students in reading and accessing grade-level mathematics include:

  • In Algebra 1, Lesson 4.7, Launch, the SWD Support, Representation: Access for Perception, would be helpful for struggling readers. The strategy includes reading the scenario and presenting the problem aloud while students annotate the task. Presenting contextual tasks both visually and auditorily increases sense-making and improves comprehension.

  • In Geometry, Lesson 2.3, students work with rigid motions and transformations while engaging in MP1. Students start by using a "guess and check" strategy as they start work with multiple transformations and are encouraged to develop strategic thinking to determine which transformation might be best to do first. Also in Geometry, Lesson 4.5, students use congruence and similarity criteria to solve problems. Students are encouraged to engage in MP6 by articulating their reasoning and using precise language and vocabulary. 

  • In Algebra 2, Lesson 7.7, Launch, students read the opening paragraph of the task and respond to problem 1 by discussing it with a partner. The materials include a language accessibility strategy that has students read the paragraph together as a class, then look at the diagram as the paragraph is read. The teacher guidance explains that presenting the information both visually and auditorily increases sense-making and improves comprehension. Students then move to question 1, which they read and discuss with a partner. Students are encouraged not to write any explanation until the partnership feels they have come up with a solid argument, which allows each student to develop a shared understanding with their partner before having to formulate a formal written response.

The materials provide multiple entry points that present a variety of representations to help struggling readers access and engage in course-level mathematics. Examples include:

  • In Algebra 1, Lesson 8.3, students work to find absolute value. In Explore, students chunk the activity, check in often with a peer, and work with tables and graphs. In Discuss, students share various aspects of how they came to their solutions, which helps struggling readers fill in any missing pieces.

  • In Geometry, Lesson 3.2, Explore, Question 4, sentence frames are provided to help students explain their thinking about what they saw in the diagram. The task provides multiple entry points for success as the materials list six possible conjectures that students could write about the quadrilateral.

  • In Algebra 2, Lesson 1.3, Retrieval Ready, Set, Go, Problems 7-15, students read a short story about Jack and the Beanstalk and answer questions about the exponential model that Jack uses to calculate the height of his beanstalk as a function of time. Students have multiple entry points to these problems because the information is provided through multiple representations: the verbal information presented in the story is accompanied by a table of values (time in hours versus height in feet) and a function expressed symbolically.

Indicator 3v

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

2/2
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series uses physical and/or virtual manipulatives to help students develop understanding of mathematical concepts. Some manipulatives---such as colored pencils, scientific calculators, and Desmos---are used routinely by students at their discretion to support their learning and explain their understanding. Examples of the manipulatives and how they are used to help students develop understanding of a concept include:

  • In Algebra 1, Lesson 1.1, students use colored pencils to shade cubes in ways that represent sequences. In Lesson 4.8E, students use colored pencils or markers to highlight how the elements from each of the matrices connect in matrix multiplication.

  • In Geometry, Unit 1, each lesson uses a physical or virtual manipulative. In Lessons 1.1-1.6, Black Line Masters (BLMs) support students as they develop definitions of geometric transformations, use geometric descriptions to transform figures, and specify sequences of transformations that map one figure onto another.

  • The materials list for Geometry, Lesson 6.8 indicates two GeoGebra apps that are intended to support students develop their conceptual understanding of Cavalieri’s Principle. 

  • In Geometry, Lesson 8.1 recommends a host of manipulatives to assist students as they explore cross sections of 3-D geometric solids. The materials list includes play-doh and dental floss for slicing solids, transparent 3-D figures to which water can be added, a sealed jar containing a colored liquid that can be tilted to illustrate possible cross sections, and flashlights for creating shadows of objects.

  • In Algebra 2, Lesson 7.4, an alternative graphing activity is provided for Explore question 4, where students cut varying lengths of spaghetti to represent line segments for specific angles of rotation, then glue those pieces to a large graph. This allows students to create a physical model of the line segment used to represent the value of the tangent for a particular angle of rotation.

  • In Algebra 2, Lesson 7.8E, the BLMs include images of the polar and coordinate planes as well as location and angle specification cards to help students as they engage with proofs and applications of trigonometric identities.

  • In Algebra 2, Lesson 9.9, Launch, students find a margin of error and a plausible interval for a sample proportion using a simulation where student pairs are given a bag of dark and light colored beans representing artifacts more than 1000 years old and artifacts less than 1000 years old, respectively. Using physical manipulatives for this simulation helps students develop conceptual understanding around creating an interval that is likely to include the population proportion.

Examples of how manipulatives are connected to written methods include:

  • In Algebra 1, Lesson 1.1, students “draw multiple diagrams with the checkerboard pattern such as a 3 ⨉ 3, 4 ⨉ 4, 7 ⨉ 7, etc., or use manipulatives to see patterns as the checkerboard increases or decreases.” Students then turn to a partner to use the following prompt to explain what they notice about the pattern: “When I looked at the diagram, I noticed _______________ and so I ____________________.” Students then “create numeric expressions that exemplify their process and require students to connect their thinking to the visual representation of the tiles.”

  • As part of the alternative graphing activity in Algebra 2, Lesson 7.4, Explore task, question 4, students draw the unit circle on a large sheet of paper so that they can indicate how the line segment is defined in that context as well. The activity then allows students to practice using appropriate tools strategically (MP 5) by prompting them to refer back to their unit circle using sentence frames such as: “I used the unit circle as a tool to think about ____ by ____,” and “I used the unit circle to calculate ____.”

Criterion 3w - 3z

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

0/0
+
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Criterion Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in course-level standards. The materials do not include or reference digital technology that provides opportunities for collaboration among teachers and/or students. The materials have a visual design that supports students in engaging thoughtfully with the subject, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

Indicator 3w

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

Examples of the materials providing digital technology and interactive tools for students include:

  • In Algebra 1, Unit 5 includes two specific GeoGebra apps for engaging students. In Lesson 5.3, students enter the parameters of constraints and a specific number of cats and dogs that are appropriately color-coded to signify “too big,” “not too big,” or “just right” for the constraint. The app provides feedback by plotting points in black if students predict the meaning of the point incorrectly (A-CED.2, A-REI.12, MPs 2 and 7). In Lesson 5.6, students interact similarly with another specifically designed GeoGebra app to examine the solution set for a system of linear inequalities. (A-CED.3, A-REI.12, MPs4 and 7)

  • In Geometry, Lesson 8.1, students visualize cross sections using digital drawing apps. Cross sections can be visualized by connecting points on the edges of 2-D drawings of the 3-D shape to form a region that lines in a plane. (G-GMD.4, MP7)

  • Digital tools and resources referenced in the Algebra 2 materials include a graphing calculator, online tools such as an online z-score calculator, Teacher.Desmos.com: Log Arithmetic, GeoGebra: Getting on the Right Wavelength, and Desmos.com: Technology for finding the inverse of an n by n matrix.

  • In Algebra 2, Lesson 7.3, a GeoGebra app supports students’ engagement by helping students visualize a Ferris wheel and the position of the rider. Students can toggle different settings such as the height, radius, and period; make predictions about the shape of the graph of the height of the rider as a function of time; and then play the simulation to check if their predictions were correct. The accompanying teacher notes explain that “technology tools can eliminate barriers and allow students to more successfully take part in their learning” and that it provides support for conceptual processing. (F-TF.5, F-BF.3, MP2)

There is no evidence of digital materials that can be customized to attend to student and/or community interest.

Indicator 3x

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials include guidance related to collaborative student groups when engaging in activities , however, these contexts are related to in-person collaboration rather than through the use of digital technology.

Indicator 3y

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials use a consistent layout and structure across units and lessons. As described in the Course Guide, “Each unit follows an instructional framework that builds from a Develop Understanding lesson to one or more Solidify Understanding lessons to one or more Practice Understanding lessons. This framework remains consistent across units and within units that have more than one cycle.” Each lesson includes: a beginning with the Learning Goals, Standards for the Lesson, Required Preparation, Progression of Learning, and Purpose as background for the teacher. The teaching cycle then follows the Launch, Explore, Discuss sequence.

The materials include images, graphics, and models that support student learning and engagement without being visually distracting. Examples include:

  • In Algebra 1, Lesson 9.1, the student learning focus is on representing data using a scatter plot, understanding the meaning of the correlation coefficient, and describing the difference between correlation and causation. The materials provide seven sets of cards that contain tables of data and scatter plots of the data. Students examine the data and put the cards in a justifiable order. In addition, students compare each scatter plot with its correlation coefficient and describe patterns.

  • In Geometry, Lesson 8.3 addresses estimation of volume based on a two-dimensional cross-section. Students develop or present a strategy for estimating the volume. The graph of the trapezoid and the two-dimensional representation of a vase are not visually distracting or confusing to students.

  • In Algebra 2, Lesson 8.4, Explore, Problem 10 provides students with a diagram to support their thinking about how the notation and table formats used in previous problems might be combined. The image is simple with arrows showing the direction of the function sequence from one component to the next, in the order in which the components are combined. This image for function composition is then revisited in the Launch task of Lesson 8.5, where students use a “starter set” of functions to build composite functions, filling in the diagram to show how their function can be decomposed into its component parts.

Examples of images, graphics, and models that clearly communicate information or support student understanding of topics, texts, or concepts include:

  • In Algebra 1, Lesson 8.4, students are provided graphs to sketch in both piecewise form and absolute form. 

  • In Geometry, Unit 6, Performance Assessment, students consider how someone might build a clay model of the Leaning Tower of Pisa. The materials provide students with a picture of the tower as well as a description of the tower’s various shapes/dimensions. While this is only a picture of the actual tower, it provides a valuable reference for students who may not be familiar with the Tower.

  • In Algebra 2, Lesson 3.8E, Jump Start, the materials provide students with a coordinate plane diagram and a series of questions intended to activate their background knowledge of vectors from a previous course. The inclusion of this type of diagram helps to model computations with complex numbers as students are able to see both the arithmetic and geometric perspective represented.

Indicator 3z

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

Narrative Evidence Only
+
-
Indicator Rating Details

The materials reviewed for Open Up High School Mathematics Traditional series provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

Examples of guidance for using embedded technology to support and enhance student learning, where applicable, include:

  • In Algebra 1, Lesson 5.3, the following guidance on how to use the embedded GeoGebra resource was provided to teachers within the teacher notes: “A GeoGebra app has been designed specifically for this task, and can be found here: https://www.geogebra.org/m/FWe7PzOO.  The app allows students to make the same mathematical decisions as described in the task below, including deciding what color to make each plotted point: the “too big” color red, the “not too big” color orange, and the “just right” color green. The app provides feedback by plotting points in black if students predict the meaning of the point incorrectly.”  In addition, the materials indicate “Provide access to the GeoGebra app as described. Technology tools can eliminate barriers and allow students to more successfully take part in their learning. Students may need direct instruction in how to access these tech tools and may benefit from a list of steps to be able to use the applet or software.” The direct instruction mentioned is not provided for teachers to be able to give to the students.

  • In Geometry, the materials often suggest the use of dynamic Geometry software without specific teacher guidance.  Lesson 2.1 is an exception, however, where the materials advise the teacher to “restrict students to using the circle-by-measure and line tools.”

  • In Algebra 2, Lesson 7.4, Launch, students visualize the graph of a tangent function using a line segment drawn tangent to the unit circle at the point (1, 0). The length of this segment changes as the angle of rotation θ changes, allowing students to visualize the magnitude of the tangent value for different angles of rotation by examining the length of this segment. In Explore, the materials provide guidance to teachers about using technology to assist with this visualization. The guidance directs teachers to find an external resource without any specificity of which “video or technology activity” would best support students’ engagement with this concept: “Connecting the tangent line on a circle diagram to the graph of a tangent function will deepen student’s understanding of the tangent function and prepare them to interpret and utilize the graph for solving problems. Find a video or technology activity that demonstrates finding the various lengths of tangent lines for angles of rotations and uses those to create the graph (or use the alternate graphing method mentioned in the teacher notes). Visualizing the creation of the tangent graph will assist in developing conceptual understanding.”

abc123

Report Published Date: 2021/06/09

Report Edition: 2021

Title ISBN Edition Publisher Year
Open Up Resources HS Mathematics Algebra 1 Student Course 9781953454812 Open Up Resources 2021
Open Up Resources HS Mathematics Algebra 1 Teacher Course 9781953454829 Open Up Resources 2021
Open Up Resources HS Mathematics Algebra 2 Student Course 9781953454836 Open Up Resources 2021
Open Up Resources HS Mathematics Algebra 2 Teacher Course 9781953454843 Open Up Resources 2021
Open Up Resources HS Mathematics Geometry Student Course 9781953454850 Open Up Resources 2021
Open Up Resources HS Mathematics Geometry Teacher Course 9781953454867 Open Up Resources 2021

Please note: Reports published beginning in 2021 will be using version 1.5 of our review tools. Version 1 of our review tools can be found here. Learn more about this change.

Math High School Review Tool

The high school review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways. 

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. 

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

Math K-8

  • Focus and Coherence - 14 possible points

    • 12-14 points: Meets Expectations

    • 8-11 points: Partially Meets Expectations

    • Below 8 points: Does Not Meet Expectations

  • Rigor and Mathematical Practices - 18 possible points

    • 16-18 points: Meets Expectations

    • 11-15 points: Partially Meets Expectations

    • Below 11 points: Does Not Meet Expectations

  • Instructional Supports and Usability - 38 possible points

    • 31-38 points: Meets Expectations

    • 23-30 points: Partially Meets Expectations

    • Below 23: Does Not Meet Expectations

Math High School

  • Focus and Coherence - 18 possible points

    • 14-18 points: Meets Expectations

    • 10-13 points: Partially Meets Expectations

    • Below 10 points: Does Not Meet Expectations

  • Rigor and Mathematical Practices - 16 possible points

    • 14-16 points: Meets Expectations

    • 10-13 points: Partially Meets Expectations

    • Below 10 points: Does Not Meet Expectations

  • Instructional Supports and Usability - 36 possible points

    • 30-36 points: Meets Expectations

    • 22-29 points: Partially Meets Expectations

    • Below 22: Does Not Meet Expectations

ELA K-2

  • Text Complexity and Quality - 58 possible points

    • 52-58 points: Meets Expectations

    • 28-51 points: Partially Meets Expectations

    • Below 28 points: Does Not Meet Expectations

  • Building Knowledge with Texts, Vocabulary, and Tasks - 32 possible points

    • 28-32 points: Meet Expectations

    • 16-27 points: Partially Meets Expectations

    • Below 16 points: Does Not Meet Expectations

  • Instructional Supports and Usability - 34 possible points

    • 30-34 points: Meets Expectations

    • 24-29 points: Partially Meets Expectations

    • Below 24 points: Does Not Meet Expectations

ELA 3-5

  • Text Complexity and Quality - 42 possible points

    • 37-42 points: Meets Expectations

    • 21-36 points: Partially Meets Expectations

    • Below 21 points: Does Not Meet Expectations

  • Building Knowledge with Texts, Vocabulary, and Tasks - 32 possible points

    • 28-32 points: Meet Expectations

    • 16-27 points: Partially Meets Expectations

    • Below 16 points: Does Not Meet Expectations

  • Instructional Supports and Usability - 34 possible points

    • 30-34 points: Meets Expectations

    • 24-29 points: Partially Meets Expectations

    • Below 24 points: Does Not Meet Expectations

ELA 6-8

  • Text Complexity and Quality - 36 possible points

    • 32-36 points: Meets Expectations

    • 18-31 points: Partially Meets Expectations

    • Below 18 points: Does Not Meet Expectations

  • Building Knowledge with Texts, Vocabulary, and Tasks - 32 possible points

    • 28-32 points: Meet Expectations

    • 16-27 points: Partially Meets Expectations

    • Below 16 points: Does Not Meet Expectations

  • Instructional Supports and Usability - 34 possible points

    • 30-34 points: Meets Expectations

    • 24-29 points: Partially Meets Expectations

    • Below 24 points: Does Not Meet Expectations


ELA High School

  • Text Complexity and Quality - 32 possible points

    • 28-32 points: Meets Expectations

    • 16-27 points: Partially Meets Expectations

    • Below 16 points: Does Not Meet Expectations

  • Building Knowledge with Texts, Vocabulary, and Tasks - 32 possible points

    • 28-32 points: Meet Expectations

    • 16-27 points: Partially Meets Expectations

    • Below 16 points: Does Not Meet Expectations

  • Instructional Supports and Usability - 34 possible points

    • 30-34 points: Meets Expectations

    • 24-29 points: Partially Meets Expectations

    • Below 24 points: Does Not Meet Expectations

Science Middle School

  • Designed for NGSS - 26 possible points

    • 22-26 points: Meets Expectations

    • 13-21 points: Partially Meets Expectations

    • Below 13 points: Does Not Meet Expectations


  • Coherence and Scope - 56 possible points

    • 48-56 points: Meets Expectations

    • 30-47 points: Partially Meets Expectations

    • Below 30 points: Does Not Meet Expectations


  • Instructional Supports and Usability - 54 possible points

    • 46-54 points: Meets Expectations

    • 29-45 points: Partially Meets Expectations

    • Below 29 points: Does Not Meet Expectations