Alignment: Overall Summary

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The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for alignment to the CCSSM for high school, Gateways 1 and 2. In Gateway 1, the instructional materials meet the expectations for focus and coherence by being 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). In Gateway 2, the instructional materials meet the expectations for rigor and balance by reflecting the balances in the Standards and helping students meet the Standards' rigorous expectations, and the materials meet the expectations for mathematical practice-content connections by meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice.

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Gateway 1:

Focus & Coherence

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

Gateway 2:

Rigor & Mathematical Practices

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

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Gateway 3:

Usability

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

Focus & Coherence

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).
18/18
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Criterion Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for focus and coherence. The instructional materials: attend to the full intent of the mathematical content contained in the high school standards for all students; attend to the full intent of the modeling process when applied to the modeling standards; spend the majority of time on the CCSSM widely applicable as prerequisites; let students fully learn each non-plus standard; engage students in mathematics at a level of sophistication appropriate to high school; make meaningful connections in a single course and throughout the series; and identify and build on knowledge from Grades 6-8 to the High School Standards.

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.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. The instructional materials address all aspects of all non-plus standards across the courses of the series.

Some examples of non-plus standards that were addressed by the series include:

• N-CN.1: In Algebra 2, Unit 3, Lesson 10, students begin to develop an understanding of the imaginary unit. In Lesson 11, students evaluate expressions that result in imaginary numbers and plot those imaginary numbers on a coordinate plane. In Activity 11.4, students develop a complex number using a coordinate plane with a real number axis and an imaginary axis.
• N-RN.2: In Algebra 2, Unit 4, Lessons 3 and 4, students engage with rational exponents. During Lesson 3, students make sense of numbers and use technology to investigate how rational exponents affect the bases. Students rewrite rational exponents as radical expressions. In Lesson 4, students use rational exponents and the properties of exponents learned from integer exponents. In Activity 4.2 Students explain why $$(5^{\frac{1}{3}})^2$$ is equivalent to $$(5^2)^\frac{1}{3}$$. Students then rewrite both of the terms as radicals.
• A-REI.4a: In Algebra 1, Unit 7, Lesson 12, students solve quadratic equations by completing the square. In the opener, students make an argument of why $$x^2+10x+20$$ is not a perfect square. The teacher notes explain the reason $$\sqrt20$$ is not an option. In the lesson, students complete a table that starts with factoring and work backward from factored to polynomial form, allowing students to use the work at the top of the table to inform their work at the bottom. Students use two examples to solve equations by completing the square. Students compare and contrast the methods and solve several equations themselves. Later, in Lesson 19, students complete and examine the steps of deriving the quadratic formula. Students discuss the steps to understand how the quadratic formula relates to completing the square.
• F-IF.7a: In Algebra 1, Unit 6, Lesson 6, students graph quadratic functions that represent physical phenomenon, interpret key features of the graph in the real-world context given in the problem, and write and interpret quadratic functions that represent physical phenomenon. The teacher notes say: “Students use a linear model to describe the height of an object that is launched directly upward at a constant speed. Because of the influence of gravity, however, the object will not continue to travel at a constant rate (eventually it will stop going higher and will start falling), so the model will have to be adjusted (MP4). They notice that this phenomenon can be represented with a quadratic function, and that adding a squared term to the linear term seems to “bend” the graph and change its direction.” After guided exploration, the students answer the question: “Why do you think the graph that represents $$d=10+46t$$ changes from a straight line to a curve when $$-16t^2$$ is added to the equation?” Through the guided exploration using technology, students interpret different parts of the function, the vertex of the graph of the function, and the zeros of the function.
• G-GPE.1: In Geometry, Unit 6, Lesson 4, the three activities support students in deriving the equation of a circle given the center and radius using the Pythagorean Theorem. Students use the Pythagorean Theorem to calculate segment length, test whether a point is on a circle, and apply that perspective to build the general equation of a circle. The three activities in Geometry, Unit 6, Lesson 6, also support students in completing the square to find the center and radius of a circle. Students complete perfect square trinomials, analyze a demonstration of completing the square, and complete the square to find the center and radius of a circle.
• G-CO.9: In Geometry, Unit 1, there are three lessons that address this standard. In Lesson 19, students critique a conjecture which states that an angle formed between angle bisectors is always a right angle. Students proceed to develop their own conjecture about vertical angles, which leads to the proof that vertical angles are congruent. In Lesson 20, students translate and rotate one of two intersecting lines to produce parallel lines cut by a transversal, and they prove theorems related to the angles formed by parallel lines cut by a transversal. In Lesson 21, the Triangle Sum Theorem is proven in two different ways using transformations.
• S-ID.4: In Algebra 2, Unit 7, Lesson 6, students find the area under a curve and connect this concept to using the mean and standard deviation to describe the proportion of the data in an approximately normal distribution. In Algebra 2, Unit 7, Lesson 7, students use the area under a normal curve to find the proportion of values in certain intervals and have the option to extend their learning by finding an interval that fits a certain percentage of the data.
• S-ID.9: In Algebra 1, Unit 3, Lesson 9, Activity 2, students distinguish between correlation and causation given different situations. Students look for relationships between the scatterplots and the words and have a discussion about causation and correlation. In Lesson 9, Activity 3, students describe situations that exhibit varying degrees of causal relationships. Students determine if situations have a very weak (or no) relationship, a strong relationship that is not causal, or a causal relationship.

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The instructional materials use the full intent of the modeling process to address nearly all of the modeling standards across the courses of the series.

Each course in the series provides modeling prompts in the teacher materials, which are separate from the units and lessons. The modeling prompts include multiple versions of a task, sample solutions, and instructions for the teacher around implementing the modeling task in the classroom. There is also guidance provided about the best time to use each prompt (e.g., “Use after Unit 4, Lesson 8”). The second task statement for each prompt typically provides some scaffolding and removes some obstacles that might prevent all students from accessing the material in the first task statement. Students engage in parts of the modeling process with the alternate prompts throughout the series.

Examples where the full intent of the modeling process is used to address modeling standards across the courses of the series include:

• In Algebra 1, Modeling Prompt 5, “Giving Bonuses” (N-Q), students determine how bonuses should be distributed among the five workers who worked on a project. Students create a proposal with at least two different methods to distribute the bonuses (formulate) to present to their boss along with a recommendation for a specific method with an argument in support of the recommended method. Students compute each employee’s bonus (compute) and provide advantages and disadvantages for each method proposed (interpret). Students also discuss which of the five employees would be most likely to complain about each method and how they would justify the method to the employee (validate).
• In Algebra 1, Modeling Prompt 9, “Planning a Concert” (A-CED.2, A-REI.4, N-Q), students propose a cost for concert tickets based on provided survey data (formulate/compute). Students consider the cost of the band, the cost of a venue, and revenue that might be generated through the sale of concessions and merchandise and how these aspects impact the cost of a ticket (interpret/compute). The students create and present a plan that includes information about the cost and the profit based on information about the venue, expenses, and ticket prices (validate/report).
• In Geometry, Modeling Prompt 8, “A New Container” (G-GMD.3, G-MG.1,3), students design a new container that must hold a volume of 16 fluid ounces. Students use any three-dimensional shape or a combination of shapes (formulate) to create a design that is appealing and meets the criteria for volume. They provide a model or prototype of their container and the calculations that prove that the container will hold 16 fluid ounces (compute/interpret/validate). The students present their designs and defend their mathematics to others (reporting). Each student/group is able to have different shapes/designs, but all presentations are considered valid if the criteria have been met.
• In Geometry, Modeling Prompt 7, “So Many Flags” (G-MG.1,3, G-SRT.8), students create a flag for Nepal, of any size, using provided instructions about its construction. Students decide the sizes of large and small flags for a parade of flags (formulate). Students compute the measure of each of the angles in the flag they have constructed, the amount of material needed to create the flags, and the amount of ribbon needed to sew ribbon along the border of each flag.
• In Algebra 2, Modeling Prompt 4, “How Big Is That?” (A-CED.A, G-GMD.3, G-MG, N-Q), students write part of a children’s book that compares the sizes of different animals by relating their size to other objects that might be familiar (formulate). Students determine how they will scale the objects to communicate the different sizes of the objects being compared and how they will scale the smaller object in order to make an appropriate comparison (compute/interpret/validate). Students present a portion of their book as well as the relevant mathematics to justify their work (validate/report). Each student/group has a choice in what they are going to compare. All results are considered valid if there is evidence that students completed the task based on the criteria.
• In Algebra 2, Modeling Prompt 6, “Swing Time” (N-Q.2,3, S-ID.6) students formulate conjectures about variables that might affect the period of a pendulum and validate their conjectures by collecting data and determining if the data makes sense in the problem. Students formulate models to demonstrate the relationship between the identified variable and period of the pendulum. Students complete computations to predict different “timed” periods that cannot be performed in class. Students revisit their work and make any necessary changes after they decide how many significant digits to use. Students report their findings throughout the task by explaining and justifying their decisions.

There are also examples of modeling scenarios within the lessons. For example, in Algebra 1, Unit 2, Lesson 1 (A-CED.2), students estimate how much a pizza party would cost. Students write expressions to show how they arrived at their estimate. Students consider many factors and identify quantities in their expressions that could change on the day of the party. Students formulate expressions to represent the parameters of the pizza party, make assumptions during this process, and set constraints. Students also compute the cost of the party based on their estimates and parameters. Groups consider how the estimated costs would change if parameters changed, allowing students to interpret their results and make adjustments to their initial estimates.

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
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites 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.A: In Algebra 2, Unit 3, Lesson 3, students apply knowledge of exponential equations and rules of exponents to develop understandings of how rational exponents are related to equivalent radical expressions. In Lesson 4, students rewrite fractional exponents as a unit fraction times a whole number and rewrite the expressions using radicals, and they connect roots, rational exponents, graphs of exponential functions, and decimal approximations. In Lesson 5, students further develop their understanding to include rational exponents, rules of exponents, and graphs to make sense of negative rational exponents (N-RN.1,2). In Algebra 2, Unit 4, Lessons 4, 6, and 7, students interpret fractional inputs for exponential functions in context. They also use properties of exponents to interpret and transform expressions that represent decay, and students use fractional exponents to answer questions about amounts of radioactive isotopes in old artifacts. (N-RN.1)
• S-ID.2: In Algebra 1, Unit 1, Lesson 5, students calculate interquartile range and discuss the importance of outliers. Students also find the Mean Absolute Deviation (MAD) and use their understanding of the MAD to interpret given scenarios. Students create two different sets of six data points which could be possible locations of pennies along a meter stick that would result in a given MAD. In Lesson 11.4, students use the interquartile range and/or the MAD to compare the spread of four data sets by examining menu prices to determine the best menu based on the greatest variability in menu options relative to price. In Lesson 12, students use the MAD to develop standard deviation by learning what happens to the standard deviation (derived through technology) when specific numbers are manipulated as in the following: the lowest value is removed; the greatest value is removed; the greatest value is doubled, etc.
• A-SSE: In Algebra 1, Units 5, 6, and 7 address many of the standards in A-SSE. For example, in Algebra 1, Unit 5, Lesson 9, students recognize and discuss similarities and differences in $$x^2$$ and $$2^x$$ as the beginning of interpreting exponential functions. Students interpret different parts of the exponential function in a real-world scenario (A-SSE.1,2). In Algebra 1, Unit 6, Lesson 8, students “explain why the diagram shows that $$6(3 + 4) = 6\cdot3 + 6\cdot4$$”. Students “draw a diagram to show that 5(x + 2) = 5x + 10.” The lesson continues using structure to find equivalent quadratic expressions (A-SSE.2,3). In Algebra 2, Unit 2, Lesson 3, students are introduced to polynomial functions and use graphing technology to write polynomials given specific characteristics (A-SSE.1,2).
• F-IF: In Algebra 1, Unit 4, students interpret and use function notation, analyze and create graphs of functions, find the domain and range of functions, and find, write, and interpret inverse functions. Students extend their work with F-IF standards in Algebra 2, Unit 2, Lesson 1 as they construct an open box and calculate the volume. Students find the largest volume, write an expression, and use graphing technology to create the graph. Students use their knowledge of the key features of graphs and domain/range to create their box.
• G-SRT: In Geometry, Unit 3, Lesson 13.3, students use similarity criteria to write statements indicating why the three triangles in the picture provided are similar. Additionally, in Lesson 15.2, students complete an activity involving task and data cards while engaging in discussion about what information is needed and why it is needed to solve the problems about triangle similarity (G-SRT.5). This is prerequisite work for G-SRT.8.

Indicator 1b.ii

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for, when used as designed, letting students fully learn each non-plus standard. The instructional materials for the series, when used as designed, enable students to fully learn all of the non-plus standards. Examples of how the materials allow students to fully learn all of the non-plus standards include:

• A-REI.4a: In Algebra 1, Unit 7, students have multiple opportunities to complete the square and derive the quadratic formula. In Lesson 12, students recognize perfect square expressions and build perfect square trinomials, and students develop the rule for completing the square. In Lesson 14, students examine visual models representing the process of completing the square and use “u-substitution” to complete the square. In Lesson 15, students find irrational solutions by completing the square. In Lesson 19, completing the square is further developed as students derive the quadratic formula. In Algebra 2, Unit 3, Lesson 16, students compare different methods for solving quadratic equations, including completing the square, and determine when it might be best to use each method. Practice sets for each lesson listed provide additional problems for students to practice completing the square.
• A-APR.6: In Algebra 2, Unit 2, Lesson 12, students divide polynomials by linear factors using area models traditionally used to support the multiplication of polynomials. The activities include division that results in a remainder. In Lesson 13, students use long division to divide polynomials, and in Lesson 15, students engage with The Remainder Theorem. In Lesson 19, students apply long division to rewrite rational expressions in order to reveal the end behavior of the function.
• F-BF.2: In Algebra 2, Unit 1, over multiple lessons, opportunities for students to work with arithmetic and geometric sequences are presented. In Lesson 5, students represent sequences graphically, numerically, and in a table, and determine if a sequence is arithmetic or geometric. In Lesson 6, students match sequences with the appropriate recursive pattern and represent a given sequence recursively. In Lesson 7, students write recursive patterns/sequences and determine the terms of the sequence. In Lesson 8, students transform recursive sequences into explicitly defined sequences. In Lesson 9, students define given sequences both recursively and non-recursively. In Lesson 10, students compare arithmetic and geometric sequences in the context of real-world applications.
• F-IF.7b: In Algebra 1, Unit 4, Lesson 12, students graph piecewise functions in applications, such as cost for shipping related to weight and renting a bike for minutes used. Absolute value functions are addressed in Algebra 1, Unit 4, Lessons 13 and 14. In Lesson 13, students create a scatter plot of the absolute guessing error calculated from guesses for the number of objects in a jar. In Lesson 14, students graph absolute guessing error again for temperatures and work with the distance function (absolute value function). Students plot graphs by hand and by the use of technology. In Geometry, Unit 5, Lesson 5, students scale the area of different objects (floor area, painting area), graph the area with the scale factor, which results in a square root function, and explain the behavior of the graph. In Geometry, Unit 5, Lesson 7, students apply the same technique when scaling volume to produce the cube root function. In Geometry, Unit 5, Lesson 18, students complete a volume problem that relates the scaling of a balloon to its volume and surface area, which revisits square root and cube root functions.
• N-CN.7: In Algebra 2, Unit 3, Lessons 17, 18, and 19, students solve quadratics using the quadratic formula and by completing the square when solutions are complex. This standard is addressed in all three lessons as well as in the practice assignments. Students continue to engage in solving equations with complex solutions in practice sets throughout Algebra 2, Unit 3.
• S-ID.9: In Algebra I, Unit 3, Lesson 9, students explore the definitions of correlation and causation. Students examine real-world scenarios and make determinations as to how the data is correlated, as well as if there is a causal relationship between the variables. In Algebra I, Unit 3, Lesson 10, students have additional opportunities to consider both correlation and causation and explain their reasoning.
• G-C.2: In Geometry, Unit 6, Lesson 14, students consider a triangle that is inscribed in a semi-circle and examine the slope of the chords, relating the hypotenuse to the diameter of the circle. In Geometry, Unit 7, Lesson 1, students define chords, central angles, and inscribed angles, considering each one’s relationship to the circle as a whole. Students examine angle measures and arc measures related to central angles and inscribed angles. Students also examine chords, similar triangles that are formed by chords, and diameters. In Geometry, Unit 7, Lesson 2, students work with inscribed angles, the relationships to the intercepted arcs, and how the “rules” for finding those angle measures are related to central angles. In the practice problems, students explain or describe the difference between central angles and inscribed angles. In Geometry, Unit 7, Lesson 3, students complete problems related to radii and segments through the points of tangency and use principles of perpendicular lines to solve problems. In Geometry, Unit 7, Lesson 14, students synthesize content from previous lessons by solving problems in the context of real-world scenarios, such as pizza (circles) and flashlight beams (arcs).

Indicator 1c

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

The instructional materials reviewed for Kendall Hunt's Illustrative Mathematics Traditional series meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The materials regularly use age-appropriate contexts, use various types of real numbers, and provide opportunities for students to apply key takeaways from grades 6-8.

Examples where the materials illustrate age-appropriate contexts for high school students include:

• In Algebra 1, Unit 3, Lesson 5, students compare pounds of ice cream sold to the outside temperature and rider service prices compared to distance traveled, as they use technology to write equations of lines. (S-ID.6, S-ID.7)
• In Algebra 1, Unit 6, Lesson 7, students work with quadratic functions to describe the number of downloads of a movie and how it impacts the revenue generated. (F-BF.1, F-IF.7)
• In Geometry, Unit 3, Lesson 16, students explore similar triangles to make a bank shot in a pool game. (G-SRT.5)
• In Geometry, Unit 8, Lesson 11, students play “Rock, Paper, Scissors” and discuss how different events influence the outcome. (S-CP.6)
• In Geometry, Modeling Prompt 4, students discuss and determine their water usage daily and weekly during different tasks performed in everyday life. Students research and “describe a container that would hold the amount of water you use in a week, a month, a year, and a lifetime”. (G-GMD.3, G-MG.1, N-Q.1-3)
• In Algebra 2, Unit 4, Lesson 18 includes applications of exploring acidity and the corresponding pH scale, measuring the intensity of earthquakes, and calculating the balance in a bank account.

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

• In Algebra 1, Unit 4, Lesson 1.1, students apply their knowledge of functions (8.F.1) as they engage with contextual relationships that do and do not represent functions (F-IF.1). In Lesson 1.2, students use their understanding related to 8.F.5 as they reason graphically about the relationship between time and the distance of a dog from a post (F-IF.4).
• In Algebra 1, Unit 5, Lesson 1, students apply ratios and proportional relationships (7.RP.A) to compare examples of linear growth and exponential growth in working the Genie problem. This builds to an understanding of exponential growth (F-LE.5, F-IF.4).
• In Grade 8, students used similar triangles to explain why the slope, m, is the same between any two distinct points on a non-vertical line in the coordinate plane, and they derived the equation y = mx + b for a line intercepting the vertical axis at b (8.EE.6). In Geometry, Unit 6, Lesson 9, students develop the point-slope form of a linear equation: y - k = m(x - h). In ensuing lessons, students write equations of lines, and intercepts are not always readily available. (A-SSE.A, G-GPE.6)
• In Geometry, Unit 2, Lesson 1.2, students describe the sequence of transformations on figures in an open space instead of on a coordinate plane with exact numbers. Students apply their knowledge of rotations, reflections, and translations from Grade 8 to move figures and visualize the movements in “Are you ready for more?”.  In this activity, students draw additional line segments in the given figures to make two congruent polygons (8.G.1,1b). In Lesson 1.4, students are offered “another opportunity to practice reasoning based on corresponding parts of figures they know to be congruent”. Using a reflection of triangles that share a side, students prove that the side shared is an angle bisector.

Examples where the instructional materials use various types of real numbers include:

• In Algebra 1, Unit 5, Lesson 4, students study exponential decay, and the numbers used are $$\frac{27}{4}$$ and $$\frac{81}{8}$$. Throughout the lesson, students work with fractions, and in Lesson 5, students work with decimals as they explore how much medicine remains in a patient's bloodstream over a period of time.
• In Algebra 1, Unit 7, students work with radicals where some are rational and others are irrational. In Lesson 13.2, students complete the square with fractions and decimals as coefficients $$(x^2 +1.6x +0.63=0)$$. In Lesson 20, students add and subtract with integers, radicals, and fractions to decide if the sums will be rational or irrational.
• In Geometry, Unit 5, Lesson 18, students determine the amount of helium, in cubic feet, needed to fill balloons of different sizes. These numbers get large (~21,000), so students would need to adjust their graphing calculator windows.
• In Algebra 1, Unit 2, Lesson 5, students graph equations using large numbers (which need to be addressed through scale) and decimals. Practice Problem 5 also incorporates decimals to the hundredths place, and students consider limitations to domains as they solve application problems.
• Algebra 2, Unit 3 includes two assessments on complex numbers and rational exponents. The Check Your Readiness assessment includes integers, integer and rational bases, radical expressions, and cube roots. The End-of-Unit Assessment extends to complex numbers.

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 instructional materials reviewed for Kendall Hunt's Illustrative Mathematics Traditional series meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series.

Examples where the materials foster coherence within courses include:

• In Algebra 1, Unit 7, Lesson 20, students solve quadratic equations using a variety of methods (A-REI.4b) and defend whether or not the solutions are rational or irrational. Students investigate sums and products of rational and irrational numbers to develop general rules about the type of number the sums and products will be (N-RN.3). In Lesson 21, students determine if solutions provided for quadratic equations are rational or irrational. After completing both of these lessons, students determine if the solutions to quadratic equations are rational or irrational.
• In Geometry, Unit 6, Lessons 4.1 and 4.2, students subtract coordinates as part of a method for calculating the distance between two points, and they use the Pythagorean Theorem to test whether points are on a circle with a given center and radius (G-GPE.4). In Lesson 4.3, students apply their work to build the general equation of a circle (G-GPE.1). In Lesson 7, students apply their understanding of distances to parabolas based on the location of a focus and directrix. In the Lesson Synthesis, students compare and contrast the work completed in Lesson 7 with the work they did in Lesson 4. In Lesson 8, students build the equation for a parabola given a focus and directrix applying their understandings from previous lessons (G-GPE.2).
• In Algebra 2, Unit 5, throughout many lessons, students work with transformations of functions, both graphically and algebraically (F-BF.3). In Lesson 1, students examine a scatter plot of data for a cooling function and use the graph of the data and two given functions to determine which function best fits the data (S-ID.6a). The same data set is also presented in Lesson 7, where students describe how a given function can be translated to better fit the given data and write the function with the identified translations. The unit ends with students modeling given data by applying transformations to write functions that best fit the data.

Examples where the materials foster coherence across courses include:

• In Algebra 1, Unit 7, Lessons 12, 13, and 14, students complete the square to solve quadratic equations (A-REI.4a). In Algebra 1, Unit 7, Lessons 22 and 23, students produce equivalent forms of quadratic expressions by completing the square to reveal properties of quadratic functions (A-SSE.3). Students use the skill of completing the square again in Geometry, Unit 6, Lessons 5 and 6, to write given equations of circles in standard form and to identify the center and radius of the circle (G-GPE.1). Completing the square is used again in Algebra 2, Unit 3, Lesson 17 to solve quadratic equations that include complex solutions.
• In Geometry, Unit 5, Lesson 7, students graph cube root functions while working backwards from the volumes of original and scaled solids to calculate scale factors (F-IF.7b). Students use the graph to analyze rates of change in the scale factor for different volume inputs. Students also graph cube root functions in Algebra 2, Unit 3, Lesson 2, as they reconnect the ideas of a square root representing a side length of a square and a cube root representing an edge length of a cube.
• In Algebra 1, Unit 5, students write exponential equations and use context to compare linear and exponential models. Throughout the unit, students graph exponential functions and identify key components (F-IF.7e). In Algebra 2, Unit 4, students build on their understanding of exponential functions from Algebra 1 where students only worked with exponential functions with domains of integers. In Algebra 2, the domain is expanded to include all real numbers as students use exponential equations to model growth and decay (F-IF.4).

Indicator 1e

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

The instructional materials reviewed for Kendall Hunt's Illustrative Mathematics Traditional series meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The instructional materials explicitly identify the standards from Grades 6-8 in the teacher materials. The Design Principles of the teacher materials state that the initial lesson in a unit is designed to activate prior knowledge and provide an entry point to new concepts. The lessons are organized in such a manner that each activity has a foreword that indicates standards by category: Building On, Addressing, and Building Towards, where appropriate. This information appears routinely in the design of the teacher materials but not in the student and family materials.

Examples where the teacher materials explicitly identify content from Grades 6-8 and build on them include:

• In Algebra 1, Unit 1, Lesson 1, the Lesson Narrative of the preparation indicates that the work of the lesson builds on 6.SP.1, although there is no specific reference to grade 6 learning in the Lesson Narrative. The standard is indicated in the Building On portion of the CCSS Standard alignments. Students begin by identifying which of four given questions does not belong; the sample responses provided for the teacher indicate that students may respond that the questions are or are not statistical (6.SP.1). Students then develop survey questions based on three given statistical questions and survey the class to collect data.
• In Algebra 1, Unit 1, Lesson 2, a connection is made to 6.SP.4 and the display of numerical data in plots on a number line, dot plots, histograms, and box plots. The materials state that this serves as a brief review of these representations and the way they are created prior to engaging in the work of S-ID.1 and S-ID.2 in ensuing lessons.
• In Algebra 1, Unit 2, Lesson 17, students build on their previous understanding of 8.EE.8 by considering systems of equations that have no solutions or infinitely many solutions. Students identify, without graphing or using algebra, if a system of linear equations is equivalent or parallel.
• In Geometry, Unit 5, Lesson 2, students build on 7.G.3, where they describe two-dimensional figures that result from slicing three-dimensional figures. Students analyze cross-sections of three-dimensional figures (G-GMD.4), and build toward G-GMD.1, where students identify three-dimensional solids given parallel, cross-sectional slices.
• In Geometry, Unit 2, Lesson 3, Measuring Dilations (G-SRT.1) builds on 8.G.3. During this lesson, students dilate a quadrilateral using different scale factors. The purpose of this activity is to understand that the different ratios of the dilations are equal.
• In Geometry, Unit 5, Lesson 16, students build on their previous understanding of 7.G.6 and 8.G.9 by solving surface area and volume problems with a real-world context. In the problems in the student materials, students maximize and minimize these geometric attributes which is an extension of previously learned skills in grades 7 and 8.
• In Algebra 2, Unit 3, Lessons 1-3 and 5, students build on previous knowledge of 8.EE. Student work extends beyond the rules of exponents that were learned in previous grades in the following ways: solving simple equations to find the missing exponents in an equivalent relationship; considering numbers expressed as square roots and determining which integers it falls between; considering unit fractions as exponents and how the rules of exponents extend to all rational numbers.

Indicator 1f

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.
0/0
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series do not explicitly identify the plus standards when plus standards are included. There are some plus standards that are explicitly taught and support the mathematics in the course. In other instances, there are plus standards for which the standard is not fully addressed. In cases where plus standards are partially addressed, the inclusion provides more detail and context for the non-plus standards, which supports the mathematics all students should study in order to be college and career ready.

The following plus standards were fully addressed:

• F-IF.7d: In Algebra 2, Unit 2, Lessons 17–19 students encounter zeros, asymptotes (including oblique), and end behavior of rational functions.
• G-GMD.2: In Geometry, Unit 5, the Lesson Narrative states “In this unit, students practice spatial visualization in three dimensions, study the effect of dilation on area and volume, and derive volume formulas using dissection arguments and Cavalieri’s Principle.” In Geometry, Unit 5, Lesson 10 students conclude that an oblique prism and a right prism that have the same height and whose bases are of equal area have the same volume. This is because their cross sections at all heights have equal area (Cavalieri’s Principle) which is then used in developing the volume formulas.
• S-CP.8: In Geometry, Unit 8, the Lesson Narrative states “Conditional probability is discussed and applied using several games and connections to everyday situations. In particular, the Multiplication Rule, P(A and B) = P(A | B)⋅P(B), is used to determine conditional probabilities. Conditional probability leads to the definition of independence of events. Students describe independence using everyday language and use the equation P(A | B) = P(A) when events A and B are independent.” In Lesson 8, students engage with the Multiplication Rule to find conditional probabilities, and in Lesson 9, students estimate conditional probabilities and compare work done with the Multiplication Rule.

The following plus standards were partially addressed:

• N-CN.B: In Algebra 2, Unit 3, Lesson 11, the Lesson Narrative states “While a deep, geometric interpretation of complex numbers in the complex plane is beyond the scope of this course, some activities in this unit use the complex plane to support student understanding. The complex plane helps students conceptualize numbers that are not on the real number line and make sense of complex addition. This is similar to how the real number line can be used to understand signed numbers and signed number addition but is not a topic itself. There are purposefully no assessment items related to the complex plane in this course.” The complex plane is then used in Lessons 11 and 12 to support students’ understanding of imaginary numbers and arithmetic with complex numbers.
• N-CN.8: In Algebra 2, Unit 3, Lesson 17.1, students match $$x^2+25$$ with $$(x-5i)(x+5i)$$. Other than this problem presenting the factored form of a quadratic polynomial with imaginary roots, complex numbers are used in solving quadratic equations and not in polynomial identities.
• N-VM: In Geometry, Unit 1, Lesson 12, the Lesson Narrative states “The concept of a directed line segment is introduced to give students language for efficiently describing the direction and length of a translation. Students know the term line segment, and so the phrase directed line segment builds on a concept they already know and connects it to the concept of translations. The word vector is purposely avoided because the geometric interpretation of a vector should arise as a consequence of future work with vectors, not as a definition.”

Plus standards not mentioned in this report do not appear in the materials.

Rigor & Mathematical Practices

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
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Criterion Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and application with a balance of all three aspects of rigor.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Throughout the series, students are expected to use multiple representations to further develop conceptual understanding.

Examples of the development of conceptual understanding include:

• N-RN.1: In Algebra 2, Unit 4, Lesson 6.1, Warm-Up, students explain how given expressions with various exponents are equivalent and provide an additional equivalent expression. This helps students develop conceptual understanding of the properties of exponents.
• A-REI.6: In Algebra 1, Unit 2, Lesson 17, students determine solutions to a system of equations through inspection and use those solutions to determine that there are infinitely many solutions to the given system. Students recognize equivalent equations and explain what equivalence means in terms of solutions to systems of linear equations. Students also interpret what the solution of a system of equations would be if the equations represent parallel lines.
• F-IF.2: In Algebra 1, Unit 4, Lesson 4, students match words to the symbolic rule of given functions. Students use symbolic notation to define the perimeter of a rectangle with a set height and varying width. Students graph the results and find both input and output values from the graph. In Algebra 1, Unit 4, Lesson 5, students expand this understanding to write functions that describe data plans for their phones and compare competing plans both symbolically and graphically. Students describe in writing how the graphic visualization matches the symbolic rule.
• G-GMD.1: In Geometry, Unit 5, Lesson 13, students partition prisms in order to build the volume formula for a pyramid as opposed to using a given formula to calculate volume. Students connect the volume of a prism to the volume of a pyramid with a base area equivalent to that of the prism.
• G-SRT.6: In Geometry, Unit 4, Lesson 4, students connect angle measurements with ratios of side lengths in right triangles. In Lesson 6, students extend their thinking about the ratios of side lengths for any values of the triangle’s angles. Students define cosine, sine, and tangent and compare the answers they get using these definitions to the table used in the previous lessons.
• S-ID.7: In Algebra 1, Unit 3, Lesson 4, students develop their understanding of slope while studying line of best fit related to a scatterplot. Students answer a series of questions to help develop their understanding of what happens to the slope of the line of best fit if one of the elements changed. An example is as follows: “How would the scatter plot and linear model change if grapefruits were used instead of oranges?” Additionally, students discuss the role of the y-intercept during this lesson by explaining what the y-intercept means in the particular context of the problem. Students repeatedly demonstrate understanding of the concept of slope and y-intercept in given data sets throughout the remainder of Algebra 1.

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. The instructional materials develop procedural skills and provide opportunities to independently demonstrate procedural skills throughout the series. The curriculum guide states, “We view procedural fluency as solving problems expected by the standards with speed, accuracy, and flexibility.” Throughout the series, procedural skills are developed through the lessons and the problem sets for each of the lessons. Each problem set has cumulative practice problems to review previously addressed procedural skills.

Examples that show opportunities for students to independently demonstrate procedural skills across the series include:

• A-SSE.1: In Algebra 1, Unit 6, and Algebra 2, Unit 2, students develop procedural skill and fluency, as they make observations related to the structure of a factored quadratic expression and the zeros of that expression when graphed as a function. Students predict possible factors and their forms by evaluating the expression for varying input values, looking at graphs, reading tables, and exploring end behavior.
• A-APR.6: In Algebra 2, Unit 2, Lesson 17, students perform polynomial division by using long division, synthetic division, and polynomial factorization in order to write a higher-order polynomial as a product of its linear and/or non-linear factors.
• F-IF.1,2: In Algebra 1, Unit 4, Lessons 2–5, students use function notation and develop fluency with substitution and calculations.
• F-IF.4: In Algebra 1, Unit 5, and Algebra 2, Unit 6, students develop procedural skill and fluency, as they explore key features of multiple types of graphs. In Algebra 1, Unit 5, over the course of nine lessons, students build an understanding of how exponential growth differs from linear growth. They encounter different contexts and use expressions, graphs, and tables to distinguish between the two types of functions. They gain fluency in how to compare two exponential functions, how they differ in their expressions, and what that will mean for growth in context. In Algebra 2, Unit 6, students use these skills with trigonometric functions, recognizing and discussing amplitude, frequency, and shifts in many and varied contexts over the course of four lessons.
• F-BF.3: In Algebra 1, Unit 4, Lesson 14, students analyze the type of transformation a constant value creates with an absolute value function. In the cumulative practice problem set, there are more problems for students to practice this skill.
• G-GPE.4: In Geometry, Unit 6, Lesson 10 practice, students write equations using parallel slopes and identify equations that are parallel to a specific line. In Geometry, Unit 6, Lesson 11, students have the same opportunity with perpendicular slopes.

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

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

Examples of students utilizing mathematical concepts and skills in engaging applications include:

• A-REI.11: In Algebra 1, Unit 4, Lesson 9, students engage with two or more graphs simultaneously, interpreting their relative features and their average rates of change in context. Examples are as follows:  population, trends of phone ownership, and the popularity of different television shows. In Activity 9.2, students compare two functions by studying graphs and statements in function notation. In Algebra 2, Unit 4, Lesson 15.3, students solve a system of exponential equations involving a cicada population using logarithms and graphing; specifically, students explain why they can use the intersection of the two graphs to estimate when the cicada population will reach 100,000.
• F-IF.6 and F-BF.1: In Algebra 1, Unit 4, Lesson 18, students use functions to model real-life applications. Students create and analyze functions to model cell phone battery power using given data. In the cumulative practice, students engage with relevant applications related to distance driven over time and the relationship between temperature and cricket chirps.
• G-SRT.8: In Geometry, Unit 4, Lesson 9.3, students use the safe ladder ratio to determine the safe ladder angle, and students use the calculated angle to decide if a ladder’s length is sufficient for a given scenario. Students also determine if it is possible to adjust the ladder to a safe angle and explain their reasoning. In Lesson 10, students solve application problems using trigonometry. Students find the perimeter of figures inscribed in a circle using trigonometric ratios, and students solve problems involving an airplane’s angle of descent and path length as it descends to its destination.
• G-MG.2: In Geometry, Unit 5, Lesson 17.3, students apply volume and density to determine the number of fish that could be housed in a tube-shaped aquarium with an open 4-foot cylinder in the middle for viewing.
• S-ID.6 and N-Q.3: In Algebra 1, Unit 3, Lesson 6, students apply residual value, line of best fit, and percent error to data related to the weight of oranges in a crate. Students also apply these concepts in practice problems 4 and 5 involving applications of car sales and temperatures.
• S-IC.1: In Algebra 2, Unit 7, Lesson 3, students evaluate the randomness in population samples. Students determine the best way to have random samples and the factors that could affect the randomness in several different scenarios. Students draw conclusions from a variety of non-routine application 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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the materials, and multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

The following are examples of balancing the three aspects of rigor in the instructional materials:

• Each lesson begins with a Warm-Up, and this is often an opportunity for students to develop their number sense or procedural fluency. After the Warm-Up, there are activities that do one or more of the following: provide context, introduce, formalize or practice vocabulary, work toward mastery, introduce a new concept, or provide an opportunity to model. The embedded classroom routines also contribute to a balance of the three aspects of rigor. These routines include the following: Analyze It, Math Talks, Group Presentations, Notice and Wonder, Think and Share, and others. At the end of the lesson, there is a synthesis activity where the teacher leads a discussion to formalize the learning. The lesson ends with a Cool-Down for students to work independently on the lesson concepts. Each of the aspects of rigor are addressed with this lesson structure throughout the series.
• In Algebra 1, Unit 6, Lesson 9, students demonstrate a balance of the three aspects of rigor while addressing A-SSE.2,3. In the Practice Problems, students determine if two representations of quadratic expressions are equivalent. Students perform calculations related to quadratic functions in the context of real-world applications, one context of which is a football player throwing a pass. In the Student Task Statements, multiple representations of factorable quadratics are presented. Students examine standard form, factored form, and a geometric representation of a factorable quadratic expression. Students explain their reasoning when determining if an expression is in factored form. A-SSE.2 is also addressed in Geometry, Unit 6, Lesson 5 when students apply the distributive property and squared forms of a binomial to derive the equations of circles. Students practice procedural skills using the distributive property and writing different forms of equivalent expressions. They also solve application problems related to equations of circles and distances. In Algebra 2, Unit 2, Lesson 23, A-SSE.2 is addressed by having students build conceptual understanding of polynomial identities. Through an application problem, students define an identity. Then, they multiply expressions to generalize patterns in polynomials, which develops procedural skill.
• In Algebra 1, Unit 1, Lessons 2 - 5, the materials provide activities that engage students in all aspects of rigor with respect to S-ID.2. Specifically, in Lesson 2.2, students represent and analyze histograms; in Lessons 3.1 and 4.1, students consider dot plots to inform a conversation about the shape of a distribution; and in Lesson 5, students calculate the measures of central tendency. In Lesson 9, students perform statistical calculations. In ensuing lessons, students further develop statistical reasoning: in Lesson 10, students consider what variables they may use to analyze a situation and describe data displays they may use to compare two sets of data; in Lesson 11, students explore and reason about symmetry in a data set; in Lesson 12, students investigate standard deviation and other measures of variability; and in Lesson 14, students investigate the effect of outliers. In Lessons 15 and 16, students compare measures of center and variability in context as well as determine the best measure of center and variability for several data sets. Students also design an experiment to answer a statistical question, collect data, analyze data using statistics, and communicate the answer to the statistical question.
• In Geometry, Unit 7, Lesson 6, students solve problems related to distance and parabolas. In the Student Task Statements, students answer questions related to the distance from the focus to the vertex of a parabola and the effect that distance might have on the shape of the parabola. They use the definition of a parabola and the distance formula to determine if a point is on the parabola. Students defend their answers and try to generalize how one would know if a point is on the parabola given a graph. Students also demonstrate an understanding of what happens to the shape of a parabola if one was to move the directrix closer to the focus.
• In Algebra 2, Unit 5, Lessons 8 and 9, students consider the impact of scaling the input or the output values of a function. They examine how graphs change based on the scaling of the input (horizontal) or output (vertical) values. In Lesson 9, Practice Problems, students determine if different statements that are made based on scaled inputs or outputs are correct given different representations of functions. Students also use data to determine an appropriate scale factor that would model the population of sloths given an initial function.
• In Algebra 2, Unit 2, Lesson 20.3, students write a simple rational equation about batting average to develop procedural skill, and they demonstrate conceptual understanding when working with a word problem and writing it algebraically. The extension and what-if questions about the rational equation address application of rational equations.

Criterion 2e - 2h

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for supporting the intentional development of the eight Mathematical Practices (MPs), in connection to the high school content standards. Overall, the materials integrate the use of the MPs with learning the mathematics content. Through the materials, students make sense of problems and persevere in solving, attend to precision, reason and explain, model and use tools, and make use of structure and repeated reasoning.

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for supporting the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards.

Examples where students make sense of problems and persevere in solving them include:

• In many units throughout the series, students answer the questions “What do you notice?” and  “What do you wonder?” in some lesson activities. The goal of these questions is to guide classroom conversation toward the mathematical material that the class is about to address. These questions increase accessibility for students by providing entry points to the context, which aids in making sense of the tasks.
• In Algebra I, Unit 4, Lesson 1, students analyze the relationship between the number of bagels purchased and the cost of the bagels to determine how three different costs could all be true.
• In Geometry, Unit 4, Lesson 11, students examine how inscribed polygons with increasing numbers of sides can lead to an approximation of $$\pi$$. Students make sense of the problem to determine appropriate methods for finding a formula to calculate the perimeter of the inscribed polygons, which leads to an approximation of $$\pi$$.
• In Algebra 2, Unit 2, Lesson 24, students create multiple right triangles from a given set of instructions. Students persevere in finding at least one example that does not create a right triangle. Towards the end of the lesson, students develop an identity that can be used to generate Pythagorean Triples.

Examples where students attend to precision include:

• In Algebra 1, Unit 4, Lesson 6, students analyze a graph containing two mappings related to two objects in time. One graph shows a linear piecewise function produced by a drone, and the other graph shows a quadratic function produced by a toy rocket. Students describe the graphs’ representations in terms of the real-world contexts.
• In Geometry, Unit 6, Lesson 7, as students articulate what they notice and wonder, they attend to precision in language they use to describe what they see. Students may initially propose less formal or imprecise language, then restate their observation with more precise language in order to communicate clearly. Relevant vocabulary includes the following: equidistant, congruent segments, and parabola.
• In Algebra 2, Unit 3, Lesson 6, students solve simple equations involving squares and square roots. The teacher notes state: “Students attend to precision when they reason about solutions to equations involving squares and square roots from the meaning of the √ symbol (MP6).” In this lesson, students explore the idea that every positive number has two square roots. The convention of giving only the positive root is also discussed in terms of its precise meaning. Students explore the use of the radical symbol as a tool of precision.

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 instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for supporting the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards. Across the series, there is an intentional development of MP2 and MP3 that reaches the full intent of the MPs. There are many examples in the instructional materials of MPs 2 and 3 where students reason abstractly and quantitatively or construct viable arguments and critique the reasoning of others.

Examples of where and how the materials use MP2 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

• In Algebra 1, Unit 1, Lesson 14, students determine whether or not to exclude an outlier. In the Student Task Statements, Problem 14, students determine if there are outliers for a data set, explain why any outliers might exist, and determine if the outliers should be included in the analysis of the data.
• In Algebra 1, Unit 5, Lesson 10, students examine data from a cooling coffee function. They must determine, from given intervals, the best interval to use for an appropriate “average rate of cooling” and support their choice.
• In Algebra 1, Unit 7, Lesson 1.3, students write a quadratic equation and are prompted not to solve it. In writing an equation and interpreting the solution in its context, students practice reasoning quantitatively and abstractly.
• In Geometry, Unit 3, Lesson 2, students create a scale model of the Solar System to verify the distance the Moon would be from the Earth when fully eclipsing the Sun.
• In Algebra 2, Unit 7, Lesson 16, students take two readings of their pulse. For one reading, they count the beats out loud while watching the clock, and for the second reading, they take a few deep breaths, close their eyes and have someone else watch the clock. They then compare the two rates. Data from the whole class is collected and a discussion held as they reason quantitatively and abstractly together.

Examples of where and how the materials use MP3 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

• In Algebra 1, Unit 1, Lesson 11.3, students explain their reasoning and critique the reasoning of others as they determine if a data display matches a written statement or not. In this activity, students have small-group discussions and examine scenarios from a classmate’s point of view. Students also construct arguments they can defend for their own matches as well as arguments for why they might disagree with their partner.
• In Algebra 1, Unit 7, Lesson 23.3, students explain why a vertex is a maximum or a minimum. Students explain their reasoning concerning which performance gives the greater maximum revenue without creating a graph. Students construct an argument, and during the class discussion, they critique the reasoning of others in the class.
• In Geometry, Unit 2, Lesson 3, students construct arguments to describe that congruence through transformations requires a series of transformations where corresponding parts match each other. In the Cumulative Practice Problem Set, Problem 2, students argue for the congruence of two triangles based on a rotation and explain their reasoning, citing the argument for congruence based on the transformation.
• In Geometry, Unit 6, Lesson 9, students construct viable arguments during the lesson synthesis by answering a question about which form of an equation of a line they prefer. In the previous lesson, students used equations in multiple forms to find out what the slope of the line is and what point each line passes through. Students explain why they prefer a specific form over another.
• In Geometry, Unit 8, Lesson 2, students, in groups, draw slips of paper with a name on them from a bag with an unknown number of slips. They record the name, replace the slip, pass the bag, and draw again. After 15 draws, each student in the group makes predictions of how many names and how many slips were in the bag. If the group has consensus, they draw another round. Each time, they construct new arguments and critique the thinking of others.
• In Algebra 2, Unit 2, Lesson 4.3, students answer questions about operations on polynomials. They experiment to develop reasons to support their answers. During the group discussion, they defend and critique the reasoning of their classmates as they describe events as subsets through taking turns in trading roles as they explain their thinking.
• In Algebra 2, Unit 4, Lesson 14, students practice constructing logical arguments when they justify solutions and explain why a certain value is a reasonable estimate for a given logarithm.

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.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for supporting the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. There are multiple problems and activities throughout each unit in which students use and create mathematical models to enrich the mathematics. Students also choose from a variety of tools throughout the lessons, including digital tools provided in a drop down menu in the online materials (MP5).

Examples where students model with mathematics include:

• In Algebra 1, Unit 2, Lesson 20.2, students solve a problem about gas in a lawn mower. The teacher materials state, “To reason about the problem, students need to interpret the descriptions carefully and consider their assumptions about the situation. To make sense of the situation, some students may define additional variables or use diagrams, tables, or other representations. Along the way, they engage in aspects of modeling (MP4)”. Students identify the important quantities in this scenario, identify the relationships, and write at least one inequality to represent their conclusions.
• In Algebra 1, Unit 4, Lesson 17, students write a linear function for data concerning the percent of cell phones in homes in the United States since 2004. Students answer questions leading to finding a model for the inverse of the function.
• In Geometry, Unit 1, Lesson 9, students use perpendicular bisectors to decide which stores in the city will be responsible for orders based on the store’s location compared to where the order will be delivered. Students use real-world situations to apply their knowledge and make approximations on their calculations to simplify distributions for a local store.
• In Geometry, Unit 7, Lesson 14, students work with a pizza slice as a model of a sector of a circle. Students compute the cost per square inch of pizza slices from four vendors by computing the sector area. This engages students in the modeling process by reporting their findings and considering other variables.
• In Algebra 2, Unit 2, Lesson 16, students engage in aspects of the modeling process by making reasonable estimations and determining reasonable constraints in the context of real-world scenarios. In “Are You Ready for More?”, students consider different aspects of manufacturing, other than simply minimizing materials, in order to make sense of an open- ended problem.
• In Algebra 2, Unit 7, Lesson 14, students speculate whether the differences of the means in small experimental groups can be reduced by randomly regrouping the data. Students approximate the distribution of simulated differences of means by using a normal distribution.

Examples where students choose and use appropriate tools strategically include:

• In Algebra 1, Unit 7, Lesson 17, students use the form of a quadratic equation as a “tool” to solve problems. Students “write quadratic equations to represent relationships and use the quadratic formula to solve problems that they did not previously have the tools to solve (other than by graphing). In some cases, the quadratic formula is the only practical way to find the solutions. In others, students can decide to use other methods that might be more straightforward.”
• In Algebra 1, Unit 5, Lesson 19.2, students compare linear and exponential growth involving simple and compound interest. Students strategically use technology, whether they make a graph (for which they will need to think carefully about the domain and range) or continue to tabulate explicit values of the two functions (likely with the aid of a calculator for the exponential function).
• In Geometry, Unit 7, Lesson 7.2 students create an arbitrary triangle, use angle bisectors and constructions to find the incenter, and construct the triangle’s inscribed circle. The narrative states: “Making dynamic geometry software available as well as tracing paper, straightedge, and compass gives students an opportunity to choose appropriate tools strategically (MP5).” The narrative also states: “Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.”
• In Geometry, Unit 8, Lesson 9 students use two-way tables as a sample space to decide if events are independent and to estimate conditional probabilities. Although technology is not required, it is recommended that technology be made available as there are opportunities for students to choose to use appropriate technology to solve problems.
• In Algebra 2, Unit 4, Lesson 5, students create an exponential function given a table of values. During this lesson, teachers make sure that students have access to a spreadsheet tool to reason about the given questions. This helps students focus on the questions rather than the calculations, and students use tools to their advantage during the lesson.
• In Algebra 2, Unit 5, Lesson 11, students apply transformations on functions to determine the best model for a data set, specifically temperature data from heating objects. The Lesson Narrative states: “This can be done by hand via experimenting, but students may also choose to use graphing technology to help choose the appropriate translations, scalings, and reflections (MP5).”

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 instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for supporting the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. Each of these MPs is cited numerous times across the series, and the Algebra 1 Extra Support Materials cite each of these MPs. Additionally, across the series, the majority of the time MP7 and MP8 are used to enrich the mathematical content, and there is intentional development of MP7 and MP8 that reaches the full intent of the MPs.

Examples of where and how the materials use MP7 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

• In Algebra 1, Unit 4, Lesson 12, students use piecewise notation to look for structure when graphing those functions.
• In Geometry, Unit 2, Lesson 13, students look for and make use of structure by working backward from the statement they are trying to prove about parallelograms.
• In Geometry, Unit 3, Lesson 5, students use Notice and Wonder to examine triangles whose midpoints connect to form other smaller triangles. Students notice these smaller triangles are dilations of the larger triangle.
• In Geometry, Unit 8, Lesson 9, students notice and make use of structure through a Math Talk as they recognize fraction bars as part of a fraction, and as representing division.
• In Algebra 2, Unit 2, Lesson 8, students make a conjecture based on creating their own function and analyzing the end behavior to see if it matches their conjecture. The focus of the lesson is “using the structure of the expressions to understand how the term with the highest exponent dictates end behavior even when other terms may have larger values at inputs nearer to zero due to coefficients.”
• In Algebra 2, Unit 7, Lesson 7, students find the area under the normal curve and interpret the proportion of values at different intervals. These problems utilize a real-world scenario, and students connect these applications to the theoretical study of the normal distribution.

Examples of where and how the materials use MP8 to enrich the mathematical content and demonstrate the full intent of the mathematical practice include:

• In Algebra 1, Unit 1, Lesson 6, students experiment by changing numbers in a provided spreadsheet to discover what and how the number impacts the outputs. Students express regularity in repeated reasoning as they observe the outcome of different inputs to generalize the operations in the formula cell.
• In Algebra 1, Unit 2, Lesson 8, students repeatedly rewrite equations to isolate different variables. Students rely on previous knowledge of solving equations to generalize their reasoning as they work with literal equations.
• In Algebra 1, Unit 6, Lesson 5.3, students look for repetition in their calculations for a falling object and how this relates to quadratic functions. The teacher materials state, “To find a new expression that describes the height of the object, students reason repeatedly about the height of the object at different times and look for regularity in their reasoning (MP8)” as they write new quadratic expressions. Students also use repetition in their calculations as they complete provided tables to determine where an object would be at a certain time and use that information to write new expressions.
• In Geometry, Unit 1, Lesson 6, students construct parallel and perpendicular lines, and students engage in MP8 as they repeatedly construct these different types of lines.
• In Geometry, Unit 7, Lesson 8, students perform multiple arc length and sector area calculations as they generalize formulas for each.
• In Algebra 2, Unit 1, Lesson 1, students look for a pattern within the Tower of Hanoi puzzle, where students complete a puzzle by building a tower. Students play the game and make some conjectures about the smallest number of moves you can make to complete the tower.
• In Algebra 2, Unit 1, Lesson 8, students use a table of values to generalize formulas for finding the nth term of a sequence. By examining patterns and applying repeated reasoning, students generalize the definition of a sequence into an equation and/or function.
• In Algebra 2, Unit 6, Lesson 10.3, students determine specific trigonometric values for large angles. “Students make connections between angles greater than 2$$\pi$$ and between 0 and 2$$\pi$$ that correspond to the same point on the unit circle (MP 8)”.

Usability

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson. It is clear when students solve problems to learn and when they apply skills.

Lessons include a Warm-Up, Activities, Synthesis, and a Cool-Down. Practice Problems are in a separate section of the instructional materials, distinguishing between problems students complete and exercises in the lessons. Warm-Ups connect prior learning or engage students for learning new material in the lesson. Students learn and practice new mathematics in lesson Activities. In the Synthesis activity, students build on their understanding of the new concept. Each activity lesson ends with a Cool-Down in which students apply what they have learned from the activities, complete preliminary practice, or complete an introduction to skills they may need in the next lesson.

Practice problems are consistently found in the Practice sets that accompany each lesson. These sets of problems include problems that support students in developing mastery of the current lesson and unit concepts and review of material from previous units. When practice problems contain content from previous lessons, students apply their skills and understandings in different ways that enhance understanding or application (e.g., increased expectations for fluency, more abstract application, or a non-routine problem).

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for not being haphazard; exercises are given in intentional sequences.

Overall, clusters of lessons within units and activities within lessons are intentionally sequenced so students develop understanding. The structure of a lesson provides students with the opportunity to activate prior learning, build procedural skill and fluency, and engage with multiple activities that are sequenced from concrete to abstract or increase in complexity. Lessons end with a Cool-Down which is aligned to the daily lesson objective. Unit sequences consistently follow progressions to support students' development of conceptual understanding and procedural skills.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for having variety in what students are asked to produce.

The instructional materials prompt students to produce products in a variety of ways. Students produce solutions within Activities and Practice, as well as participating in class, groups, and partner discussions. Materials provide opportunities for students to construct viable arguments and critique the reasoning of their peers. Students use a digital platform and paper-pencil to conduct and present their work. The materials consistently prompt students for solutions that represent the language and intent of the standards. Students use representations such as tables, number lines, area diagrams, dot plots, geometric constructions, and graphs, as well as strategically choose tools to complete their work (MP5). Lesson activities and tasks are varied within and across lessons.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The series includes a variety of virtual manipulatives and integrates hands-on activities that allow the use of physical manipulatives, for example:

• Manipulatives and other mathematical representations are consistently aligned to the expectations and concepts in the standards. The majority of manipulatives used are commonly accessible measurement and geometry tools.
• The materials provide digital applets for manipulating geometric shapes, such as GeoGebra applets, tailored to the lesson content and tasks. When physical, pictorial, or virtual manipulatives are used, they are aligned to the mathematical concepts they represent. For example, in Geometry, Lesson 5, Activity 10.2, two rectangular prisms with the same base area and the same height are used within an applet to develop Cavilieri’s Principle.
• Examples of manipulatives for Geometry include: an index card to use as a straightedge, compasses, tracing paper, blank paper, colored pencils, and scissors. Additionally, GeoGebra applets are used for constructions, to perform transformations, to explore congruence and similarity, and to visualize cross sections.

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 visual design in Kendall Hunt’s Illustrative Mathematics Traditional series is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

• The digital lesson materials for teachers follow a consistent format for each lesson. Teaching Notes with Supports for English Language Learners and Supports for Students with Disabilities are placed within the activity they support and are specific to the activity. Unit overviews follow a consistent format. The format of course overviews, units, and individual lessons are consistent across the series.
• Student-facing printable materials follow a consistent format. Tasks within a lesson are numbered to match the teacher-facing guidance. The print and visuals on the materials are clear without any distracting visuals or overabundance of text features. Teachers can assign lessons and activities to students through the platform, enabling students to access digital manipulatives, practice problems, unit assessments, and lesson visuals.
• Printable student practice problem pages frequently include enough space for students to write their answers and demonstrate their thinking.

Criterion 3f - 3l

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for supporting teacher learning and understanding of the standards. The instructional materials: support planning and providing learning experiences with quality questions; contain ample and useful notations and suggestions on how to present the content; contain full, adult-level explanations and examples of the more advanced mathematics concepts; and contain explanations of the grade-level mathematics in the context of the overall mathematics curriculum.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson consists of a detailed lesson plan accompanied by teaching notes. Included in these teaching notes are the objectives of the lesson, suggested questions for discussion, and guiding questions designed to increase classroom discourse and foster understanding of the concepts. For example, in Geometry, Unit 4, Lesson 6.2 suggests the teacher ask, “The right triangle table is useful, but what if the angle is not a multiple of 10 degrees?” In Algebra 1, Unit 3, Lesson 7, Lesson Synthesis, the curriculum suggests the following question for discussion, “What does a scatter plot look like when its line of best fit has a correlation coefficient of -0.5? Sketch it.” The teaching notes and questions for discussion support the teachers in planning and implementing lessons effectively.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for providing teacher supports with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Also, where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

• Each lesson includes the Learning Goals written for teachers and students, learning targets written for students, a list of Word/PDF documents that can be downloaded, CCSSM Standards that are “built upon” or “addressed” for the lesson, and any instructional routines to be implemented. Within the technology, there are expandable links to standards and instructional routines.
• Lessons include detailed guidance for teachers for the Warm-Up, Activities, and the Lesson Synthesis.
• Each lesson activity contains an Overview and Launch Narrative, Guidance for Teachers and Student-facing materials, Anticipated Misconceptions, “Are you ready for more?”, and an Activity Synthesis. Included within these narratives are guiding questions and additional support for students.
• The teacher materials that correspond to the student lessons provide annotations and suggestions on how to present the content. “Launch” explains how to set up the activity and what to tell students. After the activity is complete, there are often Anticipated Misconceptions in the teaching notes, which describes how students may incorrectly interpret or misunderstand concepts and includes suggestions for addressing those misconceptions.
• The materials are available in both print and digital forms. The digital format has embedded GeoGebra applets. Guidance is provided to both the teacher and the student on how to use the Geometry Toolkit and applet. For example, in Geometry, Unit 1, Lesson 1, teachers and students are provided access and time to play with the applet tools. During the Launch, teachers are encouraged to model the different tools, practice with the students, and answer questions.

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 Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for the teacher’s edition containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.

The narratives provided for each unit include information about the mathematical connections of concepts being taught. Previous and future grade levels are also referenced to show the progression of mathematics over time. Important vocabulary is included when it relates to the “big picture” of the unit.

Lesson Narratives provide specific information about the mathematical content within the lesson and are presented in adult language. These narratives contextualize the mathematics of the lesson to build teacher understanding and give guidance on what to expect from students and important vocabulary.

The Lesson Narrative for Algebra 2, Unit 3 states, “In the next set of lessons, students connect the $$\sqrt{ }$$ and $$\sqrt[3]{ }$$ symbols with solutions to quadratic and cubic equations. Students learn that a number is a square root of c if it squares to make c. In other words, square roots of c are solutions to the equation $$x^2=c$$. Students use the graph of $$y=x^2$$ to see that all positive numbers have two square roots, one positive and one negative. They learn the convention that the positive square root is given the symbol $$\sqrt{ }$$, so the positive square root of c is written $$\sqrt{c}$$ and the negative square root is written $$-\sqrt{c}$$.”

Indicator 3i

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

The Course Guide and Narratives describe how mathematical concepts are built from previous grade-level/course and lesson material. For example, in Algebra 1, Unit 4, the Lesson Narrative states, “In grade 8, students learned that a function is a rule that assigns exactly one output to each input. They represented functions in different ways—with verbal descriptions, algebraic expressions, graphs, and tables—and used functions to model relationships between quantities, linear relationships in particular.” In addition, in Algebra 1, Unit 5, the Lesson Narrative states, “Before starting this unit, students are familiar with linear functions from previous units in this course and from work in grade 8. They have been formally introduced to functions and function notation and have explored the behaviors and traits of both linear and non-linear functions. Additionally, students have spent significant time graphing, interpreting graphs, and exploring how to compare the graphs of two linear functions to each other. In this unit, students frequently use the properties of exponents, a topic developed in grade 8. They also apply their understanding of percent change from grade 7 and use an exponent to express repeated increase or decrease by the same percentage.”

For some units, there are explanations given for how the grade-level concepts fit into future high school work. For example, in Geometry, Unit 7, the Lesson Narrative states, “Students develop fluency with radian measures by shading portions of circles and working with a double number line. This is important for the transition towards Algebra 2. In that course, students will explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.”

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 Kendall Hunt’s Traditional series provide a list of concepts in the Course Guide that cross-references the standards addressed and an estimated instructional time for each unit and lesson.

• The Course Guide includes a Scope and Sequence that provides pacing information. A table, spanning 32 weeks of instruction, shows the unit that is taught each week, as well as the total number of days the unit should take to complete. In each lesson, the time an activity will take is included in the Lesson's Narrative. About These Materials in the Teacher Guide states, “Each lesson plan is designed to fit within a class period that is at least 45 minutes long.“
• In the Course Guide under Lessons and Standards, there is a table that shows which standard each lesson addresses and another table to show where a standard is found in the materials.

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 Kendall Hunt’s Illustrative Mathematics Traditional series contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Materials for each unit include an explanation to family and caregivers on what their student will be learning over the course of the unit. The Family Materials provide an overview of what the student will be learning in accessible language. For example, in Algebra 2, Unit 2, the Family Materials state, “In this unit, your student will learn about a kind of function, polynomials. (In earlier grades, students learned about two special kinds of polynomial functions: linear and quadratic functions.) A polynomial is a sum of terms involving only one letter, called a variable, where the exponents of the variable are whole numbers. For example, $$3x^3-x^2+10$$ and $$5x^6$$ are polynomials. But $$6x^{-2}+2x^{-1}-1$$ is not, because the exponents are negative. And $$2xy-7y$$ is not, because it involves more than one variable. Your student will connect different ways of representing polynomial functions, such as graphs and equations.” In addition to the explanations of the current concepts and big ideas from each unit, there are diagrams and problems/tasks for families to discuss and solve.

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 Kendall Hunt’s Illustrative Mathematics Traditional series contain explanations of the program's instructional approaches and identification of the research-based strategies.

The materials draw on research to explain and contextualize instructional routines and lesson activities. The Course Guide includes specific links to research, for example:

• “Selected activities are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014).”
• How to Use These Materials: “Some of the instructional routines, known as Mathematical Language Routines (MLR), were developed by the Stanford University UL/SCALE team.”

In the Course Guide, all of the “Instructional Routines” are fully explained.

• Math Talks found in the Warm-Ups set a routine for collecting different strategies. In the Course Guide, Instructional Routines, the materials state the following: “Math Talks build fluency by encouraging students to think about the numbers, shapes, or algebraic expressions and rely on what they know about structure, patterns, and properties of operations to mentally solve a problem. While participating in these activities, students need to be precise in their word choice and use of language (MP6). Additionally a Math Talk often provides opportunities to notice and make use of structure (MP7).”

Think-Pair-Share routines found in the Lesson Activities provide structure for engaging students in collaboration. In the Course Guide, Instructional Routines, the materials state the following: “This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking. First they have an opportunity to share their thinking in a low-stakes way with one partner, so that when they share with the class they can feel calm and confident, as well as say something meaningful that might advance everyone’s understanding. Additionally, the teacher has an opportunity to eavesdrop on the partner conversations so that they can purposefully select students to share with the class.”

Criterion 3m - 3q

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the standards. The instructional materials provide strategies for gathering information about students' prior knowledge, opportunities for identifying and addressing common student errors and misconceptions, ongoing review and practice with feedback, assessments with standards clearly denoted, and guidance to teachers for interpreting student performance and suggestions for follow-up.

Indicator 3m

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.

• Prior grade-level or course standards are indicated in the instructional materials. The lesson Warm-Up is designed to engage students' thinking about the upcoming lesson and/or to revisit previous grades' concepts or skills.
• Prior knowledge is gathered about students through the pre-unit Check Your Readiness assessments. In these assessments prerequisite skills necessary for understanding the topics in the unit are assessed. Commentary for each question provides the relevance of the questions to the topic and a list of standards assessed is provided for the teacher. For example, in Algebra 2, Unit 5, Check Your Readiness assessment problem 2 shows 7.G.1 as an aligned standard. The teacher note states, “Geometry Unit 3 Lesson 1 Activity 4, Match the Scale Factors, is an example of a brief activity that could be added to review scale factors.” The notes also state, “Vertical and horizontal stretches are not dilations because the stretch is only applied in a single direction while a dilation applies the same scale factor in all directions. Nonetheless, the idea of scaling is common to both situations.”

Indicator 3n

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

Lesson Activities include teaching notes that identify where students may make a mistake or struggle. There is a rationale that explains why the mistake could have been made, suggestions for teachers to make instructional adjustments for students, and steps teachers can take to help clear up the misconceptions. For example, in Geometry, Unit 2, Lesson 6.2, the teacher notes state, “Anticipated Misconceptions: If students are searching too far back, point students toward the proof in the warm-up activity, Information Overload. The goal is for students to understand and adapt that proof to this situation, so help students find the proof relatively quickly so they can have time to engage in productive struggle as they try to understand and adapt it.”

Indicator 3o

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure consisting of a Warm-up, Activities, Lesson Synthesis, and Cool-down provide students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently, with partners, and in groups where review, practice, and feedback are embedded into the instructional routine. Practice Problems for each lesson activity reinforce learning concepts and skills and enable students to engage with the content and receive timely feedback. In addition, discussion prompts provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

Indicator 3p

Materials offer ongoing assessments:
0/0

Indicator 3p.i

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for assessments clearly denoting which standards are being emphasized.

Assessments are accessed through the Assessment tab for each unit and are available in two print options. For each unit, there is a Check Your Readiness and an End-Unit Assessment. Longer units also include a Mid-Unit Assessment. Assessments begin with guidance for teachers on each problem, followed by the student-facing problem, solution(s), and the standard targeted.

Indicator 3p.ii

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Assessments include an answer key, and when applicable, a rubric consisting of three to four tiers, ranging from Tier 1 (work is complete, acceptable errors) to Tiers 3 and 4 (significant errors, conceptual mistakes).

Assessments include multiple choice, multiple response, short answer, restricted constructed response, and extended response. Restricted constructed response and extended response items have rubrics that are provided to evaluate the level of student responses. The restricted constructed response includes a 3-tier rubric, and the extended constructed response includes a 4-tier rubric. For these types of questions, the teacher materials provide guidance as to what is needed for each tier as well as some sample responses.

In the Assessment Teacher Guide for each End of Unit Assessment, there are narratives about what may have caused students to choose an incorrect response before the problems are shown along with the correct responses and aligned standards. For example, in Algebra 2, Unit 5, End of Unit Assessment, Problem 2, the Assessment Teacher Guide states, “Students who select A may be confusing how to represent horizontal translations using function notation. Students who select C need more work with representing shifts, reflections, and stretches using function notation. Students who select D may be confusing how to represent horizontal and vertical reflections using function notation.”

Indicator 3q

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

The instructional materials for Kendall Hunt’s Illustrative Mathematics Traditional series include opportunities for students to monitor their own progress.

For every lesson, there is a Lesson Synthesis that offers suggestions for self-monitoring such as, “... asking students to respond to prompts in a written journal, asking students to add on to a graphic organizer or concept map, or adding a new component to a persistent display like a word wall.”

For example, in Algebra 1, Unit 4, Lesson 4, the Lesson Synthesis states, “The teacher should show two function rules on the board and then ask, ‘How would you describe to a classmate who is absent today what each equation means? What would you say to help them make sense of these?”

Criterion 3r - 3y

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide a balanced portrayal of various demographic and personal characteristics. The instructional materials also consistently provide: strategies to help teachers sequence or scaffold lessons; strategies for meeting the needs of a range of learners; tasks with multiple entry-points; support, accommodations, and modifications for English Language Learners and other special populations; and opportunities for advanced students to investigate mathematics content at greater depth.

Indicator 3r

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Each lesson is designed with a Warm-Up that reviews prior knowledge and/or prepares all students for the activities that follow, and the Cool-Down reviews the concepts of the lesson.
• Within a lesson, narratives provide explicit instructional support for the teacher, including the Activity Launch, Anticipated Misconceptions, and Lesson Synthesis. This information assists teachers in making the content accessible to all learners.
• Lesson Narratives often include guidance on where to focus questions in Activities or the Lesson Synthesis.
• Optional activities are often included that can be used for additional practice or support before moving to the next activity or lesson.

Indicator 3s

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The lesson structure—Warm-Up, Activities, Lesson Synthesis, and Cool-Down—includes guidance for the teacher on the mathematics of the lesson, possible misconceptions, and specific strategies to address the needs of a range of learners. Embedded supports include:

• Mathematical Language Routines to support a range of learners to be successful are provided for the teacher throughout lessons to maximize output and cultivate conversation. For example:
• MLR1: Stronger and Clearer Each Time, in which “students think or write individually about a response, use a structured pairing strategy to have multiple opportunities to refine and clarify the response through conversation, and then finally revise their original written response.”
• MLR4: Information Gap, which “allows teachers to facilitate meaningful interactions by giving partners or team members different pieces of necessary information that must be used together to solve a problem or play a game...[S]tudents need to orally (and/or visually) share their ideas and information in order to bridge the gap.”
• MLR6: Three Reads, in order to "ensure that students know what they are being asked to do, and to create an opportunity for students to reflect on the ways mathematical questions are presented. This routine supports reading comprehension of problems and meta-awareness of mathematical language. It also supports negotiating information in a text with a partner in mathematical conversation.”
• Teaching notes appear frequently in lessons to provide additional guidance for teachers on how to adapt lessons for all learners. These teaching notes state specific needs addressed in a recommended strategy that is relevant to the given task and includes supports for Conceptual Processing, Expressive & Receptive Language, Visual-Spatial Processing, Executive Functioning, Memory, Social-Emotional Functioning, and Fine-motor Skills. For each support, there are multiple strategies teachers can employ, for example: Conceptual Processing includes strategies to Eliminate Barriers, Processing Time, Peer Tutors, Assistive Technology, Visual Aids, Graphic Organizers, and Brain Breaks.

Indicator 3t

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for embedding tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

The problem-based design engages students with complex tasks multiple times each lesson. The Warm-Up, Activities, Lesson Synthesis, and Cool-Down provide opportunities for students to apply mathematics from multiple entry points.

Specific examples of strategies found in the materials include “Notice and Wonder” and “Which One Doesn’t Belong?” The lesson and task narratives provided for teachers offer possible solution paths and presentation strategies from various levels, for example:

• In Geometry, Unit 6, Lesson 7, students consider a set of points that are equidistant from a line and a given point. Students share what they notice and what they wonder. This takes place in the Warm-Up of this lesson, and offers an opportunity for all students to access the content.
• In Algebra 1, Unit 4, Lesson 8, students compare four graphs of temperature over time. Students may realize that each of the four representations might not belong based on different criteria. This instructional routine allows students to be precise in their language and to define the parameters necessary when solving contextual problems.

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).
2/2
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for including support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

The ELL Design is highlighted in the Teacher Guide and embodies the Understanding Language/SCALE Framework from the Stanford University’s Graduate School of Education, which consists of four principles: Support Sense-Making, Optimize Outputs, Cultivate Conversation, and Maximize Meta-Awareness. In addition, there are eight Mathematical Language Routines (MLR) that were included “because they are the most effective and practical for simultaneously learning mathematical practices, content, and language.” "A Mathematical Language Routine refers to a structured but adaptable format for amplifying, accessing, and developing students’ language."

ELL Enhanced Lessons are identified in the Unit Overview. These lessons highlight specific strategies for students who have a language barrier which affects their ability to participate in a given task. Throughout lessons, a variety of instructional routines are designed to assist students in developing full understanding of math concepts and terminology. These Mathematical Language Routines include:

• MLR2, Collect and Display, in which “The teacher listens for, and scribes, the student output using written words, diagrams and pictures; this collected output can be organized, revoiced, or explicitly connected to other language in a display for all students to use.”
• MLR5, Co-Craft Questions and Problems, which “[allows] students to get inside of a context before feeling pressure to produce answers, and to create space for students to produce the language of mathematical questions themselves.”
• MLR7, Compare and Connect, which “[fosters] students’ meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, and language.”

Lesson Narratives include strategies designed to assist other special populations of students in completing specific tasks. Examples of these supports for students with disabilities include:

• Social-Emotional Functioning: Peer Tutors. Pair students with their previously identified peer tutors.
• Conceptual Processing: Eliminate Barriers. Assist students in seeing the connections between new problems and prior work. Students may benefit from a review of different representations to activate prior knowledge.
• Conceptual Processing: Processing Time. Check in with individual students as needed to assess for comprehension during each step of the activity.
• Executive Functioning: Graphic Organizers. Provide a t-chart for students to record what they notice and wonder prior to being expected to share these ideas with others.
• Memory: Processing Time. Provide students with a number line that includes rational numbers.
• Visual-Spatial Processing: Visual Aids. Provide handouts of the representations for students to draw on or highlight.

Indicator 3v

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

All students complete the same lessons and activities; however, there are some optional lessons and activities that a teacher may choose to implement with students. For example, in Algebra 1, Unit 3, Lesson 10 is an optional lesson intended to provide an opportunity for students to use skills and knowledge gained from other lessons in this unit.

“Are you ready for more?” is included in some lessons to provide students additional interactions with the key concepts of the lesson. Some of these tasks would be considered investigations at greater depth, while others are additional practice.

There is no clear guidance for the teacher on ways to specifically engage advanced students in investigating the mathematics content at greater depth.

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series provide a balanced portrayal of various demographic and personal characteristics.

• The lessons contain a variety of tasks that interest students of various demographic and personal characteristics. All names and wording are chosen with diversity in mind, and the materials do not contain gender biases.
• The high school materials include a set number of names used throughout the problems and samples (e.g., Jada, Noah, Mai, Clare, Elena, Tyler, Priya). These names are presented repeatedly and in a way that does not appear to stereotype characters by gender, race, or ethnicity.
• Characters are often presented in pairs with different solution strategies. There does not appear to be a pattern in one character using more/less sophisticated strategies.
• Modeling tasks present a wide variety of data that represents different demographic characteristics. For example, the Algebra I Modeling Prompt, College Characteristics, presents data about both private and public colleges and their associated cost. Both religiously affiliated and non-affiliated colleges are included in the data.

Indicator 3x

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series provide opportunities for teachers to use a variety of grouping strategies.

The materials offer multiple opportunities to implement grouping strategies to complete the tasks of a daily lesson. Explicit instructions are found in the Activity Narratives. Grouping strategies range from partner to small group. For example, in Algebra 2, Unit 7, Lesson 6, the narrative states, “Arrange students in groups of two. Distribute one copy of the blackline master to each group or direct students to the data on Card. Ask, “What do you think the phrase ‘within two standard deviations of the mean’ means?” (It means the interval from the value of the mean minus two times the standard deviation to the value of the mean plus two times the standard deviation.).”

In addition, the Instructional Routines implemented in many lessons offer opportunities for students to interact with the mathematics with a partner or in a small group. These routines include: Take Turns Matching or Sorting, in which students engage in sorting given sets of cards into categories; Think-Pair-Share, where students think about and test ideas as well as exchange feedback before sharing their ideas with the class; and Gallery Walk and Group Presentations, in which students generate visual displays of a mathematical problem, and students from different groups interpret the work and find connections to their own work.

Indicator 3y

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series encourage teachers to draw upon home language and culture to facilitate learning.

The Curriculum Guide includes Supporting English Language Learners from the Understanding Language/SCALE (UL/SCALE) at Stanford University’s Graduate School of Education. Promoting Language and Content Development explains the purpose of the document, the goal, and introduction of the framework. The Supporting English-language Learners document in the Course Guide states: “The goal is to provide guidance to mathematics teachers for recognizing and supporting students’ language development processes in the context of mathematical sense making. UL/SCALE provides a framework for organizing strategies and special considerations to support students in learning mathematics practice, content, and language.” The section concludes with acknowledgement of the importance of the framework: “Therefore, while the framework can and should be used to support all students learning mathematics, it is particularly well-suited to meet the needs of linguistically and culturally diverse students who are simultaneously learning mathematics while acquiring English.”

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, and they include technological opportunities for assessing students' mathematical understandings and knowledge of procedural skills as students complete the assessments in printed formats. The instructional materials include opportunities for teachers to personalize learning for all students, and the materials offer opportunities for customized, local use. The instructional materials also include opportunities for teachers and/or students to collaborate.

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.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series, integrate technology including interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the Mathematical Practices (MPs).

Warm-Ups, Activities, Cool-Downs, and Practice Problems can be assigned to small groups or individuals. These sections consistently combine MPs and content.

Teachers and students have access to math tools and virtual manipulatives within a given activity or task, when appropriate. These applets are designed using GeoGebra, Desmos, and other independent designs, for example:

• In Algebra 1, Unit 5, Lesson 19, students use Desmos to explore exponential or linear equations and determine if different graphs or functions are exponential or linear. Students are encouraged to use graphing software to help with this process.

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.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series are web-based and compatible with multiple internet browsers.

• The materials are platform-neutral and compatible with Chrome, ChromeOS, Safari, and Mozilla Firefox.
• The materials are compatible with various devices including iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser.

Indicator 3ab

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Teachers can view assessment data through reports. Materials can be assigned to small groups or individuals.

Indicator 3ac

Materials can be easily customized for individual learners.
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Indicator 3ac.i

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

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series include opportunities for teachers to personalize learning for all students.

• Kendall Hunt’s platform supports professional learning communities by being collaborative and allowing districts to customize the material.
• Lessons have been separated into components; Warm-Ups, Activities, Cool-Downs, and Practice Problems can all be assigned to small groups and individual students, depending on the needs of a particular teacher.

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.
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Mathematics Traditional series can be adapted for local use.

Assessments are available in PDF and editable Word documents.

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.).
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Indicator Rating Details

The instructional materials reviewed for Kendall Hunt’s Illustrative Traditional series incorporate technology that provides opportunities for teachers and/or students to collaborate with each other.

• Students and teachers have the opportunity to collaborate using the applets that are integrated into some of the lessons during activities.
• The Warm-Ups, Activities, Cool-Downs, and Practice Problems can be assigned to small groups to support student collaboration.
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Report Published Date: 03/26/2020

Report Edition: 2019

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.

EdReports requested that publishers fill out The Instructional Materials Technology Information document about each of their products that met our alignment criteria. This document does not evaluate the quality or desirability of any product functionality, but documents features in order to empower local schools and districts with information to select materials that will work best for them given their technological capabilities and instructional vision.

Please note: Reports published beginning in 2021 will be using version 2 of our review tools. Learn more.

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.

• 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.

Kendall Hunt's Illustrative Mathematics High School Traditional and LearnZillion Illustrative Mathematics High School Traditional draw upon the same mathematics content and therefore the scores and evidence for  Gateways 1 and 2 are the same in both programs, albeit with differences in navigation. There are differences in usability as Kendall Hunt's Illustrative Mathematics High School Traditional and LearnZillion Illustrative High School Traditional do not have the same delivery platform for the instructional materials.

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

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

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

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

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

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

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

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

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

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