## Big Ideas Learning AGA

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
Big Ideas Learning Algebra 1 Student Edition 9781644328644
Big Ideas Learning Geometry Student Edition 9781644328651
Big Ideas Learning Algebra 2 Student Edition 9781644328668
Big Ideas Learning Algebra 1 Online Student Resource 1 YR 9781647270001
Big Ideas Learning Algebra 1 Teacher Resource Package 1 YR 9781647270605
Big Ideas Learning Geometry Online Student Resource 1 YR 9781647270834
Big Ideas Learning Geometry Teacher Resource Package 1 YR 9781647271435
Big Ideas Learning Algebra 2 Online Student Resource 1 YR 9781647271664
Big Ideas Learning Algebra 2 Teacher Resource Package 1 YR 9781647272265
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## Report for High School

### Overall Summary

The materials reviewed for Big Ideas Learning AGA partially meet expectations for alignment to the CCSSM for high school. For focus and coherence, the series showed strengths in the following areas: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites, making meaningful connections in a single course and throughout the series, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. For rigor and the mathematical practices, the series showed strengths in the following areas: supporting the intentional development of students' conceptual understanding, opportunities for students to develop procedural skills, displaying a balance among the three aspects of rigor, supporting the intentional development of reasoning and explaining, and supporting the intentional development of seeing structure and generalizing.

##### High School
###### Alignment
Partially Meets Expectations
Not Rated

### Focus & Coherence

The materials reviewed for Big Ideas Learning AGA meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; spending the majority of time on content widely applicable as prerequisites; making meaningful connections in a single course and throughout the series; and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. The materials partially attend to the full intent of the modeling process, letting students fully learn each non-plus standard, and engaging students in mathematics at a level of sophistication appropriate to high school.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus & Coherence

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).

The materials reviewed for Big Ideas Learning AGA meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; spending the majority of time on content widely applicable as prerequisites; making meaningful connections in a single course and throughout the series; and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. The materials partially attend to the full intent of the modeling process, letting students fully learn each non-plus standard, and engaging students in mathematics at a level of sophistication appropriate to high school.

##### Indicator {{'1a' | indicatorName}}
The materials focus on the high school standards.*
##### Indicator {{'1a.i' | indicatorName}}
The materials attend to the full intent of the mathematical content contained in the high school standards for all students.

The materials reviewed for Big Ideas Learning AGA meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. The materials include a few instances where all aspects of the non-plus standards are not addressed across the courses of the series.

The following are examples from the Student Edition (unless otherwise noted) for which the materials attend to the full intent of the standard:

• N-RN.3: In Algebra 1, Chapter 9, Section 1, Explore It, students experiment with the sums and products of irrational and rational numbers. Students use their findings to explain why the sum or product of two rational numbers is rational, the sum of a rational number and an irrational number is irrational, and the product of a nonzero rational number and an irrational number is irrational.

• A-CED.2: In Algebra 1, Chapter 3, Section 5, Explore It, students create equations in two variables to represent the number of child tickets and the number of adult tickets sold for a charity. Then, students graph their equation on a coordinate grid and interpret the intercepts.

• A-REI.4a: In Algebra 1, Chapter 9, Section 4, students use completing the square to transform quadratic equations into an equation of the form $${{(x-p)}^{2}}=q$$. In Algebra 2, Chapter 3, Section 3, students derive the quadratic formula from the form $${{(x-p)}^{2}}=q$$.

• F-IF.7c: In Algebra 2, Chapter 4, Section 1, students graph polynomials and describe end behaviors. In Algebra 2, Chapter 4, Section 5, students identify zeros when suitable factorizations are available.

• F-BF.3: In Algebra 1, Chapter 3, Section 7, students identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x+k) for specific values of k. In Algebra 1, Chapter 4, Section 8, students recognize even and odd functions from their graphs. In Algebra 2, Chapter 4, Section 8, students recognize even and odd functions from their algebraic expressions.

• G-SRT.4: In Geometry, Chapter 8, Section 4, students prove a line parallel to one side of a triangle divides the other two proportionally. Within the same lesson, students prove the converse of the Triangle Proportionality Theorem. In Geometry, Chapter 9, Section 1, students prove the Pythagorean Theorem using triangle similarity.

• G-GPE.1: In Geometry, Chapter 10, Section 7, Explore It, students derive the equation of a circle using the Pythagorean Theorem. Within the same lesson, students complete the square to find the center and radius of a circle given an equation.

• S-ID.6a: In Algebra 1, Chapter 4, Section 4, students create linear models to fit a given data set and use the models to solve problems. In Algebra 1, Chapter 6, Section 3, students use technology to create an exponential function to fit a data set about the consumption of bottled water. Students then use the function to estimate the amount of bottled water consumed in 2022. In Algebra 1, Chapter 9, Section 2, students use technology to create a quadratic function representing the number of students with the flu after a break from school. Students then use the function to solve problems.

The materials attend to some aspects, but not all, of the following standards:

• F-LE.1a: In Algebra 1, Chapter 3, Section 6, Explore It, students create tables to determine if the rate of change is constant, and students explain how a constant rate of change represents a linear equation. In Algebra 1, Chapter 6, Section 3, the materials state, “As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor, which means consecutive y-values form equivalent ratios.” The materials do not provide opportunities to prove linear functions grow by equal differences over equal intervals or prove exponential functions grow by equal factors over equal intervals.

• F-TF.8: In Algebra 2, Chapter 10, Section 7, the materials state the Pythagorean identities but the identities are not proven within the materials. Within the same section, students use the Pythagorean identity to find $$sin{\theta }$$, $$cos{\theta }$$, or $$tan{\theta }$$.

• G-CO.2: In Geometry, Teacher Edition, Chapter 4, Section 1, teachers describe transformations as functions that take points in the plane as inputs and give other points as outputs. In Geometry, Chapter 4, Section 1, Explore It, students translate figures using technology. In Geometry, Chapter 4, Section 3, Explore It, students use technology to perform a 90° rotation, a 180° rotation, and a 270° rotation. The materials do not provide opportunities to compare transformations that preserve distance and angle to those that do not.

• G-CO.6: In Geometry, Chapter 4, Section 4, students use the definition of congruence in terms of rigid motions to decide if figures are congruent. In Geometry, Chapter 5, College and Career Readiness, students perform a composition of transformations to map one figure onto a second figure. The materials do not provide opportunities to predict the effect of a given rigid motion on a given figure.

• G-SRT.2: In Geometry, Chapter 4, Section 6, Practice, students use the definition of similarity in terms of similarity transformations to decide if two figures are similar. In Geometry, Chapter 8, Section 1, the materials state, “Because the ratio of corresponding lengths of similar polygons equals the scale factor, $${\frac {AB'} {AB}}={\frac {DE} {AB}}$$.” There is no evidence of explaining using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding sides.

• G-C.5: In Geometry, Chapter 11, Section 1, the materials define the radian measure of the angle as the constant of proportionality. In Geometry, Chapter 11, Section 2, Explore It, students derive the formula for the area of a sector. In Geometry, Chapter 11, Section 1, the materials state, “In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360°.” There is no evidence of using similarity to derive the fact that the length of the arc intercepted by an angle is proportional to the radius.

##### Indicator {{'1a.ii' | indicatorName}}
The materials attend to the full intent of the modeling process when applied to the modeling standards.

The materials reviewed for Big Ideas Learning AGA partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The materials include various aspects of the modeling process in isolation or combinations, but opportunities to engage in the full modeling process are absent from the materials. Examples in the materials with various aspects of the modeling process in isolation or combinations include, but are not limited to:

• A-CED.1: In Algebra 2, Chapter 1, Section 3, students determine whether to buy a gasoline model or an electric model vehicle. Students consider information such as the price and fuel economy of each car, the number of miles driven per year by the family, and gas or electricity prices in the area. Students must write a linear model representing the cost of the gasoline model vehicle versus cost of the electric model vehicle. Students manipulate their model when substituting the number of miles their family drives in a year. Students also analyze their results to determine which vehicle is better for their family. Finally, students research other factors using the internet that might impact the cost of vehicle ownership and reflect on how the factors may impact their final choice. Students do not report on the conclusion and the reasoning behind them.

• F-LE.2: In Algebra 1, Chapter 6, Section 4, students describe two account options where compound interest is earned on a $1000 deposit. Students write a function for an account representing the final balance after t years. Students must choose an account and explain their reasoning. Students are provided the variable t to use in their model, and students do not manipulate their model. • G-GPE.7: In Geometry, Chapter 1, Section 4, students must describe a company and create a logo for the company. The logo must contain at least two polygons with a total area of at least 50 square units. After creating the logo within a coordinate grid, students calculate the area and perimeter of the logo. Finally, students create a proposal showing how the logo relates to the company. Students do not have to interpret or analyze the results of their design. • S-ID.6b: In Algebra 1, Chapter 4, Section 5, students are given a table representing the number of text messages sent over a 5 year period. Students use technology to write a line of best fit representing the data. Then, students analyze the line of best fit to identify and interpret the correlation coefficient. Students manipulate the model to calculate residuals, make a scatter plot, and interpret the results. Finally, students validate their results by comparing the correlation coefficient and residual graph to determine if the model is a good fit for the data. Students do not report on the conclusion and the reasoning behind them. • S-IC.4: In Algebra 2, Chapter 9, Section 5, students create a statistical question and then survey a sample of at least 50 teenagers at school. Students analyze results for sample size, margin of error, and any other conclusions provided by the data. Students write a report on their findings. Students are not asked to reflect or validate their statistical findings. ##### Indicator {{'1b' | indicatorName}} The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics. ##### Indicator {{'1b.i' | indicatorName}} 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. The materials reviewed for Big Ideas Learning AGA meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs and careers. Examples of how the materials allow students to spend the majority of their time on the WAPs include: • N-RN.1: In Algebra 1, Chapter 7, Section 2, students use the meaning of rational exponents to describe and correct an error in rewriting the expression $${{({\sqrt[{3}] {2}})}^{4}}$$ in rational exponent form. Within the same section, students, “Explain how extending the properties of integer exponents to rational exponents allows you to express radicals in terms of rational expressions.” In Algebra 2, Chapter 5, Section 1, students apply understanding rational exponents by identifying which of four expressions written in radical notation or rational exponent notation does not belong. • A-SSE.1b: In Algebra 1, Chapter 1, Section 2, the materials provide two methods to solve multi-step equations. One method uses the distributive property to solve the equation while the other interprets the expression in parenthesis as a single quantity. In Algebra 1, Preparing for Chapter 7, students consider a launched rocket modeled by the expression -16t(t-13). Students complete a table of values using -16t and t-13 as separate quantities. Students reflect on the helpfulness of viewing an expression as a product of individual factors versus a single object. In Algebra 2, Chapter 6, Section 1, students consider the compound interest formula $${{A=P(1+r)}^{t}}$$. Students interpret quantities P and $${{(1+r)}^{t}}$$ before determining whether one quantity depends on the other. • F-IF.6: In Algebra 1, Chapter 8, Section 6, students calculate and interpret the average rate of change of a function over a specified interval for quadratic and exponential functions. In Algebra 1, Chapter 10, Section 1, students calculate and interpret the average rate of change of square root functions. In Algebra 1, Chapter 10, Section 2, students calculate and interpret the average rate of change of cube root functions. In Algebra 2, Chapter 10, Section 4 and Section 5, students calculate and interpret the average rate of change of trigonometric functions. • G-CO.10: In Geometry, Chapter 5, Section 1, students prove the sum of the measures of the interior angles is 180 degrees, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles, and the acute angles of a right triangle are complementary. In Geometry, Chapter 6, Section 4, students prove base angles of isosceles triangles are congruent and triangles are equiangular if and only if triangles are equilateral. In Geometry, Chapter 6, Section 4, students prove the segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length. • S-ID.7: In Algebra 1, Chapter 4, Section 5, students use technology to find an equation for a line of best fit modeling the grade point averages and number of hours spent watching television each week for several students. Students interpret the slope and y-intercept of the equation for the line of best fit. In Algebra 2, Chapter 1, Section 3, students interpret the slope and y-intercept of the equation for a line of best fit modeling the number of active users on a social media site since 2009. ##### Indicator {{'1b.ii' | indicatorName}} The materials, when used as designed, allow students to fully learn each standard. The materials reviewed for Big Ideas Learning AGA partially meet expectations for, when used as designed, letting students fully learn each non-plus standard. Throughout the series, there were many instances where students had limited opportunities to demonstrate the full intent of the non-plus standards. Examples from the Student Edition (unless otherwise noted) of non-plus standards which would not be fully learned by students include, but are not limited to: • N-Q.3: In Algebra 1, Chapter 1, Section 4, students explain how rounding affects the accuracy of an estimation. Within the same lesson, students explain how the unit of measure can affect accuracy of a measurement. The materials emphasize choosing a level of accuracy appropriate to limitation on measurement when reporting quantities within Algebra 1, Chapter 1, Section 4. Choosing a level of accuracy should be throughout the series; therefore, there are limited opportunities to choose a level of accuracy. • A-SSE.4: In Algebra 2, Chapter 11, Section 3, the materials derive the formula for the sum of a finite geometric series. Within the same lesson, students use the formula to solve problems. Students are not given the opportunity to derive the formula for the sum of a finite geometric series. • A-REI.10: In Algebra 1, Chapter 3, Section 3, the materials provide a definition for the solution of a linear equation in two variables. Within the same lesson, students explain why a line is formed when graphing a linear equation. Students are not given the opportunity to develop the understanding that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. • F-LE.5: In Algebra 1, Chapter 3, Section 6, students interpret the slope of a linear graph representing the distance a bus travels over time. Within the same lesson, students interpret the meaning of the terms and coefficients in a linear function representing the height of a paraglider. Students also interpret the meaning of the terms and coefficients in a linear function representing the depth of snow on the ground. In Algebra 1, Chapter 4, Section 4 and Section 5, students interpret slopes and y-intercepts in linear regression models. The materials do not explicitly ask students to interpret the parameters of exponential functions in terms of context. Instead, interpretations are embedded in a limited amount of problems. For instance, in Algebra 1, Chapter 6, Section 4, students are given a table representing the number of views of an online video over time. Students predict the number of views after 7 days. • F-TF.1: In Algebra 2, Chapter 10, Section 2, Explore It, students complete an exploration task to demonstrate understanding of radian measure. Students' opportunities to understand radian measure from an angle is limited to the Explore It task. • F-TF.5: In Algebra 2, Chapter 10, Section 6, Explore It, students choose a trigonometric function representing the height of a ferris wheel after two full cycles. Students have limited opportunities to choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. • G-CO.13: In Geometry, Chapter 10, Section 4, students construct an equilateral triangle and a regular hexagon inscribed in a circle. The materials provide an example of constructing a square inscribed in a circle. Students are provided no opportunities to construct a square inscribed in a circle. • G-GMD.1: In Geometry, Chapter 11, Section 1, the materials provide the formula for the circumference of a circle. Students are not provided an opportunity to make an informal argument for the formula of the circumference of a circle. In Geometry, Chapter 11, Section 2, the materials provide an informal argument for the formula of the area of a circle but do not allow students to make an informal argument. In Geometry, Chapter 12, Section 2, Explore It, students calculate the volume of a deck of cards. Students consider what occurs to the volume of the deck of cards before and after it is twisted. Then, students determine how to find the volume of a prism or cylinder. Within the same section, students use Cavalieri’s Principle to calculate volume. In Geometry, Chapter 12, Section 3, Explore It, students give an informal argument for the formula of the pyramid. In Chapter 12, Section 4, Explore It, students give an informal argument for the cone. Examples from the Student Edition (unless otherwise noted) of how the materials allow students to fully learn the non-plus standards include: • N-RN.2: In Algebra 1, Chapter 6, Section 2, students rewrite and evaluate expressions involving radicals and rational exponents. In Algebra 2, Chapter 5, Section 1, students rewrite expressions involving radicals and rational exponents using the properties of exponents. In Algebra 2, Teacher Edition, Chapter 5, Section 1, Launch the Lesson, students discuss how the properties of exponents can be applied to simplifying expressions with rational exponents. • A-APR.1: In Algebra 1, Chapter 7, Section 1, Explore It, students use Algebra tiles to find the sum and difference of polynomials. Students determine if polynomials are closed under the operations of addition and subtraction. In Algebra 1, Chapter 7, Section 1, students add and subtract polynomials. In Algebra 1, Chapter 7, Section 2, Explore It, students determine if polynomials are closed under multiplication. In Algebra 1, Chapter 7, Section 2, students multiply polynomials. In Algebra 2, Chapter 4, Section 2, students explain why polynomials are closed under the operations of addition and subtraction. Within the same lesson, students add, subtract, and multiply polynomials. • F-IF.7b: In Algebra 1, Chapter 3, Section 8, students graph absolute value functions. In Algebra 1, Chapter 4, Section 7, students graph piecewise and step functions. In Algebra 1, Chapter 10, Section 1, students graph square root functions. In Algebra 1, Chapter 10, Section 2, students graph cube root functions. • G-C.3: In Geometry, Chapter 6, Section 2, students construct circumscribed circles of a right triangle, an obtuse triangle, an acute isosceles triangle, and an equilateral triangle. Within the same lesson, students construct inscribed circles of triangles. In Geometry, Chapter 10, Section 4, students copy and complete a paragraph proof proving the Inscribed Quadrilateral Theorem. • S-ID.5: In Algebra 1, Chapter 11, Section 4, students find and interpret marginal frequencies. Within the same lesson, students summarize categorical data for two categories in two-way frequency tables and interpret marginal frequencies. Students also find joint, marginal, and conditional frequencies from two-way tables. In Geometry, Chapter 13, Section 2, students interpret join relative frequencies and marginal relative frequencies. ##### Indicator {{'1c' | indicatorName}} The materials require students to engage in mathematics at a level of sophistication appropriate to high school. The materials reviewed for Big Ideas Learning AGA partially meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The materials regularly use age appropriate contexts and apply key takeaways from grades 6-8, yet do not vary the types of real numbers being used. Examples where materials regularly use age appropriate contexts include: • In Algebra 1, Chapter 1, Section 4, students measure an object in their classroom or at their home. Students must measure using two different tools and two different units of measurement. Students must determine if one measurement is more accurate than the other. Then, students calculate the perimeter and area of their classroom using obtained measurements of the floor. • In Geometry, Chapter 12, Section 2, students are given an illustration containing the dimensions of two boxes of cereal. Students determine which box of cereal is a better buy. • In Algebra 2, Chapter 5, Section 6, students are given a scenario where they have a coupon for$10 off an entire purchase and a coupon for 20% off an entire purchase. Students use a composition of functions to determine the order in which they must use the coupons to get a lesser total.

Examples where materials apply key takeaways from Grades 6-8 include:

• In Algebra 1, Chapter 5, Section 7, students apply key takeaways to determine whether the inverse of a linear, quadratic, cubic, square root, and rational function is a function (8.F.1).

• In Geometry, Chapter 8, Section 1, students analyze proportional relations to calculate side lengths, perimeters, or areas of two similar figures (7.RP.A).

• In Algebra 2, Chapter 7, Section 4, Explore It, students apply key takeaways of adding and subtracting numerical rational expressions before adding and subtracting rational expressions with variables (7.NS.1 and 7.NS.2).

Examples where materials do not vary the types of real numbers being used include, but are not limited to:

• In Algebra 1, Chapter 2, Section 5, students solve two-sided linear equations. The six exercises with non-integer values include inequalities with coefficient values of $${{\frac {2} {3}}}$$, $${{\frac {3} {4}}}$$, 2.5, and $${{\frac {1} {2}}}$$. Students do not have opportunities to compute with more complex non-integer values.

• In Geometry, Chapter 1, Section 3, students calculate distance and midpoint from a set of coordinates. All of the coordinates given consist of integer values.

• In Geometry, Chapter 5, Section 8, students use coordinates to write coordinate proofs. All of the coordinates given are integer values and the solutions consist of mainly integers.

• In Algebra 2, Chapter 1, Section 4, students solve a system of linear equations with three unknown values. Within the practice exercises, the linear equations consist of mostly integers. There are three instances where students have a solution with a non-integer value.

• In Algebra 2, Chapter 3, Section 1, students solve quadratic equations by graphing, using square roots, and factoring. Throughout the section, the quadratic equations have primarily integer coefficients. The solutions are also primarily integers with few rational or irrational solutions.

##### Indicator {{'1d' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards. The materials foster coherence through meaningful mathematical connections in a single course and throughout the series.

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

• In Algebra 1, Chapter 3, Section 1 and Section 4, students develop a formal definition for functions (F-IF.1). In Algebra 1, Chapter 8, Section 1, students build on their understanding of functions to interpret key features of graphs and tables representing functions (F-IF.4).

• In Geometry, Chapter 8, Section 2, students develop the Angle-Angle criterion to prove triangles are similar (G-SRT.3). In Geometry, Chapter 9, Section 4 and Section 5, students build upon similar triangles by establishing that side ratios in right triangles are properties of the angles in the triangle leading to the definitions of trigonometric ratios (G-SRT.6).

• In Algebra 2, Chapter 4, Section 4, students use the structure of polynomials to rewrite the polynomial in factored form (A-SSE.2). In Algebra 2, Chapter 6, Section 5, students use the structure of logarithmic functions to rewrite the functions (A-SSE.2). In Algebra 2, Chapter 11, Section 3 and Section 4, students build on their understanding of rewriting expressions to develop the formula for the sum of a finite geometric series (A-SSE.4).

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

• In Algebra 1, Chapter 7, Lesson 4, students calculate the solutions of polynomials. Within the same lesson students calculate roots of quadratic equations and explain the meaning of the solutions. In Algebra 1, Chapter 9, Lesson 5, students write quadratic equations with no real solutions (A-REI.4b). In Algebra 2, Chapter 3, Lesson 3, students solve quadratic equations by using square roots, completing the square, or factoring (N-CN.7). In Algebra 2, Chapter 3, Lesson 3, students’ build upon understanding of solving quadratic equations with real and complex roots by writing functions in vertex form to identify characteristics of the function (F-IF.8).

• In Algebra 1, Chapter 1, Section 1, students explain steps for solving one-step linear equations. In Algebra 1, Chapter 1, Section 2, students explain steps for solving multi-step equations. In Algebra 1, Chapter 1, Section 5, students explain steps for solving linear equations with variables on two sides. In Geometry, Chapter 2, Section 4, students explain steps for solving linear equations. In Algebra 2, Chapter 5, Section 4, students explain steps for solving radical equations (A-REI.1).

• In Algebra 1, Chapter 3, Section 6, and in Chapter 8, Section 1, students interpret key features of functions (F-IF.4). In Algebra 2, Chapter 2, Section 1 through Section 3, students build on functions by graphing polynomial functions (F-IF.7c). Finally, in Algebra 2, Chapter 2, Section 4, students calculate the average rate of change in polynomial functions (F-IF.6).

##### Indicator {{'1e' | indicatorName}}
The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.

The materials reviewed for Big Ideas Learning AGA meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. Throughout the series, the materials provide a Chapter Progression chart located at the beginning of each chapter in the Teaching Edition. The “Coherence Through the Grades” chart provides identification of prior learning from middle school, current learning within the chapter, and connections to future learning. The online Teacher Edition materials contain the standards for prior learning, current learning, and future learning while the physical Teacher Edition materials do not contain the standard name.

Examples where the materials make connections between grades 6-8 and high school concepts and allow students to extend their previous knowledge include:

• In middle school, students analyze and solve pairs of simultaneous linear equations (8.EE.8). In Algebra 1, Chapter 5, Section 1 through Section 5, students solve systems of linear equations both graphically and algebraically (A-REI.6). In Algebra 1, Chapter 5, Section 5, students use properties of equality to prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other equation produces a system with the same solution (A-REI.5).

• Students build upon their knowledge of properties of integer (8.EE.1) exponents when writing equivalent expressions involving integer exponents. In Algebra 1, Chapter 6, Section 1, students use properties of integer exponents and begin writing expressions with rational exponents as radical expression (N-RN.2). In Algebra 2, Chapter 5, Section 1 and Section 2, students extend their knowledge of properties of integer exponents to include rational exponents (N-RN.1).

• In Geometry, Chapter 3, Section 2, students prove relationships between pairs of angles formed when parallel lines are cut by a transversal (G-CO.9) which extends their knowledge of the angles created when parallel lines are cut by a transversal (8.G.5).

##### Indicator {{'1f' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA use the plus standards to coherently support the mathematics which all students should study in order to be college and career ready. In some instances, the plus standards are fully addressed and coherently support the mathematics which all students should study in order to be college and career ready, but for others, the materials do not fully address the plus standards or some plus standards are not addressed at all.

The following plus standards are fully addressed within the series:

• N-CN.3: In Algebra 2, Chapter 3, Section 2, students determine the complex conjugate given a complex number.

• N-CN.8: In Algebra 2, Chapter 3, Section 2, students extend polynomial identities to the complex numbers.

• N-CN.9: In Algebra 2, Chapter 4, Section 6, students know the Fundamental Theorem of Algebra and show that it is true for quadratic polynomials.

• N-VM.6: In Algebra 2, Chapter 12, Section 1, students use matrices to represent and manipulate data of real-life problems.

• N-VM.7: In Algebra 2, Chapter 12, Section 1, students multiply matrices by scalars to produce new matrices.

• N-VM.8: In Algebra 2, Chapter 12, Section 1, students add, subtract and multiply matrices.

• N-VM.9: In Algebra 2, Chapter 12, Section 2, students show that matrix multiplication for square matrices is not a commutative operation. Within the same lesson, the materials state that matrix multiplication for square matrices still satisfies the associative and distributive properties.

• N-VM.10: In Algebra 2, Chapter 12, Section 4, the materials define the identity matrix. Within the same section, students understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 1 in the real numbers. Students also give an example of a matrix that does not have an inverse.

• N-VM.12: In Algebra 2, Chapter 12, Section 3, Explore It, students work with 2 x 2 matrices to interpret the absolute value of the determinant in terms of area.

• A-APR.5: In Algebra 2, Chapter 4, Section 2, students use Pascal’s Triangle to expand binomials.

• A-APR.7: In Algebra 2, Chapter 7, Section 3, Explore It, students determine if rational expressions are closed under multiplication and division. In Algebra 2, Chapter 7, Section 3, students multiply and divide rational expressions. In Algebra 2, Chapter 7, Section 4, Explore It, students determine if rational expressions are closed under addition and subtraction. In Algebra 2, Chapter 7, Section 4, students add and subtract rational expressions.

• A-REI.8: In Algebra 2, Chapter 12, Section 4, students represent a system of linear equations as a single matrix equation in a vector variable.

• A-REI.9: In Algebra 2, Chapter 12, Section 4, Explore It, students use technology to find the inverse of a matrix. Within the same section, students solve matrix equations.

• F-BF.1c: In Algebra 2, Chapter 5, Section 6, students compose functions.

• F-BF.4b: In Algebra 2, Chapter 5, Section 7, students verify by composition that one function is the inverse of another.

• F-BF.4c: In Algebra 1, Chapter 10, Section 9, students read values of an inverse function from a graph or a table.

• F-BF.4d: In Algebra 2, Chapter 5, Section 7, the materials demonstrate how to produce an invertible function from a non-invertible function by restricting the domain.

• F-BF.5: In Algebra 2, Chapter 6, Section 3, the materials provide examples to help students understand the inverse relationship between exponents and logarithms. The examples also show how to use this relationship to solve problems involving logarithms and exponents.

• F-TF.3: In Algebra 2, Chapter 10, Section 3, students use special right triangles to determine geometrically the values of sine, cosine and tangent. Students also use the unit circle to express the values of sine, cosine, and tangent for $$x$$, $${\pi }+x$$, and $$2{\pi }+x$$.

• G-SRT.10: In Geometry, Chapter 9, Section 7, students prove the Law of Sines and use it to solve problems. Within the same section, students prove the Law of Cosines and use it to solve problems.

• G-SRT.11: In Geometry, Chapter 9, Section 7, students understand and apply the Law of Sines and the Law of Cosines to find unknown measurements.

• G-C.4: In Geometry, Chapter 10, Section 1, students construct a tangent line from a point outside a given circle to the circle.

• G-GMD.2: In Geometry, Chapter 12, Section 2, the materials give an informal argument using Cavalieri’s principle for the formulas for the volume of prisms and cylinders. In Geometry, Chapter 12, Section 5, the materials give an informal argument using Cavalieri’s principle for the volume of spheres.

• S-CP.8: In Geometry, Chapter 13, Section 4, the materials state the general Multiplication Rule but name it Probability of Dependent Events. Within the same lesson, students use the formula to calculate probability.

• S-CP.9: In Geometry, Chapter 13, Section 5, students use permutations and combinations to compute probabilities of events and solve problems.

• S-MD.1: In Geometry, Chapter 13, Section 7, students define random variables and construct a histogram displaying outcomes of random variables.

• S-MD.3: In Geometry, Chapter 13, Section 7, students develop probability models for random variables in which probabilities are theoretical.

• S-MD.4: In Geometry, Chapter 13, Section 6, the materials develop a probability model for a random variable which probabilities are assigned empirically. The materials provide a scenario where students must ask 6 randomly chosen teenagers to spend time with friends online daily. The materials provide a histogram of the distribution. Then, students interpret the binomial distribution.

• S-MD.6: In Algebra 2, Chapter 8, Section 1 through Section 5, students use probability in making fair decisions by spinning wheels and picking cards or marbles.

• S-MD.7: In Geometry, Chapter 13, Section 5, the materials provide an example of determining the accuracy of a test for diabetes. A tree diagram is then used to find all possible outcomes of having diabetes versus not having diabetes and the probabilities of those outcomes.

The following plus standards are partially addressed within the series:

• N-CN.4: In Algebra 2, Chapter 3, Section 2, students match complex numbers with a point on a rectangular plane. Students do not represent complex numbers on the complex plane in polar form.

• F-IF.7d: In Algebra 2, Chapter 7, Section 2, students graph rational functions and identify asymptotes. Students do not identify zeros or end behaviors of rational functions.

• F-TF.4: In Algebra 2, Chapter 10, Section 7, students determine which of the 6 trigonometric functions are odd and even. There is no connection to the unit circle to explain symmetry.

• F-TF.9: In Algebra 2, Chapter 10, Section 8, the materials provide the addition and subtraction formulas for sine, cosine, and tangent. However, the formulas are not proven. Within the same lesson, students use the formulas to solve problems.

• G-SRT.9: In Geometry, Chapter 9, Section 7, the formula A=12ab sin(C)is given in the materials and used to find the area. The formula is not derived.

The following plus standards are not addressed in the series:

• N-CN.5:

• N-CN.6

• N-VM.1 - 3

• N-VM.4

• N-VM.5

• N-VM.11

• G-GPE.3

• S-MD.2

• S-MD.5a

• S-MD.5b

### Rigor & Mathematical Practices

##### Gateway 2
Partially Meets Expectations

#### Criterion 2.1: Rigor

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.

The materials reviewed for Big Ideas Learning AGA meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Overall, conceptual understanding and procedural skills are developed and demonstrated by students, but students are provided limited opportunities to engage in non-routine application of mathematics.

##### Indicator {{'2a' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Many of the opportunities for conceptual understanding are in the Explore It, activities located at the beginning of every chapter. In the Teacher Edition, there are also additional opportunities for conceptual understanding given in Laurie’s Notes.

Examples across the series that develop conceptual understanding include:

• A-APR.2: In Algebra 2, Chapter 4, Section 3, Explore It, students use technology to explore the graph of $${{x}^{3}}+2{{x}^{2}}-x-2$$ divided by the binomial x+a for given values of a. Students develop conceptual understanding through making observations about the graphs and drawing conclusions about their observations.

• G-SRT.6: In Geometry, Chapter 9, Section 4, Explore It, students use technology to construct a right scalene triangle with several perpendicular segments drawn to the base of the triangle. Students use the definition of tangent to write the tangent ratios for the acute angles and then compare the values. Students generalize their finding by determining if the size of the right triangle affects the tangent values or whether the angle measure affects the tangent ratios. In Geometry, Chapter 9, Section 4, students demonstrate understanding of tangent ratios by explaining how the tangent of an acute angle in a right triangle changes as the angle measure increases.

• S-ID.6a: In Algebra 1, Chapter 4, Section 4, Explore It, students are given data from a survey of 179 married couples. Each person in the survey gave their age and the data collected was shown in a graph. Students develop conceptual understanding of linear functions suggested by the data to make observations, notice patterns in the data, and explain how patterns represent data.

Examples across the series where students independently demonstrate conceptual understanding include:

• N-RN.1: In Algebra 2, Chapter 5, Section 1, students are given the expressions $${{({{a}^{\frac {1} {n}}})}^{m}}$$, $${{({\sqrt[{n}] {a}})}^{m}}$$, $${{({\sqrt[{m}] {a}})}^{-n}}$$, and $${{a}^{\frac {m} {n}}}$$. Students must determine which expression does not belong and justify their decision.

• A-REI.12: In Algebra 1, Chapter 5, Section 7, students are given a graph of two linear equations with five plotted points. Students must replace the equal sign in the two graphed linear equations with inequality symbols such that two of the plotted points are solutions.

• G-CO.1: In Geometry, Chapter 1, Section 1, students develop conceptual understanding of parallelism by determining if parallel lines always, sometimes, or never intersect. Within the same sections, students also determine if two points always, sometimes, or never form a line.

##### Indicator {{'2b' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. Opportunities for students to independently develop procedural skills are located within the Self-Assessment exercises, the Practice exercises, the Review and Refresh exercises, and the supplemental resources.

Examples of the materials developing procedural skills and students independently demonstrating procedural skills include:

• A-SSE.2: In Algebra 2, Chapter 6, Section 1, students justify the steps needed to rewrite an exponential function. In Algebra 2, Chapter 6, Section 3, students rewrite functions in exponential and logarithmic form. In Algebra 2, Chapter 6, Section 5, students rewrite logarithmic expressions by condensing or expanding them.

• A-APR.1: In Algebra 1, Chapter 7, Section 1, students independently calculate the sum and difference of polynomials. In Algebra 1, Chapter 7, Section 2, students independently calculate products of polynomials using the Distributive Property and a table. In Algebra 1, Chapter 7, Section 3, students independently calculate the products of polynomials.

• F-BF.4a: In Algebra 2, Chapter 5, Section 7, students find inverses of linear, quadratic, cubic, square root, and cube root functions.

• G-GPE.4: In Geometry, Chapter 5, Section 8, students write coordinate proofs to prove geometric theorems. In Geometry, Chapter 10, Section 7, students use coordinates to prove or disprove whether a coordinate lies on a circle.

##### Indicator {{'2c' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA partially meets expectations that the materials support the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially when called for in specific content standards or clusters. Most sections within the series have “Modeling Real Life” exercises where students independently engage in routine application problems, but the materials have missed opportunities for students to engage in non-routine application of mathematics.

Examples that show missed opportunities for students to engage in non-routine application of mathematics throughout the series include, but are not limited to:

• A-CED.3: In Algebra 1, Chapter 5, Section 6, students are given the weight of two large boxes and three small boxes as well as the weight of one large box and four small boxes. Students are asked to write and graph an inequality representing the amount of large and small boxes a 200 pound person can carry in an elevator with a 2000 pound weight limit. Students are instructed how to solve the problem using a similar mathematical procedure that is found within the section.

• A-REI.4: In Algebra 2, Chapter 3, Section 3, students are given the equation y^2+10y+20x-15=0. Students are instructed to write the equation in standard form and identify the vertex, focus, and directrix. Students are not engaging in non-routine application, since they are being instructed what to do.

• F-IF.6: In Algebra 1, Chapter 10, Section 2, students are instructed to write a cube root function given that it passes through the point (3, 4), and has an average rate of change of -1 over the interval of x= -5 to x=2. Within the same section students are given an example showing how to compare the average rate of change of a cubic function graphed and a cubic function. During the solution steps of the example, students are shown how to calculate the rate of change of a cubic function over a given interval.

• F-IF.7a: In Algebra 2, Chapter 2, Section 2, the materials provide an example with a graph modeling the path of a golf ball and an equation modeling the path of a second golf ball. In the example, students determine which shot travelled higher and which shot travelled farther before hitting the ground. Within the same sections, students are given a verbal description of a kicker soccer ball and an equation modeling the path of a second kicked soccer ball. Students determine which ball travelled high and which ball traveled farther before hitting the ground.

• G-SRT.8: In Geometry, Chapter 9, Section 5, the materials provide an example where students use trigonometric ratios to calculate the distance from a base of a mountain to the student. The example provides a visual of the mountain and the pertinent information needed to calculate the distance. Within the same section, students independently use the visual given in the example to calculate the distance from the base of the mountain to the student given a new angle of depression.

• G-GMD.3: In Geometry, Chapter 12, Section 5, students research the amount of propane needed to heat their current residence in a year. Students are given a model of a propane tank with a height of 37.5 inches and a width of 9 feet 11 inches. Students must calculate the volume of the propane tank to determine how often the tank will need to be refilled. Although there is some research involved where students need to calculate the amount of propane needed to heat their residence, the calculation of the volume is routine.

##### Indicator {{'2d' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA meet expectations that 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. The Explore It sections contain multiple aspects of rigor to develop students’ mathematical understanding while the independent practice sections are mainly procedural with a balance between conceptual understanding and application throughout the section.

Application problems are presented throughout the materials in the Explore Its, Independent Practice, and Self-Assessments. Examples of procedural skills and conceptual understanding being presented independently throughout the materials include:

• In Algebra 1, Chapter 7, Section 5, students develop procedural skills by factoring polynomials and solving polynomials by factoring (A-SSE.3a).

• In Algebra 2, Chapter 4, Section 1, Explore It, students develop conceptual understanding by identifying functions that are polynomials, graphing the polynomials, describing end behaviors, and determining the effects of exponents and leading coefficients. Students compare two graphs to determine if the graphs are cubic or quartic. Conceptual understanding is also developed when students generalize characteristics of cubic functions and quartic functions (F-IF.7c).

Examples of multiple aspects of rigor being engaged simultaneously to develop students mathematical understanding of a single topic of study throughout the materials include:

• In Algebra 1, Chapter 8, Section 6, Explore it, students develop conceptual understanding through an application problem involving three cars traveling at the same time at different speeds. Students develop conceptual understanding by determining which car has a constant speed and which car has the greatest acceleration (F-LE.3).

• In Geometry, Chapter 9, Section 6, Explore it, students develop procedural skills by calculating measure of an angle when given a trigonometric ratio. Students demonstrate conceptual understanding by explaining how technology can verify angle measures and explaining how to calculate the measures of two acute angles when given side lengths. Within the same section, students use procedural knowledge of trigonometry to calculate the acute angles in a right triangle created by leaning a firefighter ladder against a building (G-SRT.8).

• In Algebra 2, Chapter 8, Section 3, Explore it, students develop procedural skills by determining different probabilities involving six pieces of paper numbered 1 through 6. Students develop conceptual understanding by comparing and contrasting the probabilities found. Within the same section students are given two events. Event A is the probability of the first number being divisible by 3 and Event B is the probability of the second number being greater than 2. Students calculate P(B|A), P(A and B), and P(A). Students develop conceptual understanding by using the previous probabilities to generalize a formula for P(B|A) in terms of P(A and B)and P(A) (S-CP.6).

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

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

##### Indicator {{'2e' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA partially meet expectations that the materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards. Although the materials use MP6 to enrich the mathematical content, there are many examples of misleading identifications of MP1.

Examples of misleading identification of MP1 include, but are not limited to:

• In Algebra 1, Chapter 6, Section 4, students calculate the approximate monthly percent increase in a population and estimate the population after 4 years given an initial population of 25,000 with an annual percent increase of 5.5%. This problem solving task prompts you to look at Example 6 since both tasks are similar, therefore students will not have to make sense of the problem to determine that they can replicate the problem-solving method from Example 6.

• In Algebra 1, Chapter 11, Section 4, students are given expressions to represent the amount of child and adult tickets sold for both the main floor and a balcony. Students are then asked to find what percent of tickets are adult tickets and what percent of child tickets are balcony tickets. Since this problem is in a section about making two-way tables, students will not have to make sense of the problem to determine that a two-way table can be used as an entry point to the solution.

• In Geometry, Chapter 4, Section 6, students have to determine whether the composition of rotations and dilations preserve the commutative property. The students will not need to persevere as these properties of rotations and dilations have already been explored in 8th grade mathematics.

• In Geometry, Chapter 13, Section 3, students are given a table to determine if a company should change the recipe of a snack, based on whether the consumer market will change very little or expand very rapidly. Similar examples are presented throughout the section where students have to find conditional probability and use conditional probability to make a decision. Students will not need to make sense of the problem to determine that the probability models from this section will allow them to solve this task.

• In Algebra 2, Chapter 6, Section 1, students are given a formula that predicts the eggs a chicken can produce given its age in weeks. Similar problems are completed in this section so students do not need to make sense of the problem to look for entry points to the solution.

• In Algebra 2, Chapter 7, Section 4, students determine the time it would take to finish a race given a table showing rates of swimming, biking, and running. This task does not allow students to persevere in the grade level math because students can substitute the given value from the question into the expressions given. This will allow them to find the total time it takes to complete the race without having to persevere to solve this problem.

Examples where MP6 is used to enrich the mathematical content includes:

• In Algebra 1, Chapter 11, Section 3, students describe why the mean is used to describe the center and the standard deviation is used to describe variation for a symmetric data set. Students also describe why the median is used to describe the center and the 5 number summary is used to describe the variation for a skewed data set.

• In Geometry, Teacher Edition, Chapter 1, Section 4, the materials include an example explaining how to calculate the perimeter of a triangle in a coordinate plane. The distance formula is used to find the lengths of two sides and lengths are expressed as radicals. After finding the perimeter, the final solution is a decimal. Laurie's notes extends the example by having students discuss the difference between leaving the answer as an exact answer using radicals versus an approximation using decimals.

• In Algebra 2, Chapter 8, Section 1, Explore It, students describe possible outcomes of different experiments. Students must then understand mathematical terms by discussing the difference between an event being impossible and an event being certain.

##### Indicator {{'2f' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA meet expectations for supporting the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. The majority of the time MP2 and MP3 are used to enrich the mathematical content and are intentionally developed to reach the full intent of the MPs.

Examples of MP2 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

• Algebra 1, Chapter 3, Section 5, Example 3 provides the equation 6x+10y=180 to model the number of people that can sit at a small table and a large table at a banquet for 180 people. The material include a Mathematical Practice box asking students what the terms 6x and 10y represent in this context. Students are attending to the meaning of quantities.

• In Geometry, Chapter 4, Section 3, students determine the coordinates of two endpoints after rotation 630 degrees and 900 degrees about the origin. Students reason abstractly to determine the new coordinate for the endpoints.

• In Algebra 2, Chapter 5, Section 7, students are given the ordered pairs (-2, 5), (0, 1), (3, -6), and (7, n) and are told a function passes through the points. Students find values of n so that the inverse is a function and must explain their reasoning.

Examples of MP3 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

• In Algebra 1, Chapter 7, Section 7, Exercise 41, students describe two methods use to simplify $${{(2x-5)}^{2}}-{{(x-4)}^{2}}$$. Then, students choose which of the two methods they would use to simplify the expression and provide an explanation about their choice.

• In Geometry, Teacher Edition, Chapter 7, Section 2, Laurie’s Notes, students write a proof for the Parallelogram Opposite Sides Theorem. After writing the proof, students compare and critique proofs made by other students.

• In Algebra 2, Chapter 9, Preparing for Chapter 9, students are given a table of results describing 3 different surveys used to determine if people would like more funding to monitor volcanic activity. Students collaborate with a partner to explain confidence levels in the conclusions of the results. Finally, students must write a survey question and sample to use for a valid conclusion.

##### Indicator {{'2g' | indicatorName}}
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.

The instructional materials for Big Ideas Learning AGA partially meet expectations that the materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. Although the materials use MP5 to enrich the mathematical content, materials do not develop the full intent of MP4.

Examples where the full intent of MP4 is not developed include, but are not limited to:

• In Algebra 1, Chapter 5, Section 1, students determine whether two people starting at different points of a hiking trail, who are walking at different speeds will meet after one hour of hiking and also determine how much longer would it take the second finisher to complete the hiking trail than the first. Students are not able to make a conjecture because the conjecture is made for them via the friend’s suggestion. Additionally, students are not prompted to build or improve upon a model which represents the problem.

• In Algebra 1, Chapter 9, Section 5, students write an equation to model the height of a football after being kicked with a given initial height and vertical velocity. Students are instructed to use the function h=-16t^{2}+v_{0}t+s_{0} where h is the height, t is the time, v_{0} is the initial vertical velocity, and s_{0} is the initial height. Students need only substitute the given information into the given equation.

• In Geometry, Chapter 1, Section 5, students are given an image of a bird sculpture and are instructed to find the measure of the bird’s total wingspan. In the model, students are given two angles and their corresponding measures. Students subtract the two measures to find another angle. The model is provided instead of allowing students to create a model to represent the scenario.

• In Geometry, Chapter 10, Section 4, students are asked to determine the length of a line segment that shows a seam on a circular cutting board. A model of a right triangle is drawn on an image of the cutting board, so students do not need to create a model or determine a strategy to solve the task.

• In Algebra 2, Chapter 3, Section 3, students calculate the maximum height of a birdie and the amount of time it takes for the birdie to hit the ground. Students are given the model h=-16t^{2}+32t+4 where h represents height and t represents seconds after the birdie is hit.

• In Algebra 2, Chapter 6, Section 6, students calculate the diameter of a telescope lens revealing stars with an apparent magnitude of 12. Students are given M=5logD+2 where M represents magnitude and D represents diameter.

• In Algebra 2, Chapter 10, Section 6, students are tasked with volunteering to clean a beach at a large body of water 3 days from now. Students are told that the best time to do this is low tide. Students have to find the accurate times and depths of low and high tides on a recent day at a location of their choice by researching. Then they are instructed to write a sinusoidal model using this data. Students do not need to determine a representation or strategy as it is given to them.

Examples where MP5 is used to enrich the mathematical content includes:

• In Algebra 1, Chapter 7, Section 6, Explore It, students use algebra tiles to factor polynomials that do not have a leading coefficient of 1. Students are given an algebra tile model. Students then write the polynomial represented by the algebra tiles and write the polynomial in factored form. Students must also describe a strategy to factor a trinomial that does not use algebra tiles. Students are also asked, “Why might algebra tiles be an inefficient way to factor polynomials involving greater numbers, such as 2x^{2}+47x+23?” This reminds students about the limitation of using algebra tiles as a tool.

• In Geometry, Chapter 6, Section 1, Explore It, students use technology to explore the distances between any point on a perpendicular bisector and the distances between any point on the angle bisector and the sides of the angle. Students choose which technology tools to utilize to explore the relationships.

• In Algebra 2, Chapter 4, Section 1, students are given the following scenario: “Your friend uses technology to graph f(x)=(x-1)(x-2)(x+12) in the viewing window -10\leq x\leq10,-10\leq y\leq10, and says the graph is a parabola.” Students use technology to verify the friend’s assumption while detecting errors that can occur when utilizing technology.

##### Indicator {{'2h' | indicatorName}}
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.

The materials reviewed for Big Ideas Learning AGA meet expectations for supporting the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. The majority of the time MP7 and MP8 are used to enrich the mathematical content and are intentionally developed to reach the full intent of the MPs.

Examples of MP7 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

• In Algebra 1, Chapter 11, Section 2, Explore It, students interpret two box-and-whisker plots. One box-and-whisker plot represents the body mass of a ninth-grade class and the other represents the height of roller coasters. Students are asked to determine what the box and length represent and what the whiskers and its length represent within the context of the data.

• In Geometry, Chapter 7, Section 5, students use their understanding of the structure of trapezoids and mid-segments to write an equation and calculate the value of x.

• In Algebra 2, Chapter 1, Section 1, students are given the functions f(x)=|x-4| and g(x)=|x|-4. Students attend to structure by determining if the two functions are the same.

Examples of MP8 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

• In Algebra 1, Chapter 6, Section 1, Explore It, students explore properties of exponent by choosing several values for variables to find a pattern for exponent properties. Students find patterns in order to generalize rules for the properties.

• In Geometry, Chapter 13, Section 6, students complete a table calculating nPr and nCr when n=3and r=0,1,2,3. Students generalize their finding to write an inequality relating nPr and nCr for any value.

• In Algebra 2, Chapter 6, Preparing for Chapter 6, students are given a table representing the percentage of carbon-14 remaining after the death of an organism. Students must analyze the table to determine if calculations are repeated. Then, students write an equation using y to represent the amount of carbon-14 and t to represent years after death based on patterns discovered within the table.

### Usability

Not Rated

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
##### Indicator {{'3a' | indicatorName}}
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.
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
##### Indicator {{'3c' | indicatorName}}
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.
##### Indicator {{'3d' | indicatorName}}
Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
##### Indicator {{'3g' | indicatorName}}
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.
##### Indicator {{'3h' | indicatorName}}
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.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
##### Indicator {{'3j' | indicatorName}}
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).
##### Indicator {{'3k' | indicatorName}}
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.
##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
##### Indicator {{'3n' | indicatorName}}
Materials provide support for teachers to identify and address common student errors and misconceptions.
##### Indicator {{'3o' | indicatorName}}
Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
##### Indicator {{'3r' | indicatorName}}
Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
##### Indicator {{'3u' | indicatorName}}
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).
##### Indicator {{'3v' | indicatorName}}
Materials provide support for advanced students to investigate mathematics content at greater depth.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

#### Criterion 3.5: Technology Use

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
##### Indicator {{'3aa' | indicatorName}}
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.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners.
##### Indicator {{'3ac.i' | indicatorName}}
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
##### Indicator {{'3ac.ii' | indicatorName}}
Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
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.).
##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

## Report Overview

### Summary of Alignment & Usability for Big Ideas Learning AGA | Math

#### Math High School

The materials reviewed for Big Ideas Learning AGA partially meet expectations for alignment to the CCSSM for high school. For focus and coherence, the series showed strengths in the following areas: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites, making meaningful connections in a single course and throughout the series, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. For rigor and the mathematical practices, the series showed strengths in the following areas: supporting the intentional development of students' conceptual understanding, opportunities for students to develop procedural skills, displaying a balance among the three aspects of rigor, supporting the intentional development of reasoning and explaining, and supporting the intentional development of seeing structure and generalizing.

##### High School
###### Alignment
Partially Meets Expectations
Not Rated

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###### Usability
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