Alignment: Overall Summary

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet expectations for alignment to the CCSSM for high school. The materials meet the expectations for focus and coherence and attend to the full intent of the mathematical content standards. The materials also attend fully to the modeling process when applied to the modeling standards. The materials meet the expectations for rigor and the Mathematical Practices by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, and the materials also meaningfully connect the Standards for Mathematical Content with the Mathematical Practices.

See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
15
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
9
14
16
15
14-16
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
21
30
36
30
30-36
Meets Expectations
22-29
Partially Meets Expectations
0-21
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional 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" (p. 57 of CCSSM).
15/18
+
-
Criterion Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for focus and coherence. Overall, the instructional 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” (page 57 of CCSSM). The materials do include almost all of the non-plus standards across the series, and the full intent of the modeling process is attended to throughout the courses. The materials also give students the opportunities to appropriately engage with mathematics at a high school level, and they make meaningful connections among the mathematical topics within and across courses.

Indicator 1a

The materials focus on the high school standards.*
0/0

Indicator 1a.i

The materials attend to the full intent of the mathematical content contained in the high school standards for all students.
4/4
+
-
Indicator Rating Details

The instructional materials reviewed for the series meet the expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. Overall, the instructional materials address almost all of the non-plus standards, and almost all parts of them, across the series.

Below are examples of standards that are addressed across the series:

  • In Course 2 Units 1, 4 and 8, students use functions fitted to data to solve problems in the context of the data, investigate the effect of outliers and influential points on regression lines, and summarize categorical data (S-ID). In Course 3, Units 1 and 4, students extend their ability to reason statistically and investigate samples and variation (S-IC).
  • The standards from A-SSE are represented throughout the series. In Course 1, students explore linear, quadratic, inverse variation, and exponential patterns of change. In Course 2, students analyze and use linear, exponential, and quadratic functions in realistic situations. In Course 3, students’ understanding is extended with graphing linear, quadratic, and inverse variation functions; solving inequalities graphically; solving quadratic equations algebraically; graphing linear equations in two variables; and solving systems of linear equations in two variables.

There is one standard, G-GPE.2, that is not addressed within the three courses in the series, and there is one standard, F-TF.8, that is partially addressed in the instructional materials. For F-TF.8, problem 11 on page 68 in Course 3 gives students the opportunity to prove the Pythagorean identity, but there are not other opportunities in the three courses of the series for students to use that identity to find trigonometric ratios of an angle given one trigonometric ratio of the angle and the quadrant in which the angle lies.

Indicator 1a.ii

The 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 instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for attending to the full intent of the modeling process when applied to the modeling standards. The Core-Plus Mathematics integrated series addresses mathematical modeling throughout the entire series. Through various components of the curriculum, including Investigations, Summarize the Mathematics, and Think About the Situation, students are able to explore all facets of the modeling process.

Particular instances where students have opportunities to experience the entire modeling process include:

  • Course 1, Unit 5, Lesson 2, Exponential Decay: Among the standards listed for this lesson are the modeling standards N-Q.1; A-CED.2; F-IF.4, 5, 7; F-BF.1; all of F-LE except F-LE.4; and S-ID.6. The lesson begins with a discussion of the 2010 BP oil spill in the Gulf of Mexico. The students are asked to think about a simulation experiment intended to model the cleanup efforts. Students work through the experiment and are shown two possible ways to analyze the results (linear and exponential). Students then complete the experiments, design and do experiments and then find equations to model data from given experiments which leads to an understanding of when and why an exponential model may be the best. Students do a ball bounce rebound experiment that will lead to an exponential result, are asked to analyze their results and support their thinking with regards to the best model. Results are verified by using different types of balls and students use a “NOW-NEXT” approach to developing a pattern. Students then move to a problem looking at prescription drug level decay in the body. After each experiment students are asked to check their understanding of what they have just observed. Students are presented with a set of real world situations and are asked to write equations to model exponential decay, then verify and justify their thinking.
  • Course 2, Unit 8 Lesson 1, Probability Distributions: Among the standards listed for this lesson are the modeling standards S-ID.5; S-CD.1 - 5, 6, 8; and S-MD.1-3, 5, 6. The lesson begins with a discussion of physical characteristics as determined by genes. Students are asked how to determine the probability one might have any particular characteristic. The discussion then leads to the multiplication rule, and students are given opportunities to formulate ideas about when and how this rule can and should be applied. This leads to the concept of conditional probability. The students are given situations to explore which lead to the definition of conditional probability. They are then given situations where they have to understand and identify dependent and independent events and determine the probability of such events and varying conditions. Students work in groups and must be ready to explain and defend their work at each stage. In one application problem (problem 1, page 536) they are given information about using the tire valves on a car to determine if a parking ticket is warranted. The last section of this question asks if they think the judge ruled the owner was guilty or not guilty based on their analysis of the data.
  • Course 3, Unit 2, Lesson 2, Inequalities in two variables: Among the standards listed for this lesson are the modeling standards A-SSE.1; A-CED.1, 2, 3; F-IF.4, 5, 7; and F-LE.1, 5. The lesson starts with a discussion of an assembly plant that must assemble and test two types of video game systems. The plant must maximize profit while staying within available time constraints. Students are asked to think about the situation and what might be needed to determine the best use of time. The discussion leads to finding equations which could be used together to find an answer. The students are then given a situation with which they are familiar from previous courses, selling tickets to a concert. After they have developed the inequalities they are asked to graph them and determine how they could use the graphs to determine “a feasible solution area.” They are asked to explain and defend their reasoning. At this point the idea of linear programming is introduced as a way to bring profit into the picture. At the end of the lesson they are asked to go back and work through the video game plant problem presented at the start of the lesson. There are two possible solutions for the system, and they must chose and defend their choice.

Course 1 provides an introduction to modeling linear relationships in Unit 3, modeling discrete mathematics in Unit 4, and modeling probability in Unit 8, and the following are instances where different parts of the modeling process are highlighted for students:

  • Unit 3, Lesson 1, Investigation 3 allows for students to use technology to address A-SSE.1, F-IF.6 and F-BF.2 through manipulating various parts of an expression (Time Flies, pages 163 - 164) to find a rule to model situations that appear to be linear in nature. Extension opportunities are suggested for students to collect their own data by selecting a nearby airline hub and search its schedule for nonstop flights.
  • Unit 5, Lesson 1, Investigation 1 has students explore a variety of situations involving exponential growth to address A-CED.1, A-CED.2, A-REI.10, F-LE.1 and F-LE.2 (Pay It Forward, pages 290 – 293) and develops student understanding and skill in recognizing and modeling these patterns.

Course 2 further develops modeling through geometric transformations in Unit 3, optimization in Unit 6, and probability in Unit 8, and the following are instances where different parts of the modeling process are highlighted for students:

  • Unit 1, Lesson 3, within Think About This Situation multiple representations, graphing and symbolic with equations, are used to introduce systems of equations within a context to address A-SSE.1, A-CED.1-3, A-REI.11 and F-BF.1 (pages 50-53). Students are asked to identify parts of the problem and solutions, eventually leading to the focus of the standard, a solution to a system being an (x, y) value.
  • Unit 7, Lesson 2, Investigation 3 has students explore, in a real-life setting and with software, triangles that are possible when two sides and an angle opposite one of those sides are given to address G-MG.1 and G-MG.3 (Propping Open a Cold Frame Box, pages 498 – 501). Students develop criteria for identifying the conditions under which this given information determines two, one or no triangles.

Course 3 attends to students' modeling capabilities through linear programming in Unit 2, polynomial functions in Unit 5, periodic functions in Unit 6, and recursion and iteration in Unit 7, and the following is an instance where different parts of the modeling process are highlighted for students:

  • Unit 2, Lesson 2 permits students to investigate multiple scenarios that can be analyzed with linear programming for standards A-CED.1-3 and introduces students to various methods for doing so, including graphing and creating grids. Balancing Astronaut Diets (page 134) analyzes nutritional values as used as an example for A-CED.3. Summarize the Mathematics after Investigation 2 (page 136) requires students to compare the different problems to analyze common features.

Indicator 1b

The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
0/0

Indicator 1b.i

The 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 for this series, when used as designed, meet the expectation for allowing students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, post-secondary programs, and careers. The following examples show how the standards/clusters specified in the Publisher's Criteria as Widely Applicable Prerequisites (WAPs) are addressed across the entire series.

  • The Algebra standards are included throughout the series. Evidence is found in Course 1, Units 1, 3, 4, 5 and 7; Course 2, Units 1, 2 and 5; and Course 3, Units 1, 2, 5, 7 and 8.
  • The Function standards are included throughout the series. Evidence is found in Course 1, Units 1, 3, 5 and 7; Course 2, Units 1 and 5; and Course 3, Units 2, 5, 6, 7 and 8.
  • A variety of functions are interpreted and analyzed. Course 1 focuses on linear, exponential, and quadratic functions. Course 2 reviews and extends to power, non-linear, and trigonometric functions, and Course 3 focuses on polynomial, rational, circular and inverse functions.

Prerequisite material was mostly limited to Course 1: Unit 1, Lesson 1; Unit 2, Lesson 1; and Unit 3, Lesson 1. This material was identified by the publisher within the Unit Planning Guide as optional content, depending on students' prior learning experiences.

Indicator 1b.ii

The materials, when used as designed, allow students to fully learn each standard.
2/4
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-
Indicator Rating Details

The materials, when used as designed, partially meet the expectation for allowing students to fully learn each non-plus standard. In general, the series addressed many of the standards in a way that would allow students to learn the standards fully. However, there are cases where the standards are not fully addressed or where the instructional materials devoted to the standard was insufficient.

All non-plus standards, other than G-GPE.2, are referenced at least once. The following are examples where the materials partially meet the expectation for allowing students to fully learn a standard.

  • N-RN.1 Course 1, Unit 5, Lesson 2, Investigation 5: There is one section where rational exponents are used to allow students the opportunity to extend their knowledge of the properties of exponents to rational exponents (pages 335-337). However, the On Your Own exercises on page 344 do not contain problems with rational exponents (as indicated with the CCSS Guide To Core-Plus Mathematics document provided online).
  • N-RN.3 Course 3, Unit 1, Lesson 3: Students are provided one problem (page 70, Question 27) as an extension problem for which they are to provide an argument for this standard.
  • N-Q.1: Units are attended to repetitively throughout the instructional materials, especially in Course 1, Units 2, 3, and 5 and Course 2, Unit 1, where this standard is addressed. However, the portion of this standard regarding interpreting the scale and the origin in graphs and data displays is not specifically addressed in the problems. Most lessons begin with a table of values and then use that data to create a graph. Within Course 1, Unit 3, Lesson 1, (page T152) a note for the instructor indicates to watch for an opportunity to address scales on graphs as students work on this unit. Student or teacher prompts that could allow an opportunity for discussion and/or interpretation instead provide all the necessary information for students such as Course 1, page 295, "Investigate the number of bacteria expected after 8 hours if the starting number of bacteria is 30, 40, 60 or 100, instead of 25. For each starting number at time 0 ..."
  • N-Q.2: Students are given opportunities to work with appropriate quantities when creating models for problems. However, many of these quantities are prescribed for students rather than allowing students to define their own quantities. Students are provided limited opportunities to independently identify quantities to represent a context; rather, students are provided with pre-labeled tables or graphs with pre-determined numbers making the quantities that they represent obvious to the student. This prescriptive definition by the materials does not allow students to develop their own understanding of how the quantities relate to the problem.
  • N-CN.1, 2, 7: Lessons 2 and 4 of Unit 5 in Course 3 address these non-plus standards, so students are provided with limited opportunities to work with them.
  • A-APR.2 Course 3, Unit 5, Lesson 1: In the series, two problems address the Remainder Theorem, Course 1, problem 19 on page 521 and Course 3, the On Your Own problem 21 on page 345. Students are not provided sufficient opportunities to make connections between the A-APR standards and to identify the relationship between zeros, factors, and the Remainder Theorem.
  • A-APR.4 Course 2, Unit 5, Lesson 1: Students are provided one problem as an extension (page 355, Question 39) to prove the Pythagorean theorem and its converse. No other polynomial identities are provided for students to prove.
  • A-REI.5: Students are provided one opportunity to prove this standard, Course 2, page 67, problem 24. This standard is listed in the CCSS Guide to Core-Plus Mathematics document provided online as being addressed in Course 1, pages 197-200, 204-211 and 236, but these pages do not contain problems where this standard is proven.
  • G-CO.3: Course 1, Unit 6, Lesson 2: Students are given limited opportunities to investigate with quadrilaterals, especially trapezoids, however there are many cases for regular polygons.
  • G-GPE.6: This standard is addressed by parts d and e of problem 8 on page 174 in Course 2 and by problem 15 on page 186 in Course 2. Besides part f of problem 15 on page 186, all opportunities to engage with this standard have students find the point on a segment that bisects the segment.
  • G-SRT.6 and 7: Students have limited opportunities to work with these standards within the three courses of the series. These standards are addressed in Course 2, Unit 7, Lesson 1.
  • S-IC.4: Course 3, Unit 4, Lesson 2, Extensions page 279, problem 17 and page 280, problem 20: Students are presented only two examples for this standard. The two problems do not allow students to simulate the experiment. Alignment to this standard is only indicated within the guide found online.

Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for requiring students to engage in mathematics at a level of sophistication appropriate to high school.

Students engage in investigations throughout each unit that ground the standards in real-world contexts appropriate for high school use. The following are examples from various Units and Lessons within Courses 1, 2 and 3 that highlight how the series uses different types of numbers, different forms of equations, and different tools throughout that are appropriate to high school.

  • In Unit 3 of Course 1, Lessons 2 and 3 have students working with linear equations and inequalities. During Lesson 2, students see equations in various forms, such as part a of the Check Your Understanding on page 194, and they also work with inequalities in various forms with non-integer coefficients and non-integer solutions, for an example, see problem 5 on page 196.
  • In Unit 7 of Course 1, Lesson 2 has students determine equivalent quadratic expressions that are initially written in different forms, such as part a of Check Your Understanding on page 494. In Lesson 3, students solve quadratic equations that are not written in the same form, such as standard, factored, or vertex, or do not have integer coefficients, and even when the coefficients are integers, there are some equations that have irrational numbers as solutions. For an example of an equation with irrational solutions, see problem 8 on page 519.
  • In Unit 4 of Course 2, Lesson 2 offers students multiple opportunities to analyze sets of data through least squares regression and correlation. The data sets have different sizes which are appropriate to high school, and the numbers within the data sets also vary. The least squares regression lines that are created do not just have integers as coefficients.
  • In Unit 5 of Course 2, Lesson 3 gives students the opportunity to work with common logarithms and exponential equations. In this setting, the materials do not restrict exponents to integer values, and some equations have non-integer solutions, for an example, see problems 7-9 on page 385.
  • In Course 3, Unit 2 engages students with multiple types of inequalities, for an example, see problem 3 on page 116. The inequalities are written in various forms throughout the unit, as on page 110, and the coefficients of the variables within the inequalities are not always integers, as in problem 1 on page 110. Even when the coefficients are integers, the solutions to the inequalities are not always integers, for an example, see problem 6e on page 114.
  • In Unit 5 of Course 3, Lesson 3 engages students with rational functions. In this lesson, students have to create their own rational functions given other types of functions where the coefficients of the variables are not integers, and the solutions to the rational functions are also not integers. Also, in this lesson, students are presented with varying tools, such as manually drawing graphs or using technology to create graphs, that are all appropriate to high school to help them solve the problems.

Indicator 1d

The 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
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Indicator Rating Details

The materials meet the expectation for fostering coherence through meaningful connections in a single course and throughout the series. Overall, connections between and across multiple standards are made in meaningful ways.

In Core-Plus Mathematics Course 1, the teacher material clearly references units which refer back to middle school understandings within Unit 1, Lesson 1; Unit 2, Lesson 1; and Unit 3, Lesson 1 indicating within the Planning Guide that these lessons are optional, depending on students' middle school background.

Teachers are cautioned that the materials need to be taught in the order they appear to assure coherence because each subsequent topic will depend on previously covered material. The implementation guide (page 6) states, "The eight Core-Plus Mathematics units in each course should be taught in the order they have been developed to retain the learning progressions, coherence, and connections designed into the program."

The student and teacher materials often refer back to prior lessons to make connections and/or build understanding. Specific examples of connections between and among conceptual categories include:

  • Course 1, Unit 1, Lesson 1, “Cause and Effect:” While stating it may be omitted if students come with a very strong middle school preparation, this lesson is an example of how these materials provide coherence. The lesson objectives ask students to “develop disposition to look for cause-and-effect” and “review and develop” skills covered in middle school. The lesson also foreshadows some change patterns that students will address later in this course, or in a subsequent course. The use of “patterns of change” for the opening Unit, which connects Algebra, Functions, and Statistics and Probability, starts the high school courses with a cohesive and coherent theme.
  • F-LE.2: Course 1, Unit 1, Lesson 2, Investigation 1 asks students to interpret population change data including creating and analyzing tables to write Now-Next rules, as a precursor or foundation for recursive function rules, F-BF.2.
  • A-SSE.3, A-APR.3, A-CED.1,2, A-REI.4,7,11, and F-BF.1: Course 2, Unit 5, Lesson 2, On Your Own, Connections pages 370-373, students are asked to find the number of solutions that might arise in solving a system of equations where some equations are non-linear. They are asked to recall the methods they previously used to solve systems of linear equations (tables, graphs and algebra) and apply those methods to solve new types of systems. They are asked to speculate on the possible number of solutions they may need to look for in each type of system.

Two examples of connections made within the courses are:

  • S-ID.6: Within Course 1, Unit 2 "Patterns in Data" begins to build the conceptual connection between univariate and bivariate data. In Unit 3, students' build on their prior experiences with linear relationship to strengthen their ability to recognize data patterns, graphs, and problem situations that indicate such linearity conditions.
  • Within Course 2, Unit 5, Lesson 2 Investigation 1, question 4 asks students to "recall from work with multivariable relations..." connecting this topic back to Unit 1 in that course.

Several examples of connections made between the courses are:

  • Within Course 2, students learn about how to solve systems of linear equations with graphing, substitution and elimination in Unit 1, then learn how to apply matrices to solve linear equations in Unit 2, and revisit the concept of systems of equations with nonlinear equations in Unit 5, even explicitly suggesting the use of graphs to explore possible solutions (first brought up in Unit 1). This idea is further built upon within Course 3, in Unit 2 where students apply their knowledge of systems of equations to linear programming as on page 131.
  • A-SSE.1 - 3; F-IF.2,4, and 8: Course 2, Unit 5 Lesson 1 Investigation 3 connects to previous content topics in discussing quadratic expressions as products of linear expressions and further connecting the distributive property to multiply those linear expressions and expand the quadratic. Quadratics are addressed again in Unit 5 of Course 3, and the book clearly states "in your previous work with linear, and quadratic polynomial functions...." before continuing on with a lesson on the zeroes of polynomial functions. (page 329)
  • G-CO.2, 4, 6, 9, 12: In Course 3, pages T1C–T1E give the key geometric concepts and relationships from Courses 1 and 2 that will be needed to implement the unit.

An opportunity to make connections between standards is missed in Course 3, Unit 5, Lessons 2 and 4. The materials provide limited opportunities to connect solving quadratic equations that have complex solutions, N-CN.7, with graphing quadratic functions, F-IF.7a.

Indicator 1e

The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.
1/2
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Indicator Rating Details

The instructional materials reviewed for the series partially meet the expectation that the materials explicitly identify and build on knowledge from Grades 6-8 to the high school standards. Content from Grades 6-8 is present, but it is not clearly identified and aligned to specific standards from Grades 6-8.

In Core-Plus Mathematics Course 1, the Planning Guide provided for the teacher indicates that the following lessons are optional, Unit 1, Lesson 1; Unit 2, Lesson 1; and Unit 3, Lesson 1, depending on students' middle school background. Also noted in Course 1 Unit 6, “We realize that geometric experiences of students in the middle-school grades are often uneven. Review exercises in Course 1 Units 1-5 have been carefully designed to revisit or build up these geometric understandings."

Prior standards are used to support the progression into high school standards, but the materials do not explicitly identify the standards on which they are building. Below are examples of where the materials do not reference standards from Grades 6-8 for the purpose of building on students' prior knowledge:

  • Course 1, Unit 1, Lesson 1 (pages 2-8): This introduction to linear functions is more closely aligned to 8.F.3 and 8.F.4 than F-IF.4 and F-IF.5. Later lessons in the unit, however, build the process with functions from middle grade standards to high school standards.
  • Course 1, Unit 5, Lessons 1 and 2: The content found in Investigation 5 of Lesson 1 and Investigation 4 of Lesson 2 aligns more closely to 8.EE.1,3 than N-RN.1.
  • Course 2, Unit 3, Lesson 2: Starting with page 196, the use of transformations begins with two-dimensional figures by moving lines to lines and angles to angles, which is aligned to 8.G.1-5. Similarity is first introduced using size transformations, which are linked to dilations during Lesson 2 and again in Course 3, Unit 3. There is no specific mention that dilations are addressed by 8.G.3, 4.

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.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series do not explicitly identify the plus standards, when included, and although they do coherently support the mathematics which all students should study in order to be college-and career-ready, the plus standards could not be easily omitted from the materials without disrupting the sequencing of the materials. The plus standards, when included within the three courses, are identified in the CCSS Guide to Core-Plus Mathematics, but the plus standards are not explicitly identified in any of the other teacher materials. Especially at the lesson level, there is no distinction made between non-plus and plus standards that are "Focused on" or "Connected to."

In the planning guide for each unit, the materials note which problems to complete and investigations to omit when following the CCSSM pathway through the series, and when this information is combined with the identification of standards at the lesson level, teachers would be able to determine which plus standards could be omitted and which ones should be included. Not all of the investigations that address plus standards can be omitted in the CCSSM pathway, so there are investigations and lessons addressing plus standards that all students are supposed to complete when utilizing this series. For an example of a lesson that addresses plus standards but is not supposed to be omitted from the CCSSM pathway in the materials, see the Planning Guide for Unit 7 of Course 2 on page T457D and the aligned CCSSM for Lesson 2 of Unit 7 on page T488.

Below are some locations where the plus standards are addressed in Course 1:

  • N-VM.6: Lesson 1 in Unit 4
  • G-GMD.2: Lesson 3 in Unit 6
  • S-CP.9: Lesson 2 in Unit 8
  • S-MD.A: Lessons 1 and 2 in Unit 8

Below are some locations where the plus standards are addressed in Course 2:

  • N-VM.6-8: Lessons 1 and 2 in Unit 2, Lesson 3 in Unit 3
  • N-VM.9,10: Lesson 3 in Unit 2
  • N-VM.12: Lesson 3 in Unit 3
  • A-REI.8,9: Lesson 3 in Unit 2
  • G-SRT.9-11: Lesson 2 in Unit 7
  • S-CP.8: Lesson 1 in Unit 8
  • S-MD.A: Lessons 2 and 3 in Unit 8
  • S-MD.B: Lesson 2 in Unit 8

Below are some locations where the plus standards are addressed in Course 3:

  • N-CN.4,9: Lesson 2 in Unit 5
  • N-VM.9: Lesson 2 in Unit 7
  • N-VM.12: Lesson 2 in Unit 6
  • A-APR.7: Lesson 3 in Unit 5
  • A-REI.8,9: Lesson 2 in Unit 7
  • F-IF.7d: Lesson 3 in Unit 5
  • F-BF.4c,d: Lessons 1 and 3 in Unit 8
  • F-BF.5: Lesson 2 in Unit 8
  • F-TF.3: Lesson 2 in Unit 6
  • F-TF.6,7: Lesson 3 in Unit 8
  • G-SRT.10,11: Lesson 1 in Unit 3
  • G-C.4: Lesson 1 in Unit 6
  • S-CP.8: Lesson 3 in Unit 4
  • S-MD.A: Lesson 2 in Unit 4
  • S-MD.7: Lesson 3in Unit 4, Lesson 1 in Unit 6

Many of the plus standards listed in this report are fully addressed and developed within the three courses of this series, which includes but are not limited to N-VM.6-10, G-C.4, and S-MD.A.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

Criterion 2a - 2d

Rigor and Balance: The instructional 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 instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for rigor and balance. Overall, the instructional 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 ability to utilize mathematical concepts and skills in engaging applications. There are instances in the materials where the three aspects of rigor are enhanced separately, and there are also instances in the materials where two or more of the aspects are enhanced together.

Indicator 2a

Attention to Conceptual Understanding: The 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
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Indicator Rating Details

The instructional materials reviewed for this series meet the expectation that the materials support the intentional development of students' conceptual understanding of key mathematical concepts. The instructional materials engage students in an inquiry-based investigative structure, allowing for students to develop their reasoning and critical thinking skills as it applies to their conceptual development in mathematics. The Core-Plus Mathematics integrated series promotes mathematical reasoning through various components, including Think About This Situation found at the beginning of every lesson and the Summarize the Mathematics prompts found throughout each lesson. Students further develop conceptual understanding by working collaboratively with their peers and sharing their ideas aloud during class discussions, as indicated in the instructional materials.

Core-Plus Mathematics provides sets of On Your Own (OYO) homework tasks, which include both contextual and non-contextual work with the mathematical concepts developed in that lesson. One type of task in OYO sets are the Connections. These tasks help students to build links between mathematical and statistical topics they have studied in the lesson and to connect those topics with other mathematics that they know. Additionally, it is recommended that student solutions to Connections tasks be discussed in class, which provides students with opportunities to compare and discuss student work and synthesize key ideas into deeper conceptual understanding. The final lesson in each unit, Looking Back, offers students the opportunity to review and to synthesize the key mathematical concepts developed in the unit.

Concepts build over many lessons within and between each course in the series. Specific examples are:

  • A-REI.10: In Unit 3 of Course 1, Lesson 2 explores lines of best fit for data showing the change in percentage of male and female doctors in the U.S. since 1960. The implication is that the number of female doctors will soon equal and, perhaps, surpass the number of male doctors. The materials present a structured discussion and mathematical analysis of the possible implications of using these graphs for making assumptions. The conversation also includes the use of inequalities to create a more robust view of the situation.
  • F-IF.A: In Course 1, Unit 5 begins to develop students' conceptual understanding of rate of change through a graphical analysis of the growth of an exponential situation and then follows up at the end of the investigation with students comparing tables, graphs, and rules for two similar situations and sharing out with the class.
  • A-SSE.1 and A-REI.10: In Course 2, Unit 1 builds students' conceptual knowledge through first introducing multivariable linear equations in Lesson 2 and then having students express given relationships in equivalent forms. The task in Lesson 3 is to find one pair (x,y) of values that satisfies two linear equations.
  • G-SRT.6: Unit 7 of Course 2 on trigonometry builds on concepts from Course 1 about the rigid nature of triangles and how certain relationships in a triangle can fix the shape and/or size of the triangle. Investigation 1 of Lesson 1 uses a series of application problems that review what students have previously learned. Students are then introduced to an angle in “standard position” on the plane and asked to find ratios of sides from several triangles formed by a given angle and points on the line created by the angle. Standards from N-Q, A-REI, and F-IF are addressed as students discover the defined trigonometric ratios.
  • A-REI.A: In Unit 1 of Course 3, Lesson 3 begins Investigation 2 with a description of a reasoning process that encourages students and teachers (page T58) to utilize a process of reasoning in solving problems.
  • G-CO and G-SRT: In Course 3, Unit 3 develops students' conceptual understanding of similarity through analysis of Escher works and tiling patterns and how different components relate to one another.

Indicator 2b

Attention to Procedural Skill and Fluency: The 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

Materials of Core-Plus Mathematics meet the expectation for providing intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific standards or clusters. Overall, the clusters and standards that specifically relate to procedural skills and fluencies are addressed.

Students develop procedural skills, including creating graphs and tables and writing rules and equations, through investigative work in a variety of contextual examples. Additionally, students are given the opportunity to check themselves with the Check Your Understanding sections found toward the end of the investigation. These problems are usually based in contexts but not directly related to the work throughout the investigation which enables students to engage in the mathematics through multiple contexts.

One type of task in On Your Own sets are the Just-In-Time Review and Distributed Practice. These tasks provide opportunities for Just In Time review of concepts and skills needed in the following lesson and distributed practice of mathematical skills to maintain procedural fluency. A clock icon near the solution in the Teacher Guide designates Just In Time review tasks.

The materials offer sufficient opportunities for students to understand the procedures, and examples of how the materials address select cluster(s) or standard(s) that specifically relate to procedural skill and fluency include:

  • A-SSE.1b: In Unit 5 of Course 1, Lesson 1 introduces the procedure for compounding interest and gives students the opportunity to interpret both the expression for the formula and the parts of the expression.
  • A-SSE.2: There are many opportunities for students to use the structure of an expression to identify ways to rewrite it. Within Unit 7 of Course 1, page 497 offers ample opportunity for students to work with and identify patterns in the multiplication of linear expressions and the creation of quadratics.
  • A-SSE.3a: Within Unit 5 of Course 2, pages 336-344 offer many opportunities to develop procedural fluency with factoring a quadratic expression to reveal the zeros of the function it defines. There are more opportunities on page 348. Page 355 gives students an opportunity to provide justifications for each step of deriving the quadratic formula from the standard form of a quadratic equation.
  • A-SSE.3c: Within Unit 5 of Course 2, Lesson 3 has many opportunities to use the properties of exponents to transform expressions for exponential functions, and the lesson also addresses rewriting polynomial, logarithmic and exponential expressions. Lesson 4 provides more opportunities for students to engage with this standard.
  • G-GPE.4: In Unit 3 of Course 2, Lesson 1 uses coordinates to prove simple geometric theorems algebraically and begins with a detailed example that highlights how to use coordinates when creating a proof.
  • G-SRT.5: In Unit 3 of Course 3, Lesson 1 gives ample opportunities for students to work with and develop using similarity criteria for triangles to solve problems and prove relationships in geometric figures.

Indicator 2c

Attention to Applications: The 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

Materials of Core-Plus Mathematics meet the expectation that the 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. The Core-Plus Mathematics integrated series was written using a context-based approach to mathematics, and accordingly, it includes numerous opportunities for students to work through a variety of contextual applications for each of the mathematical concepts addressed in the series. Students practice with multiple ideas throughout the different investigations within a lesson, as well as independently in the "On Your Own" student practice sets.

One type of task in On Your Own (OYO) sets are the Applications. These tasks provide opportunities for students to apply their understanding of the ideas they have learned in the lesson. The series includes numerous applications across the series, and examples of select domain(s), cluster(s), or standard(s) that specifically relate to applications include, but are not limited to:

  • A-SSE, F-IF, F-BF, and F-LE: In Course 1, Unit 1 analyzes patterns of change using tables, graphs and algebraic rules in a variety of contextualized situations, including bungee jumping, price setting, and income.
  • G-SRT: In Course 2, Unit 7 develops students' contextualized understanding of trigonometric functions through calculating distances using the angle of elevation.
  • G-CO, G-C, and G-MG: In Course 3, Unit 6 develops students' contextualized understandings of circular motion and periodic functions through first understanding circles and their properties (notably tangent lines) and then applying these concepts to pulleys and sprockets to study angular and linear velocity.
  • S-ID.2: In Unit 2 of Course 1, Lesson 1 develops statistics with regard to distribution of data and appropriate shape. Graphs, tables, and discussion through questioning often involve contextual problems which help students make sense of the data and conclusions.
  • A-APR.B: In Unit 5 of Course 2, Lesson 1 connects parabolas, their zeros, and factors to contextual situations.
  • F-IF.B: In Unit 2 of Course 3, Lesson 1 utilizes line graphs, parabolas, and polynomials to introduce functions and their parts. This introduction quickly leads to interpreting solutions for the functions within the contexts given for the problems.

Indicator 2d

Balance: 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 instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for not always treating the three aspects of rigor together nor always treating them separately. Overall, the three aspects of rigor are balanced with respect to the standards being addressed. The series provides students the opportunity to develop procedural skills and conceptual understandings through contextualized applications. The materials include a variety of different contexts with which mathematical topics can be applied and promote students' conceptual development in understanding the meaning of the mathematics.

In addition to the classroom investigations, Core-Plus Mathematics integrated provides sets of On Your Own homework tasks, which are designed to engage students in applications and conceptual understandings of their evolving mathematical knowledge. The following are examples of balancing the three aspects of rigor in the instructional materials:

  • In Unit 1 of Course 1, Lesson 3 begins with a section on patterns of change. The use of symbols, shapes, tables, graphs, discussions and contexts within this lesson offers students the opportunity to engage with and develop each aspect of rigor as they work.
  • In Course 1, Unit 3 balances the aspects of rigor by establishing a foundation of conceptual understanding for linear growth and creating and using algebraic rules to express and solve for information about contextualized problems, including prices and earnings.
  • In Course 2, Unit 5 balances the aspects of rigor by developing procedural fluency with solving nonlinear equations and using students' prior conceptual understanding of systems of equations to analyze real-world examples of nonlinear systems of equations, including supply and demand.
  • In Unit 3 of Course 2, Lesson 1 uses technology and algebraic expressions to represent geometric shapes and ideas in the coordinate plane. Initially, there seems to be only connections to conceptual understanding and engaging applications, but procedural skill and fluency are built in through continuing work on page 172.
  • In Unit 1 of Course 3, Lesson 2 uses parallel lines and transversals and geometric figures to work through understanding of proof. Throughout this section, procedural skills and conceptual understandings are treated separately as appropriate.

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
7/8
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Criterion Rating Details

The instructional materials reviewed for this series meet the expectation that the materials support the intentional development of the MPs, in connection to the high school content standards. Overall, the mathematical practices are integrated with the content standards throughout the series.

The following are examples of how the materials support the intentional development of the MPs across the courses for students by supporting teachers in implementing them in their classrooms.

  • The Overview for each course describes to teachers how the MPs help to connect content strands across the units and courses. It also describes how the MPs are part of Investigations, Reflections, and orchestrating lessons.
  • Throughout the lessons and investigations in the teacher materials, there are boxes labeled Mathematical Practices that highlight which practices are used within certain problems, for example, page T359 in Course 1.
  • There are also boxes labeled CCSS Mathematical Practice throughout the teacher materials that describe which MPS are used in particular problems, for example, for example, page T173 in Course 2.
  • There are some problems for students to complete entitled Reflecting on Mathematical Practices, and in the teacher materials, there are explanations as to how the students should answer, for example, page T105 in Course 3.

Course scope and sequence charts do not include identification of MPs with chapters or lessons, but on pages 7-8 of the CCSS Guide to Core-Plus Mathematics, which can be downloaded from the online resources, multiple problems that highlight each MP in each of the three courses are listed.

Indicator 2e

The 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.
1/2
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Indicator Rating Details

The materials partially meet the expectation of supporting the intentional development of overarching, mathematical practices (MP1 and MP6), in connection to the high school content standards, as required by the Standards for Mathematical Practice (MPs). Overall, MP1 and MP6 are used to enrich the mathematical content and are not treated separately from the content standards, but in the series, there are instances of imprecise mathematical language.

Examples of imprecise mathematical language. include, but are not limited to:

  • In Unit 3 of Course 2, Lesson 2 has students write "Coordinate Models" (or symbolic rules) which are the transformation "function." The directions ask students to state the rule in words and symbolic form or write a coordinate rule rather than to describe the transformation as a function.
  • Throughout Courses 2 and Course 3, the materials use the term “size transformation” rather than dilation. A size transformation is connected to a similarity transformation on page 215 of Course 2 and on page 234 of Course 3.
  • In order to introduce the use of the terms domain and range, along with the formal use of function notation, in Course 1, teachers will need to read the specific sections of the teacher materials on pages T3 and T157-158.

Listed below are examples of where MP1 is used to enrich the mathematical content:

  • In Unit 1 of Course 1 on page 8, Investigation 2 has students reasoning through different scenarios embedded in a game of chance. Students have to make sense of the game of chance in order to be able to simulate it, and after persevering in finding multiple solutions through the simulation, students record their results in table form and analyze them with graphs and algebraic rules.
  • In Unit 5 of Course 2, Lesson 1 walks through investigations of quadratic expressions and equations with regard to expanding and factoring, a process that continues through a description of the quadratic formula. Students are able to make sense of the process and persevere in developing the formula because of how the problems are sequenced across the lesson.

Listed below are examples of where MP6 is used to enrich the mathematical content:

  • In Unit 3 of Course 1, problem 17 on page 175 provides students with two tables of information and requires them to use a spreadsheet to reproduce the tables. Students are encouraged to think critically about the relationship between the numbers and to write precise rules within the spreadsheet that would produce the tables of data given to them.
  • In Unit 4 of Course 2, page 261 asks students to work cooperatively to make a table to help determine a Spearman's rank correlation for ranking types of music. Students must be precise with their data to perform their calculations.

Indicator 2f

The 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 meet the expectation of supporting the intentional development of reasoning and explaining (MP2 and MP3), in connection to the high school content standards, as required by the Standards for Mathematical Practice (MPs). Overall, the majority of the time MP2 and MP3 are used to enrich the mathematical content and are not treated separately from the content standards. Throughout the materials, students are expected to reason abstractly and quantitatively as well as construct viable arguments and critique the reasoning of others.

Listed below are examples of where MP2 is used to enrich the mathematical content:

  • In Course 1, Unit 2, Lesson 2, Investigation 4 introduces students to the idea of standard deviation as a measure of variability, after working on quantitative variability in Box Plots and Histograms. The investigation looks first at distance on the coordinate plane then moves, in a structured way, from the distance formula to an abstract understanding of deviation. All along the way, students are asked to make and explain the connections between abstract numbers and the quantities they represent.
  • In Course 3, Unit 5, Lesson 1, the On Your Own on page 339 contains a lengthy situation where students are asked to look at a rule for a function and determine output values for certain inputs. They are then asked to give a reasonable domain and range for the situation and to explain why a given income function makes sense in the situation. They are then given an expense function for the situation and asked to use all known information to answer questions about the profit prospects for the company.

Listed below are examples of where MP3 is used to enrich the mathematical content:

  • In Course 1, Unit 6 on page 374, students are asked to reason through determining triangle congruence using corresponding parts of triangles. In doing so, students are provided with reasoning and justifications and are asked to explain if the reasoning given is correct and why it is correct.
  • In Course 3, Unit 3, Lesson 1, Investigation 1 gives information and a diagram showing possible similar shapes to students, and they are asked how they might test to see if the shapes were similar and how to go about proving their methods. Students are asked to compare answers with others and resolve differences.

Although not explicitly labeled in the majority of cases, MP2 and MP3 are sometimes used together to enhance the content. Listed below are examples of where both MP2 and MP3 are used to enhance the content.

  • In Course 1, Unit 2, Lesson 1, On your own sections are often used to address reasoning and explaining. In this case, students are asked to describe and connect distributions to shapes and context.
  • In Course 2, Unit 5, problems 30-32 on page 353 ask students to predict "common errors" when expanding quadratic expressions and offer explanations for how to help students understand the errors, and students also justify how they themselves decide on the best method to solve a quadratic equation. Then, problem 32 asks students to explain how concrete examples can help to make sense of factoring quadratic expressions, which requires students to make connections between quantities and abstract mathematical concepts.

Indicator 2g

The 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 meet the expectation of supporting the intentional development of modeling and using tools (MP4 and MP5), in connection to the high school content standards, as required by the Standards for Mathematical Practice (MPs). Overall, the majority of the time MP4 and MP5 are used to enrich the mathematical content and are not treated separately from the content standards. Throughout the materials, students are expected to model with mathematics and use tools strategically.

Listed below are examples of where MP4 is used to enrich the mathematical content:

  • In Course 1, Unit 8 is entitled "Patterns in Chance." There are multiple opportunities for students to engage with MP4 during the unit, and in particular, the Check Your Understanding on pages 557-558 engages students in making assumptions and approximations explicit, deciding whether data are consistent with a proposed model, and revising the proposed model if that is deemed necessary.
  • In Course 2, Unit 7, Lesson 3 requires students to analyze a sailing situation by first modeling it with a diagram that represents the problem. Then, students use trigonometry to find unknown information regarding the path of the ship.

Listed below are examples of where MP5 is used to enrich the mathematical content:

  • On page 420 of Unit 6 in Course 1, students are encouraged to use interactive geometry software or other tools to investigate properties of regular polygons, including central angle measurements and interior/exterior angle measurements.
  • In Lesson 2 of Unit 6 in Course 3, problems 5-7 of Investigation 4 engage students in a context where many tools could be utilized to help students solve the problem. In problems 5 and 6, students could draw graphs of the context manually or with technology to model the context, or they could select various physical objects to help them make sense of the problem. In problem 7, students could use various technological tools to create generalizations about the scenario.

Indicator 2h

The 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 meet the expectation of supporting the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards, as required by the Standards for Mathematical Practice (MPs). Overall, the majority of the time MP7 and MP8 are used to enrich the mathematical content and are not treated separately from the content standards. Throughout the materials, support is present for the intentional development of seeing structure and generalizing.

Listed below are a few examples of where MP7 is used to enrich the mathematical content:

  • In Course 1, Unit 5, Lesson 1, the Summarize the Mathematics on page 303 asks students to explain how they would chose a regression model for a data set based on the patterns they found in the data.
  • In Course 2, Unit 1, Lesson 3, part d of Summarize the Mathematics has students explain how they might tell the number of solutions for a system of linear equations just by looking at the equations.
  • In Course 3, Unit 2, Lesson 1, Investigation 2 on pages 112-113 prompts students to discuss what the graph of a quadratic function would look like by using the expression only. In particular, students find the number and values of zeros of the function and speculate on regions that would satisfy quadratic inequalities related to the given quadratic functions.

Listed below are a few examples of where MP8 is used to enrich the mathematical content:

  • In Course 1, Unit 5, Lesson 2, students use repeated applications of the Pythagorean Theorem to find the formula for the length of the diagonal of any square.
  • In Course 2, Unit 8, Lesson 3, Investigation 3 has students use repeated trials to develop the formula for Expected Value.
  • In Course 3, Unit 5, Lesson 1, Investigation 2 gives students the opportunity to work through an income/cost/profit situation for which they have previously developed a set of equations. By repeatedly operating with the equations in different scenarios, the students develop “rules” for how to operate with polynomial expressions and the implications of the operations on the resulting polynomial.

Although not explicity labeled in the majority of cases, MP7 and MP8 are sometimes used together to enhance the content.  Listed below are examples of where both MP7 and MP8 are used to enhance the content.  

  • In Course 2 Unit 3, Lesson 2, students have opportunities to work with transformations of coordinates on a plane that creates the structure for what later becomes a set of mathematical rules for geometric transformations.
  • In Course 3, Unit 3, Lesson 1, students engage with designs created using similar figures. Initially, students are prompted to examine a specific design to determine the structure that exists among the similar figures in the design. Then, after repeatedly examining the structure of designs based on similar figures, students are asked to determine sufficient conditions for knowing when two figures are similar.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the materials are well-designed and take into account effective lesson structure and pacing. The design of the materials, in print and in the eBook, distinguishes between problems and exercises, and it also is not haphazard. The consistent order of the sections, Investigations followed by Applications delineated as On Your Own, Connections, Reflections, Extensions, and Review, helps to make students accustomed to the layout. Throughout the materials, students are asked to present their understanding of the mathematics in a variety of ways, and the materials also integrate the use of physical and virtual manipulatives that are faithful representations of mathematical objects.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the underlying design of the materials distinguishes between problems and exercises. The materials clearly organize learning in a specified order of an Investigation phase, sometimes with multiple concepts, followed by an On Your Own phase. Problems for learning new mathematics are within the Investigation phase, and exercises which build mastery and student capacity for a given skill with application are in the On Your Own phase. Items for application require multiple representations and extend learning, and they do build on knowledge based in the Investigation phases. Similarly, problems in the Investigation phase often contain real-world applications but use the application to introduce concepts and build knowledge. This structure is repeated throughout each of the courses. For example, in Course 2, Unit 5, Lesson 1, the Investigation phase begins on page 327 with multiple investigations followed by the On Your Own phase on page 345.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the design of assignments is not haphazard and tasks are given in intentional sequences. Throughout the curriculum, assignments are given in an intentional manner, often building capacity for the learner through reasoning. This progression includes the development of mathematically accurate vocabulary, methods, and formulas. Examples that highlight how the design of the assignments is not haphazard and tasks are given in intentional sequences include: the investigations in Lesson 2 of Unit 2 in Course 1; the applications in Lesson 2 of Unit 5 in Course 2; and the investigations in Lesson 1 of Unit 7 in Course 3.

Indicator 3c

There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that there is variety in how students are asked to present the mathematics. The materials require students to engage in mathematics in a number of ways to solve various types of problems that include evaluating expressions, making predictions based on a set of data, estimating measurements and using geometric tools, and comparing/contrasting information from a diagram. Examples of these types of problems can be found on page 67 in the materials for Course 1. Other problems allow students to engage in the process of solving a problem through planning and to build a mathematical model from given data (Course 2, Unit 6, Lesson 2, page 435-452, applications section). At other times, students are asked to give explanations, write equations, and create a diagram (Course 3, Unit 1, Lesson 2, page 44).

Indicator 3d

Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series have manipulatives, both virtual and physical, that are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

Physical manipulatives are utilized to introduce reasoning in problem solving. For example, counters are used in a problem referencing consecutive integers in Course 1, Unit 1, Lesson 1. In Course 1, Unit 6, Lesson 1 on page 371, virtual manipulatives are used to generate work with triangle congruence, and they are also used in Course 2, Unit 6, Overview on page T399A, to construct vertex-edge graphs to investigate problems and concepts in modeling and optimization.

The series makes use of a wide range of virtual manipulatives available within CPMP-Tools, and there are physical manipulatives needed for each course listed within the Planning Guide. A few examples of these include, but are not limited to rubber bands, meter sticks, compass, straightedge, protractor, rulers, pennies, dice, stopwatch, bouncy balls, linkage strips and pipe cleaners.

Indicator 3e

The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series have a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the subject. The materials keep a consistent layout for units and lessons. In general, the sections appear in the following order: Investigations followed by Applications delineated as On Your Own, Connections, Reflections, Extensions, and Review. Lessons frequently include other sections to enhance students' depth of knowledge with a variety of approaches that include Think about this Situation, Summarize the Mathematics, and Promoting Mathematical Discourse. Pictures and models used throughout the series support student learning as they are connected directly to an investigation or problems being solved. The figures and models used are not distracting from the mathematical content.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for supporting teacher learning and understanding of the Standards. There are plenty of questions provided to teachers to aid in planning and providing effective learning experiences, and the materials contain numerous ways in which they help teachers present the mathematical content and use embedded technology to aid students' learning. The materials do include adult-level explanations to help teachers increase their own learning. Although there are focus and connected standards provided for each lesson, the materials do not clearly explain the vertical progression of the standards across the series or how the learning of the lessons fits into a vertical progression of learning.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that teachers are provided quality questions to guide students' mathematical development. The opening page of the lessons contains a scenario that touches on the mathematics to be studied, and the next page contains a section titled Think About This Situation where students are given questions to discuss. Guiding questions are provided for teachers and students at the beginning of each investigation. The teacher edition provides typical student responses that might be expected and suggestions for follow-up questions to enrich the discussion. With the teacher edition, there is an additional Promoting Mathematical Discourse section for some lessons where a sample discussion is given for use in planning. The Implementation Guide suggests that teachers work through these pages together during planning.

In the student edition, within a lesson at the end of each Investigation, there is a Summarize the Mathematics section that provides a series of well-designed questions to have students reflect on what they have learned. The teacher edition provides the same support for Summarize the Mathematics as was mentioned above for Think About This Situation. For an example, see Course 2, Unit 4.

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the teacher edition contains ample and useful annotations. There are annotations in the margins and in the narrative related to the lesson implementation. There are also boxes labeled “Instructional Notes” that cover points like specific goals for a particular question, where and how a topic was previously addressed, helpful reminders for students, thoughts on pacing, and concepts students may not yet fully understand. Other special boxes include Assignment Note, Differentiation, Teaching Resources, Key Idea, Collaboration Skills, Possible Misconception and Common Error.

CPMP Tools is an online dynamic software package embedded in the instructional materials that is referenced extensively and is freely available to the students in and out of class time. It is employed in every unit across all three courses. In the teacher edition there are boxes titled “Technology Note,” which offer guidance to teachers on the use of CPMP Tools that supports and enhances student learning. For an example, see Course 2, Unit 3, Lesson 1 starting on page T162. The use of this tool is also referenced in the planning guide at the start of each unit. (Course 2, page T161D)

Indicator 3h

Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.
2/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the teacher edition contains adult-level discussion of the mathematics. Special boxes in the teacher edition are used to give teachers an “advanced perspective” on some of the material covered. Course 3, page T116B, has such an example. There are also “Additional Resources” that refer teachers to specific publications that may enhance their understanding of the topics (Course 1 on page T367). In some cases, there is a list of additional references in the overview of the Unit (Course 1 on page T237).

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
1/2
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that the teacher edition addresses the standards in the context of their place in the entire series. The materials for the series do not provide a vertical progression for the standards in the series. For some units, the materials provide general references in the Unit Overview as to how current content fits into the vertical progression of learning, for example, page T319 in Course 3, but these general references are not provided for all units, for example, page T73-73A in Course 1. At the beginning of each lesson, there is a list of standards that are "Focused on" and "Connected to" in the lesson, for example, page T462 in Course 1, but this list does not make references to any other lessons in the series. The combination of the list of standards for each lesson and the general references in the Unit Overview could explain the role of the specific standards in the context of the overall series, but the inconsistency of the general references leaves the explanation of the role of the specific standards in the context of the overall series incomplete.

Indicator 3j

Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series have planning guides in the teacher edition for each unit of each course. They appear at the start of each unit and are broken down by lesson with a pacing guide giving the total days for coverage including assessment. The guide also includes objectives for each lesson and suggested assignments for each investigation for full coverage. Teachers may add additional help or enrichment to the suggested assignments. There is also a list of additional resources by lesson included in the planning guide (Course 3, page T161). In addition, at the back of the student textbook, there is a listing of the standards covered in each Investigation for each lesson for every unit in the course (Course 3, page 638).

At the start of each lesson in a unit, there is a page in the teacher guide that indicates which standards are “focused on” or “connected to” in the lesson. This page also contains an explanation of what will happen in the lesson and, depending on the lesson, additional information may be included. (Course 3, page T162).

Indicator 3k

Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series contain strategies that provide for communications with students and parents about the mathematics covered, support opportunities, and progress indicators. The Implementation Guide has an entire section on outreach to parents (page 24). It contains sample letters that might be sent to parents describing the program and shares a link for parent resources, www.wmich.edu/cpmp/parentresource.html. This website provides information for parents that includes an overview of the content, a video of what the classroom will look like, and suggestions on how parents can help their student to understand the key mathematical ideas in units from each of the three courses. Also included are selected solutions, partial solutions, and hints for homework tasks. There is a description of the Math Toolkit where students keep a personal online notebook that parents can access to aid in homework and study help. There are also links to research on the methodology behind the curriculum design.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
0/0
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Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series contain explanations as to why certain approaches are taken. The Implementing Core-Plus Mathematics Guide for teachers includes detailed explanations that address why the materials take the approach they do. The Classroom Implementation section, pages 31-75, addresses the methods employed, how and why they should be used, and provides references to research that supports the methods used and their inclusion in the classroom.

Also, at the beginning of each unit, the Unit Overview page of the Teacher’s Edition includes a discussion of the pedagogy that will be implemented and why it is appropriate. Whether the context is new to students (Course 1, page T361) or building on prior knowledge (Course 2, page T521), other information related to pedagogy, technology, misconceptions, and background knowledge of the context is also provided.

The materials do reference research-based instructional approaches beyond the Implementation Guide. The teacher editions for each course reference research in the teacher notes for pertinent lessons (Course 1, page T268 “Instructional Note" and page T293 “ELL Tips;” Course 2, page T116 ”Equity;” and Course 3, page T58A “Differentiation” ).

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
7/10
+
-
Criterion Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that the materials offer teachers resources and tools to collect ongoing data about student progress on the Standards. The lessons offer some opportunities to informally assess students' prior knowledge, and feedback for review and practice exercises is limited. The assessments provided do not clearly denote which standards are being emphasized, but the assessments do provide sufficient guidance for teachers in following up on student performance.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation for gathering students' prior knowledge within and across grade levels/courses. There are no formal assessments of prior knowledge or connections to learning from Grades 6-8 or previous courses. There are some instances in the materials where students' prior knowledge is assessed, for example the Lesson Launch on pages T108-109 in Course 3, and used to launch an investigation into new learning, but these informal assessments are not a part of all units or lessons. For example, in Course 2, Unit 3 addresses transformations and distance, but the materials do not include any opportunities for teachers, formally or informally, to determine what prior knowledge students might have about these topics from either Grades 6-8 or Course 1. There are some Instructional Notes that address prior knowledge, such as on page T114A in Course 3, but these Instructional Notes are inconsistently placed throughout the materials. Also, the Review section in the On Your Own homework sets provide an opportunity to review previous concepts and skills, but there is limited support for teachers as to how the information gathered from the review problems could be used in current or future lessons.

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that teachers are given support to identify and to address common student errors and misconceptions. There are multiple teaching tips provided, referred to as "Common Error," for example, page T219 in Course 1, or "Possible Misconception," for example, page T507A in Course 2, to assist teachers with addressing these needs in their classroom. Additionally, there are problems included in the materials that allow for students to identify errors and critique reasoning.

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that the materials in the series provide opportunities for ongoing review and practice of both skills and concepts. Although opportunities to review concepts and skills are provided through Summarize the Mathematics tasks, On Your Own Review practice problems, and Looking Back Lessons, attention to feedback is limited to answer guides for questions and in some Instructional Notes, for example, page T221 in Course 1 and page T328 in Course 2.

Indicator 3p

Materials offer ongoing assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that standards are clearly denoted. Assessments created in the eAssessments tool through ConnectED have the ability to denote CCSSM (listed as National Standards), but standards are not explicitly identified for formative or summative assessments that are provided. Standards are identified at the beginning of each unit/lesson, but individual problems in assessments are not labeled with standards.

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that assessments provided include sufficient guidance in interpreting scores by having answer keys and solutions to all assessments, detailed answers and solutions for lesson components (On Your Own homework, Check Your Understanding, Think about the Situation, and Summarize the Mathematics), and both specific and general scoring rubrics. The implementation guide also provides guidance for how to create specific rubrics for individual questions.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
+
-
Indicator Rating Details

The materials in the series encourage students to monitor their own progress. The Core-Plus Implementation Guide suggests that students keep a journal in which to reflect on their mathematical struggles and successes. Per the guide, "Journals also encourage students to assess their own understanding of, and feelings about, the mathematics they are studying." Additionally, teachers are encouraged to implement portfolios in their classroom as a way for students and teachers to monitor student progress. According to the implementation guide, "Typically, portfolios provide a tool for assessing one or more of the following outcomes: student thinking, growth over time, mathematical connections, a student's views on herself or himself as a mathematician, and the problem-solving process as employed by the student."

Within the curricular materials, students are able to assess themselves using the Check Your Understanding for every investigation as well as through guided class discussions. The remaining types of tasks in On Your Own sets include Reflections which provide opportunities for students to re-examine their thinking about ideas in the lesson.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
8/10
+
-
Criterion Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that the materials support teachers in differentiating instruction for diverse learners within and across courses. The instructional materials do not provide specific strategies to aid teachers in implementing differentiated instruction, and there is not enough scaffolding provided for students whose mathematical knowledge is not at their current course level. There is a Spanish Glossary in each student textbook, and there are boxes labeled ELL Tips that give suggestions for the teacher that could aid in instruction. Parent communication is available in Spanish.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that scaffolding or sequencing strategies are provided to teachers that allows the content to be accessed by all learners. Problems are often set up to engage students at multiple levels, including Investigation, Application and Extension sections with multiple representations and questioning. Content builds throughout the lessons and units to develop comprehension. Most prominent is the use of a logical sequence of questions within context to note patterns and to help students generate solutions, for example, Lesson 2 in Unit 2, Course 3.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation that the materials provide teachers with strategies for meeting the needs of a range of learners. Specific strategies or materials for helping teachers implement differentiated instruction for a range of learners are limited to a brief section in the Overview of each course (page xii in Course 3) and some boxes labeled Differentiation placed at different points in the courses, for example page T202 in Course 1, page T78 in Course 2 and page T58A in Course 3. There is sufficient scaffolding provided for students to obtain new knowledge when they have the prerequisite knowledge for their current course, but the instructional materials do not provide sufficient scaffolding support for teachers to address the needs of students whose mathematical knowledge is not at their current course level. Also, complex vocabulary is used within the materials and may not be accessible to all learners, and there is limited aid provided for teachers on this issue within some of the Differentiation boxes, for example, page T216 in Course 1.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation that the materials provide problems with multiple entry-points that can be solved through a variety of strategies or representations. Questioning can be tiered with multiple entry points sequenced for logical reasoning and content development, for example, page T252 in Course 2. Most of the multiple step questions require a majority, if not all, of the MPs, but questions can also be specific with one solution and a single entry point. As a whole, content is experienced through a variety of mathematical representations with equations, graphs, diagrams, tables, charts, and verbal explanations consistently throughout the materials, for example, Investigation 1 in Course 1, Unit 5, Lesson 1.

Indicator 3u

Materials provide support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series partially meet the expectation for providing support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems). Beyond ELL, there was no support found for special populations such as students not reading at grade level. There is a Spanish Glossary in each student textbook, and there are boxes labeled ELL Tips that give suggestions for the teacher that could aid in instruction. The location of these boxes can be found in the Index of Mathematical Topics at the back of each teacher edition.

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series meet the expectation for providing support for advanced students to investigate mathematics content at greater depth. The Implementation Guide, on page 2, states; “Differences in student performance and interest can be accommodated by the depth and level of abstraction to which core topics are pursued, by the nature and degree of difficulty of applications, and by providing opportunities for student choice of homework tasks and projects.” The extensions tasks, included in the On Your Own section of each lesson, reveal how well students are able to extend the present content beyond the level addressed in the investigations. Teachers can pick and choose assignment problems for students to meet their level of understanding or sophistication.

The teacher edition Unit Overview contains notes of what types of enrichment are available within the lessons (Course 1, Unit 6, page T361; Course 2, Unit 1, page T1D; and Course 3, Unit 3, page T161A, paragraph 4). Within the lessons, there are Differentiation boxes that supply additional enrichment ideas. (Course 1, Unit 6, page T421; Course 2, Unit 7 page 507; and Course 3, Unit 2, page T116B). A complete list of differentiation boxes can be found in the Index of Mathematical Topics at the back of each teacher edition.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/0
+
-
Indicator Rating Details

The few pictures that do contain people show a variety of race, ethnic, and personal characteristics. Examples include Course 1, pages 324, 356, 442 and 579; Course 2, pages 1, 49, 98, 353, 363 and 421; and Course 3, pages 74, 171, 216, 230 and 327. The wording of problems in the exercises uses a variety of names and cultural references.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
+
-
Indicator Rating Details

The instructional materials provide opportunities for teachers to use a variety of grouping strategies. The Implementation Guide provides an entire section (pages 41 – 45) related to the pedagogy of collaborative learning, how to form and manage groups, and some effective techniques that can be used. There are also grouping suggestions throughout the teacher edition and boxes labeled Collaboration Skill that contain suggestions for group work. The location of these boxes can be found in the Index of Mathematical Topics at the back of each teacher edition.

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed encourage teachers to draw upon home language and culture to facilitate learning. There is a reference in the Implementation Guide on page 53 to practices that promote equity for ELL students. There is a note on page 43 to make sure that groups are ethnically mixed, and there is also a reference on page 52 that, when wanted, students should be allowed to restate problems in their native language.

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
+
-
Criterion Rating Details

The instructional materials reviewed for the Core-Plus Mathematics integrated series support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms. The materials provide access to many e-tools through ConnectEd. Additionally, the technological tools provided allow teachers to create their own assessments as well as collaborate with other teachers and their students through different features within the materials.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
+
-
Indicator Rating Details

The materials integrate technology, manipulatives, and dynamic software in ways that engage all students in the MPs. In addition to providing suggestions for how to use calculators and spreadsheets within the curriculum, the materials provide their own software, CPMP Tools, which has the capabilities of modeling geometry, algebra, statistics and discrete mathematics. CPMP Tools is used throughout the texts to engage students in a variety of ways including:

  • In Course 1, Unit 3, Lesson 1, Applications link directly to data located in CPMP Tools. Students can then use the software to plot the data and find a linear model. Alternatively, students can use their graphing calculator and enter the data in lists, produce a scatterplot, and find a model using the linear regression function already present in their graphing calculator.
  • In Course 2, Graphing Technology Lab, the Glencoe Personal Tutor presents a teacher explaining a step-by-step solution to a problem that includes a linear-quadratic system of equations.
  • In Course 3, Unit 3, Composing Size Transformations provides students with opportunities to work with the interactive geometry software in CPMP Tools.

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
+
-
Indicator Rating Details

The digital resources are accessible on Windows, Mac and Linux OS and require Java in order to run on those systems. CPMP Tools are built using Java WebStart, which permits safe, easy, and reliable distribution of software and software updates across different types of computers, but cellphones and tablets, excluding the Surface Pro, do not support Java in a way that will allow CPMP Tools to run.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
+
-
Indicator Rating Details

The materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. Teachers have access to the eAssessments through ConnectED, which is the online access to the instructional materials. Teachers can use pre-made tests or create tests from question banks (both pre-existing and teacher created) and can either print the assessments or assign them digitally for students to access and complete in ConnectED. Teachers have the ability to edit the number of times students may work on the assessment online, how long they can access it, when they can access it, and can choose to scramble questions. The assessments are not adaptive, but assessment questions can be selected by type of question and standard in order to elicit the type of response a teacher is looking for, conceptual or procedural fluency. Additionally, teachers can create their own assessment questions, including incorporating interactive elements using HTML5 or Flash technology in order for a teacher to better build questions to assess the type of understanding they are seeking.

Indicator 3ac

Materials can be easily customized for individual learners.
0/0

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
0/0
+
-
Indicator Rating Details

The materials in the series do not provide adaptive technology. Individualization of assignments and assessments would have to be done by the teacher using the eAssessments tools.

Indicator 3ac.ii

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
+
-
Indicator Rating Details

The digital materials are not able to be customized to match student/community interest.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
+
-
Indicator Rating Details

The materials allow students and teachers to collaborate with one another through both messaging and discussion features. Teachers can collaborate with one another through sharing courses and materials.

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Additional Publication Details

Report Published Date: 09/23/2016

Report Edition: 2015

Title ISBN Edition Publisher Year
978-0-07-665794-0
978-0-07-665795-7
978-0-07-665796-4
978-0-07-665797-1
978-0-07-665798-8
978-0-07-665799-5
978-0-07-665800-8
978-0-07-665801-5
978-0-07-665802-2

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. 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).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, 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.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

The High School review rubric identifies the criteria and indicators for high quality instructional materials. The rubric 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 rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The High School Evidence Guides complement the rubric 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.

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