Alignment: Overall Summary

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for Alignment to the CCSSM. The materials partially meet expectations for Focus and Coherence as they show strengths in: attending to the full intent of the mathematical content for all students; spending the majority of time on content widely applicable as prerequisites; and allowing students to fully learn each standard. The materials partially meet expectations for Rigor and Mathematical Practices as they meet expectations for Rigor and Balance and partially meet expectations for Practice-Content Connections. Within Rigor and Balance, students independently demonstrate each of the three aspects of Rigor, and within Practice-Content Connections, the materials intentionally develop reasoning and explaining (MPs 2 and 3) and seeing structure and generalizing (MPs 7 and 8).

See Rating Scale Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
9
14
18
12
14-18
Meets Expectations
10-13
Partially Meets Expectations
0-9
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

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

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Partially Meets Expectations

Criterion 1a - 1f

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).
12/18
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Criterion Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content for all students; spending the majority of time on content widely applicable as prerequisites; and allowing students to fully learn each standard. The materials partially meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school and making meaningful connections in a single course and throughout the series. The materials do not meet expectations for attending to the full intent of the modeling process and explicitly identifying and building 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.
4/4
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Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students.

The materials attend to the full intent of the following standards:

  • N-RN.3: In Algebra 1, Extend 1-4, students complete a table by determining the sum and product of each set of rational numbers. Students use the table to prove that the set of rational numbers is closed under addition and multiplication. In Algebra 1, Extend 7-4 states that “a conjecture can be made that the sum or product of a nonzero rational number and irrational number is an irrational number.” Also in Extend 7-4, the materials provide proofs for a product of a nonzero rational number and an irrational number that is irrational and the sum of a rational number and an irrational number that is irrational.
  • A-REI.4a: In Algebra 1, Lesson 9-5, students write and solve quadratic functions in vertex form by completing the square. In Algebra 1, Lesson 9-6, the derivation of the Quadratic Formula by completing the square is provided within the materials. In the Algebra 1, Interactive Student Guide (ISG), Solving by Using the Quadratic Formula, students follow steps to derive the Quadratic Formula by completing the square.
  • F-IF.4: In Algebra 1, Lesson 1-8, students interpret intercepts of the graph, symmetry, relative extrema, and end behavior from graphs of functions. Students estimate where the function is increasing, decreasing, positive, and negative. In Algebra 1, Lesson 9-1, students determine maximum or minimum values of quadratic equations. In Algebra 2, Lesson 2-2, students examine a table of values depicting the change in height of a kicked football, describe symmetry in the graph of the table, and interpret what the symmetry implies about the ball. In Algebra 2, Lesson 2-3, students estimate the relative maxima and minima using a table of values. In Algebra 2, Lesson 9-5, students find the amplitude and period of trigonometric functions and graph the functions.
  • F-IF.7b: In Algebra 1, Lesson 3-7, students graph step functions and piecewise-defined functions. In Algebra 1, Lesson 3-8, students graph absolute value functions. In Algebra 2, Lesson 2-5, students graph step functions, piecewise-defined functions, and absolute value functions. In Algebra 2, Lesson 5-4, students graph square root functions. In Algebra 2, Lesson 5-5, students graph cube root functions.
  • G-CO.12: In Geometry, Lessons 1-2, 1-3, and 1-4, students work with the definition of constructions to copy a segment using a compass, construct a segment bisector, copy an angle, and construct an angle bisector using a straightedge and compass. In Geometry, Extend 1-5, students follow instructions to construct “a line perpendicular to a given line through a point on the line, or through a point not on the line.” Students use constructions to observe similarities between two constructions. Students also compare perpendicular bisector constructions to segment bisector constructions. In Geometry, Explore 2-7, students use dynamic geometric software to construct parallel lines and a transversal to explore angles. In Geometry, Lesson 2-9, the instructions for constructing parallel lines through a point not on the line is provided within the materials. In Geometry, Extend 3-5, students explore constructions of parallel lines and perpendicular bisectors using a reflective device.
  • G-SRT.5: In Geometry, Lesson 4-2, students prove triangles are congruent using two-column proofs and students calculate missing values in congruent figures. In Geometry, Lessons 4-3 and 4-4, students prove triangles are congruent using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side congruence criteria, and students calculate values using congruent triangles. In Geometry, Lesson 4-5, students write two-column proofs to prove right triangles are congruent. In Geometry, Lesson 7-3, students prove triangles are similar using the Angle-Angle Similarity Criteria and students identify triangles as similar or not similar. If the triangles are similar, students calculate missing measures within each problem. In Geometry, Lesson 7-4, students prove triangles similar using Side-Side-Side or Side-Angle-Side similarity criteria and students use similar triangles to solve real-world scenarios.
  • S-ID.6a: In Algebra 1, Lesson 4-4, students create scatter plots to determine a relationship between the variables in a set of data and draw a line of best fit to create an equation in slope-intercept form best representing the data. In Algebra 1, Lesson 4-6, students write regression equations to represent data and use the equations to make estimations.

The materials do not attend to the full intent of the following standards:

  • F-LE.3: In Algebra 1, Extend 9-8, students determine if a table of values represents a linear, quadratic, or exponential regression equation. Students are given instructions on how to use a graphing calculator to determine the regression equations. Students are not provided an opportunity to observe that a quantity increasing exponentially will eventually exceed a quantity increasing linearly or quadratically.

Indicator 1a.ii

The materials attend to the full intent of the modeling process when applied to the modeling standards.
0/2
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Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series do not meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The instructional materials do not include some aspects of the modeling process across the series and students do not complete the entire modeling cycle independently due to excessive scaffolding. While aspects of the modeling process are present within the series, students do not make assumptions or develop their own solution strategies. Students analyze application problems and real-world scenarios, but the variables, parameters, units, and/or equations are frequently identified within the problems. Examples of students not completing the entire modeling cycle include: 

  • In Algebra 1, Chapter 1 Project, Want to be Your Own Boss, students develop a business plan as an entrepreneur. Students research challenges and factors involved in creating a business. Students write expressions representing rent, salary per employee, and other expenses. Students do not formulate their own variables as the materials state, “in terms of months m, employees x, or both months and employees.” Students also write expressions representing operating costs to evaluate costs for months with employees (A-CED.1). After the business plan is complete, students evaluate peer business reports to determine if the plans are valid based on the guidelines given within the rubric and description of the plan. Finally, students report, using presentation software, their business plans to their peers.
  • In the Geometry Interactive Student Guide (ISG), Spherical Geometry, students use a diagram with approximate dimensions of a liquid propane tank containing five gallons of propane when full. Students identify a solid that models the tank in order to use the formula of the solid to calculate volume. The materials state, “Let h represent the height of propane left in the tank at any time and g represent the gallons of propane remaining. If the ratio of h to 14 is always equal to the ratio of g to 5, express h in terms of g” (A-CED.4). Students do not formulate variables independently or make assumptions about the problem. A second diagram of the fuel gauge showing the amount of propane in the tank is given. Students express the angle the pointer makes with the empty marker in terms of the volume of the fuel in the tank, g, and the height of the fuel in the tank, h (G-GMD.3, G-MG.1). Students validate the reasonableness of the answer and compute whether or not there is enough propane for a cookout.
  • In the Algebra 2 ISG, Performance Task, A Complicated Greeting, students use technology to sketch a graph of the function $$p(t)=[\frac{-152}{65}\vert t-65 \vert+152]sin(\frac{9\pi}{130}t)+152$$. Students determine the maximum height of the Bungee Drop and write a function for the vertical height of a Ferris wheel with a radius of 150 feet and the lowest point at 4 feet. Students do not formulate variables as the materials state, “Write a function for the vertical height h of a point on the wheel at a certain time t such that it starts at a height of 4 feet.” Students calculate the number of times the two rides will reach the same height during three minutes of riding. Students do not make assumptions but are instructed to assume the rides are continuous. Students also do not validate or report their findings (F-TF.5).
  • In Algebra 2, Lesson 8-6, the materials state, “Find a set of real-world data that appears to be normally distributed.” Students use the data to calculate the range of values associated with the distributions. Students do not make assumptions about the data but are told it must be normally distributed. Students also do not validate, report, or interpret the data (S-ID.4).

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 the Glencoe Traditional series meet expectations for, when used as designed, spending the majority of time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs, and careers. The Interactive Student Guide (ISG) offers additional time on the WAPs, but there is no pacing guide to instruct teachers on its use. Examples of how the materials enable students to spend the majority of their time on the WAPs include: 

  • N-Q.1: In Algebra 1, Lesson 2-6, students determine the distance in centimeters when given the scale that 2 centimeters = 120 miles. Students calculate the actual height of a space shuttle from a model that is 110.3 inches tall when 1 inch equals 1.67 feet.
  • A-SSE: In the Algebra 1 ISG, Variables and Expressions, students interpret the expression 8x+12.5y+6 by explaining what the coefficients and terms represent (A-SSE.1a). In Algebra 1, Lessons 7-1, 7-2, and 7-3, students apply the properties of exponents to rewrite expressions. In Algebra 2, Lesson 3-4, students rewrite expressions by factoring and, in Lesson 3-5, students rewrite functions in vertex form to identify the vertex (A-SSE.2). In the Algebra 1 ISG, Solving by Factoring, students calculate the zeros of quadratic functions by factoring (A-SSE.3a).
  • F-IF.6: In Algebra 1, Lesson 3-3, students calculate the rate of change given ordered pairs or a graph. In Extend 7-9, students calculate the average rate of change of exponential functions. In Algebra 2, Lesson 1-3, students use a table showing Lisa’s temperature during a 3-day illness to calculate the average rate of change, determine if the answer is reasonable, and explain what the rate means.
  • G-CO.9: In Geometry, Lesson 2-6, students prove the Supplement Theorem, the Complement Theorem, the Reflexive Property of Angle Congruence, the Transitive Property of Angle Congruence, and Right Angle Theorems. In the Geometry ISG, Proving Theorems About Angles, students write a paragraph proof for the Vertical Angle Theorem, the Supplement Theorem, and the Complement Theorem. In Geometry, Lesson 2-7, students write a two-column proof for the Alternate Exterior Angles Theorem and the Consecutive Interior Angles Theorem. In the Geometry ISG, Angles and Parallel Lines, students prove the Alternate Interior Angle Theorem by completing a chart and students complete a paragraph proof of the Perpendicular Transversal Theorem.
  • S-IC.1: In Algebra 2, Lesson 8-1, students determine reasonable inferences and bias that might affect the validity of inferences based on random samples of data.

Indicator 1b.ii

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

The instructional materials reviewed for the Glencoe Traditional series meet expectations for, when used as designed, letting students fully learn each non-plus standard. Although students fully learn many non-plus standards within the lessons, there are some non-plus standards which are minimally addressed within the lessons or are only available within the Interactive Student Guide (ISG).Examples of students fully learning the non-plus standards include:

  • N-CN.2: In Algebra 2, Lesson 3-3, students use the relation $$i^2=-1$$ and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. In the Algebra 2 ISG, Real and Complex Numbers, students use the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  • A-CED.1: In Algebra 1, Lessons 2-1, 2-2, 2-3, and 2-4, students create linear equations in one variable and use them to solve problems. In Algebra 1, Lessons 5-1, 5-2, 5-3, 5-4, and 5-5, students create linear inequalities in one variable and use them to solve problems. In Algebra 1, Lesson 9-3, students write a quadratic equation representing the height of an object in terms of time and use the equation to calculate how long the object stays in the air. In Algebra 1, Lesson 9-6, students create an equation representing the area of text covering three-fourths of a poster and solve the equation using the quadratic formula to determine the margins of the poster. In Algebra 2, Lesson 1-1, students create linear equations in one variable and use the equation to solve problems. In the Algebra 2 ISG, Solving by Factoring, students create quadratic equations in one variable and factor the equations to solve problems. In Algebra 2, Lesson 6-2, students write an exponential function to represent a 2015 investment of $10,000 that grows to $16,960 by 2027 and use the function to determine the amount of money after a set number of years. In Algebra 2, Lesson 7-6, students create rational equations and inequalities in one variable to solve problems.
  • A-REI.6: In Algebra 1, Lesson 6-1, students solve systems of linear equations by graphing. In Extend 6-1, students use graphing calculators to solve systems of linear equations. In Algebra 1, Lesson 6-2, students solve systems of linear equations by substitution. In Lessons 6-3 and 6-4, students solve systems of linear equations by elimination. In Algebra 1, Lesson 6-5, students determine the best method to solve systems of linear equations and solve them. In Extend 6-5, students solve systems of equations using augmented matrices.
  • F-IF.7a: In Algebra 1, Lesson 3-1, students calculate x- and y-intercepts to graph linear equations. In the Algebra 1 ISG, Graphing Linear Functions, students graph linear functions and identify the intercepts. In Algebra 1, Lesson 9-1, students identify intercepts, maximum or minimum values, domain, and range, and students graph quadratic functions. In the Algebra 1 ISG, Graphing Quadratic Functions, students graph quadratic functions and identify the intercepts and the maximum or minimum value of the functions.
  • F-TF.5: In Algebra 2, Lesson 9-5, students write trigonometric functions for real-world scenarios. In the Algebra 2 ISG, Graphing Trigonometric Functions, students determine the amplitude and period of the possible sine or cosine function representing the height above or below the axle of a ferris wheel at a state fair. Within the scenario, students find the value of f(0) to determine if the function has the form of $$f(\theta)=asinb\theta$$ or $$f(\theta)=acosb\theta$$. Students also write the trigonometric function and graph the function on the coordinate grid.
  • G-CO.3: In the Geometry ISG, Symmetry, students identify rotational symmetry of a rectangle, parallelogram, isosceles trapezoid, and regular pentagon. Students determine the order and magnitude of symmetry for each figure. Students describe rotations of an equilateral triangle, a scalene triangle, and a regular hexagon that will map the figure onto itself. Students identify lines of reflectional symmetry in a rectangle, parallelogram, isosceles trapezoid, and a regular pentagon. Students also sketch graphs from a given description of the symmetry.
  • G-GPE.2: In Geometry, Lesson 9-8, students derive the equation of a parabola given the focus and directrix. In the Geometry ISG, Equations of Parabolas, students follow steps to derive the equation of a parabola with directrix y=-p and focus F(0,p). Students also derive equations of parabolas given a focus and directrix to graph the parabola.
  • S-ID.1: In Algebra 1, Lesson 10-2, students represent data through dot plots, bar graphs, and histograms, and from given sets of data, students create an appropriate graph of the data. In the Algebra 1 ISG, Performance Task, students make a box plot to represent the scores of two divers from 20 diving meets.

Examples of students fully learning standards through the ISGs include:

  • A-APR.1: In Algebra 1, Lesson 8-1, students add and subtract polynomials and in Lesson 8-2, students multiply polynomials. In the Algebra 1 ISG, Adding and Subtracting Polynomials, students determine if the set of polynomials is closed under addition, subtraction, and multiplication.
  • A-REI.1: In the Algebra 1 ISG, Equations, students explain each step in solving equations by using one or more mathematical properties.
  • F-TF.8: In the Algebra 2 ISG, Verifying the Pythagorean Identity, students verify the Pythagorean identity using a circle on a coordinate grid with a radius equal to 1.
  • G-SRT.1a: In the Geometry ISG, Dilations, students investigate properties of dilations using Geometer’s Sketchpad. In Geometry, Explore 7-1, students analyze the effect of dilations on figures.
  • G-GMD.1: In the Geometry ISG, Circles and Circumference, students give an informal argument for the formula of the circumference of a circle. In the Geometry ISG, Volumes of Prisms and Cylinders, students write a general formula used to find the volume of cylinders and students also give an informal argument for the formula of the volume of pyramids using Cavalieri’s Principle.
  • S-IC.5: In the Algebra 2 ISG, Designing a Study, students compare a control group and an experimental group of a memory test treatment. Students calculate mean scores of each group for comparison and use a calculator’s random number generator to decide if the differences between parameters are significant.

Students do not fully learn the following standard:

  • A-REI.10: In Algebra 1, Lesson 1-7, students do not demonstrate understanding that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. Instead, the materials state, “Every solution of the equation is represented by a point on a graph. The graph of an equation is the set of all its solutions, which often forms a curve or a line.” 

Indicator 1c

The materials require students to engage in mathematics at a level of sophistication appropriate to high school.
1/2
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Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The instructional materials regularly use age appropriate contexts and apply key takeaways from Grades 6-8, yet do not vary the types of real numbers being used. 

Examples where materials regularly use age appropriate contexts include:

  • In Algebra 1, Lesson 2-2, students write one-step equations representing job occupations. Students are given approximations from the Bureau of Labor and Statistics and write one-step equations representing the number of people employed in production and repair occupations.
  • In Geometry, Lesson 8-5, students complete a scenario involving two water slides 50 meters apart. The shorter slide has an angle of depression of 15 degrees and is approximately 15 meters tall. Students calculate the distance from the top of the tall water slide to the ground using characteristics of right triangles and angles of depression.
  • In Algebra 2, Lesson 6-10, students encounter a scenario involving population growth in the state of Oregon. Students write an exponential growth equation representing the scenario. Students use the equation to predict the population of Oregon in 2025 and the year Oregon will have a population of six million people.

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

  • In the Algebra 1 Interactive Student Guide (ISG), Modeling: Exponential Functions, students apply key takeaways from ratios and proportional relationships (7.RP.A) by interpreting key features of both linear and exponential functions (F-LE.5, F-IF.4).
  • In the Geometry ISG, Parts of Similar Triangles, students apply knowledge of proportional quantities (7.RP.2a) to explain how to calculate side lengths of similar triangles and prove triangle similarity (G-SRT.5).
  • In Geometry, Lessons 2-5, 2-6, 2-7, and 2-9, students apply key takeaways of angles and line relationships (8.G.5) to prove segment and angle relationships (G-CO.9).
  • In Algebra 2, Lesson 3-3, students perform operations on complex numbers (N-CN.1,2) using mathematical properties such as the commutative property of addition (6.EE.3).

Examples where materials do not vary the types of real numbers being used include:

  • In Algebra 1, Lesson 8-1, students add and subtract polynomials. Within the problem sets, students write a polynomial in standard form with a rational coefficient.
  • In the Algebra 1 ISG, Graphing Linear Functions, students interpret tables of linear models. All tables consist of integer x and y values, so students model real-world situations without interpreting or graphing non-integer values.
  • In Geometry, Lesson 9-5, students calculate angle measures and arc lengths using characteristics of secants and tangents. All given angle measures and arc lengths are whole numbers. Students do not calculate using fractions or decimal values.
  • In the Geometry ISG, Translations, students describe translations using mapping functions and translate figures given translation vectors. The translation vectors consist of integers, except for one translation vector with a decimal value of -2.5.
  • In Algebra 2, Lesson 2-5, students graph piecewise, absolute value, and step functions. Students also write functions based on graphs. The majority of the functions utilize integer coefficients and constants, except for the decimal values of 0.5 and -0.5.
  • In the Algebra 2ISG, Analyzing Graphs of Polynomial Functions, students complete a chart with integer x-values using the function $$f(x)=2x^3-7x^2+4x+4$$ and students graph polynomial functions given characteristics of polynomials. The majority of the polynomial characteristics involve integer values. Students graph one polynomial function with a relative maximum at x = -2.5.

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.
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Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for being mathematically coherent and making meaningful connections in a single course and throughout the series. The materials include meaningful connections in a single course and throughout the series, but the materials also omit some connections in a single course or throughout the series. The materials identify connections within the series by listing prior standards addressed at the beginning of each chapter and lesson and each chapter begins with Then-Now statements connecting prior learning to expected learning for each lesson.

Examples where the materials foster coherence through meaningful mathematical connections in a single course or throughout the series include:

  • In Geometry, Teacher Edition, Lesson 4-7, Track Your Progress, a chart is given with Then-Now statements. Teachers are provided the standards used within the lesson (G-CO.10, G-GPE.4) and the standards connected to the lesson (G-CO.7,8).
  • In the Algebra 2 ISG, Solving Quadratic Equations by Graphing, students graph quadratic equations to find solutions and in the Algebra 2 ISG, Solving by Factoring, students solve quadratic equations by factoring. In the Algebra 2 ISG, Solving by Using the Quadratic Formula and the Discriminant, the materials state, “You have solved some quadratic equations by graphing, by factoring, and by completing the square” (F-IF.8a; A-SSE.2) and students solve quadratic equations by using the quadratic formula. (N-CN.7; A-SSE.1b)
  • In Algebra 1, Lesson 2-1, students write and solve equations in one variable (A-CED.1). In Geometry, Lesson 2-7, students find the value of the variable in the figure given parallel lines and a transversal by writing and solving equations in one variable (G-CO.9, A-CED.1).
  • In Algebra 1, Lessons 6-1, 6-2, 6-3, and 6-4, students use substitution, elimination, and graphing to solve systems of equations (A-REI.6). In Algebra 1, Lesson 9-7, the materials state, “Like solving systems of linear equations, you can solve systems of linear and quadratic equations by graphing the equation on the same coordinate plane.” Students make connections between methods of solving systems of linear equations with solving systems of linear and quadratic equations. Students also solve systems of linear and quadratic equations graphically or algebraically (A-REI.7).

Examples where the materials do not foster coherence by omitting some appropriate and required connections in a single course or throughout the series include:

  • In Geometry, Lessons 3-1, 3-2, and 3-3, students transform figures by reflection, rotation, translation, and dilation (G-CO.A,B). In Algebra 2, Lesson 2-6, students perform and describe transformations of parent functions (F-BF.3). There is no connection made to the transformations in the previous course.
  • In Algebra 2, Lesson 3-2, students solve quadratic equations by graphing (A-REI.4). There is no connection made to Algebra 1, Lesson 9-3, where students also solve quadratic equations by graphing. Many of the examples in both lessons are identical.
  • In Algebra 1, Lesson 9-5, students solve quadratic equations by completing the square (A-REI.4b). In Geometry, Lesson 9-7, students create equations of circles by completing the square (G-GPE.1). In Algebra 2, Lesson 3-5, students solve quadratic equations by completing the square involving real and complex solutions (A-REI.4b). There is no connection made between the courses involving completing the square.

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 the Glencoe Traditional series do not meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The instructional materials do not allow students to extend their previous knowledge by making  connections between Grades 6-8 and high school concepts.

Throughout the series, the materials provide Track Your Progress sections in the Teacher Edition. These include the Mathematical Background needed for the lesson as well as a Then-Now-Next chart. The chart provides previous standards connected to the lesson, standards taught within the lesson, and standards being taught in the future. Some of the standards from Grades 6-8 are listed, but standards from Grades 6-8 are often presented as new standards for students to learn. The following examples are examples where the materials do not explicitly identify and/or build upon standards from Grades 6-8:

  • In Algebra 1, Lesson 1-2, students use order of operations to evaluate equations and simplify expressions. There is no connection made to students applying properties of operations to expand expressions (7.EE.1). Order of operations is presented as a new standard and students are given the steps of the order of operations within a Key Concept chart.
  • In Algebra 1, Lessons 2-2, 2-3, and 2-4, students solve one-step, two-step, and multi-step equations in one variable. There is no connection made to students solving equations in one variable (8.EE.7).
  • In Algebra 1, Lesson 5-1, students write and solve inequalities with one variable. There is no connection made to constructing simple inequalities in one-variable (7.EE.4).
  • In Algebra 1, Lessons 6-1 through 6-4, students solve systems of equations using graphing, substitution, or elimination. There is no connection made to 8.EE.8 in which students solve pairs of simultaneous linear equations.
  • In Geometry, Lessons 3-1, 3-2, and 3-3, students perform transformations on geometric figures. There is no connection made to the effects of transformations on two-dimensional figures (8.G.A).
  • In Geometry, Lesson 8-2, students use the Pythagorean Theorem and its converse to solve problems. There is no connection made to 8.G.7 in which students apply the Pythagorean Theorem and its converse to calculate unknown side lengths of right triangles. Within the same lesson, students prove the converse of the Pythagorean Theorem and students are provided with a proof of the Pythagorean Theorem using geometric mean. There is no connection made within the lesson to proving the Pythagorean Theorem (8.G.6).

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.
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Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series explicitly identify several of the plus standards, but the materials do not use the plus standards to coherently support the mathematics which all students should study in order to be college and career ready.

The following plus standards are fully addressed within the series: 

  • N-CN.3: In Algebra 2, Lesson 3-3, students simplify quotients of complex numbers by using complex conjugates.
  • N-CN.8: In Algebra 2, Lessons 3-4, 3-5, and 3-6, students extend polynomial identities to complex numbers.
  • N-CN.9: In Algebra 2, Lesson 4-9, students use the Fundamental Theorem of Algebra with quadratic polynomials to determine the number and types of roots.
  • N-VM.2,3: In the Geometry ISG, Directed Line Segments and Vectors, students write the component form of vectors, and students solve problems involving speed and direction by drawing a vector to represent the situation. 
  • A-APR.5: In Algebra 2, Lesson 4-2, students apply the Binomial Theorem to expand binomials. 
  • A-APR.7: In Algebra 2, Lesson 7-1, students multiply and divide rational expressions. In Algebra 2, Lesson 7-2, students add and subtract rational expressions.
  • F-IF.7d: In Algebra 2, Lesson 7-4, students graph rational functions and identify zeros and asymptotes when suitable factorizations are available.
  • F-BF.1c: In Algebra 2, Lesson 5-2, students evaluate compositions of functions and compose functions representing real-world scenarios.
  • F-BF.4b,4d: In Algebra 2, Lesson 5-3, students verify that two functions are inverses using composition and students restrict the domain in order to write the inverse function.
  • F-BF.5: In Algebra 2, Lesson 6-4, students write the inverse for exponential functions and logarithmic functions.
  • F-TF.7: In Algebra 2, Lesson 10-5, students use inverse functions to solve trigonometric equations.
  • G-SRT.9,10: In the Geometry ISG, The Law of Sines and Law of Cosines, students derive the area of a triangle by drawing an auxiliary line. Students also prove the Law of Sines and the Law Cosines and use them to solve problems.
  • G-SRT.11: In Geometry, Lessons 8-6 and 8-7, students apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
  • G-C.4: In Geometry, Lesson 9-5, students draw a common tangent line for two circles by constructing a tangent line from a point outside a given circle to the circle.
  • S-MD.6,7: In Algebra 2, Lesson 8-7, students use probabilities to make fair decisions and analyze decisions and strategies using probability concepts.
  • S-CP.8: In Geometry, Lesson 12-5, students apply the general Multiplication rule and interpret their solutions in terms of the model.
  • S-CP.9: In Geometry, Lesson 12-3, students are given the definition for permutation and combination. Students also use permutations and combinations to solve problems.

The following plus standards are partially addressed within the series:

  • N-VM.1,4a: In the Geometry ISG, Directed Line Segments and Vectors, the materials state, “A vector is a quantity that has both a direction and a magnitude.” Students determine the magnitude and direction of vectors and sketch vectors to interpret real-world problems. Students add vectors but do not subtract vectors.
  • F-TF.3: In Algebra 2, Lesson 9-1, students use special right triangles to determine geometrically the values of sine, cosine, and tangent. Students do not use the unit circle to express the values of sine, cosine, and tangent.
  • F-TF.4: In Algebra 2, Lesson 9-4, students identify the periodicity of trigonometric functions, but do not use the unit circle to explain symmetry.

The following plus standards are not addressed in the series:

  • N-CN.4,5,6
  • N-VM.4b,4c,5-12
  • A-REI.8,9
  • G-GPE.3
  • G-GMD.2
  • S-MD.1-5b

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

Criterion 2a - 2d

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.
7/8
+
-
Criterion Rating Details

The instructional materials reviewed for the Glencoe Traditional series meet expectations for Rigor and Balance. The materials provide students opportunities to independently demonstrate conceptual understanding, procedural skills, and application, and the materials partially balance the 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
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.The instructional materials develop conceptual understanding and provide opportunities for students to independently demonstrate conceptual understanding and most of the opportunities for students to develop conceptual understanding are located in the Interactive Student Guides (ISG). 

Examples of the materials developing conceptual understanding and students independently demonstrating conceptual understanding include: 

  • A-APR.1: In the Algebra 1 ISG, Adding and Subtracting Polynomials, students compare the behavior of polynomials to integers under addition and subtraction and write a conjecture describing closure under addition and subtraction of polynomials. In the Algebra 1 ISG, Multiplying a Polynomial by a Monomial, students determine if polynomials are closed under multiplication by proving the product of a monomial and a polynomial is a polynomial.
  • A-REI.11: In the Algebra 2 ISG, Solving Polynomial Equations, students use a graphing calculator to sketch $$f(x)=x^4-2x-5$$ and $$g(x)=-x^6+3x^2+3$$ and estimate the points of intersection. The materials state, “Explain the algebraic significance of a point of intersection on the graphs of f(x) and g(x).” Within the same lesson, students critique the reasoning of a student who claims two functions have no solutions due to no intersections and explain the reasoning behind their critique.
  • F-LE.1: In the Algebra 1 ISG, Analyzing Functions with Successive Differences, students complete a table of values for a linear function, a quadratic function, and an exponential function. Students compare charts with other students in order to make conjectures about each function. Students “look for connections between different function types and their successive differences and successive ratios.” Throughout the lesson, students explain connections between the type of function and the model of the scenario.
  • G-SRT.6: In the Geometry ISG, Trigonometry, students explore ratios in similar triangles by using Geometer’s Sketchpad. Students explain what they notice about side lengths when changing the size of the triangle. Students also examine two triangles with different side lengths and congruent angles to “explain why $$\frac{BC}{AB}=\frac{EF}{DE}$$. What does this tell you about any right triangle with a 37° angle.” From the task, students determine trigonometric ratios for right triangles with an acute angle.
  • S-CP.5: In the Geometry ISG, Conditional Probability, students are given a scenario where event A represents owning a house and event B represents owning a car. Students must determine if the events are independent or dependent as well as compare the P(A|B) to P(B|A). After making the comparison, students must explain their reasoning using precise vocabulary.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe 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 throughout the series and students independently demonstrate procedural skills across the courses. 

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

  • A-SSE.2: In Algebra 1, Lesson 8-5, students rewrite quadratics into equivalent factored forms. Students use the distributive property and factoring by grouping in order to rewrite quadratic expressions and polynomials.
  • A-APR.3: In Algebra 2, Lesson 4-9, students factor polynomials to calculate the number and type of roots and sketch graphs based on the zeros. Students also match an appropriate graph to a given zero.
  • F-IF.7e: In Algebra 2, Lesson 6-1, students graph exponential functions and state the domain and range of the function. In Algebra 2, Lesson 6-4, students graph logarithmic functions independently. In Algebra 2, Lesson 9-6, students graph trigonometric functions after identifying amplitude, period, vertical shift, and the equation of the midline.
  • G-GMD.3: In Geometry, Lesson 11-2, students calculate the volume of different prisms, cylinders, and composite solids. In Geometry, Lesson 11-2, Preparing for Assessment, students calculate the volume of various three dimensional shapes.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series meet expectations for supporting the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially when called for in specific content standards or clusters. Students engage in routine and non-routine applications of mathematics throughout the series and demonstrate the use of mathematics flexibly in a variety of contexts.

Examples of students engaging in routine and non-routine application of mathematics and demonstrating the use of mathematics flexibly in a variety of contexts include: 

  • F-TF.5: In Algebra 2, Lesson 9-6, students solve a non-routine application by writing a trigonometric function to model the movement of carousel horses according to a list of provided constraints. Students also consider how to make changes to their function if the characteristics of the carousel change.
  • G-SRT.8: In the Geometry ISG, Angles of Elevation and Depression, students use trigonometric ratios to write a formula to calculate the height of a rock formation knowing the height of a geologist is 1.8m. Students also calculate the width of a lake given a helicopter with an altitude of 450 meters and two angles of depression.
  • G-MG.2: In Geometry, Lesson 11-7, students determine a solid with the greatest density when given certain conditions. The materials state, “A cylinder and a sphere have the same mass. The height of the cylinder is equal to its radius. The radius of the sphere is equal to the radius of a cylinder.” Students determine the greater density and explain their reasoning.
  • S-ID.2: In the Algebra 1 ISG, Comparing Sets of Data, students plan a vacation based on weather history. Students examine two charts showing the rainy days over a 10-year period. Students use the data to “determine the shape of each distribution and use the appropriate statistics to find the center and spread for each set of data.” Students provide advice on the better place to visit for vacation and explain their reasoning.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially 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 in the materials, but there is over-emphasis of one of the three aspects of rigor. The majority of the lessons in the materials address procedural skills and some address application. Students complete series of examples addressing procedural skills followed by an application. Students also complete Check Your Understanding, Practice and Problem Solving, and Higher Order Thinking (HOT) Problems. The ISG develops conceptual understanding and students also complete a practice section within the ISG focused on conceptual understanding.

Examples of the materials over-emphasizing procedural skills include:

  • In Algebra 1, Lesson 5-3, and the ISG, Solving Multi-Step Inequalities, students write and solve multi-step inequalities (A-CED.1; A-REI.3). Most of the examples in the lesson involve procedural skills and, in the Check Your Understanding and Practice and Problem Solving, procedural skills are also primarily addressed with an application. In the ISG, students complete problems that develop conceptual understanding by justifying their steps, critiquing the reasoning of a student, describing a method, and explaining if the solution is reasonable.
  • In Algebra 1, Lesson 7-5, the materials address graphing exponential functions and identifying data that is exponential (F-IF.7e; F-LE.5). Three of the four examples emphasize procedural skills and Example 3 is an application for students to graph and interpret. In Check Your Understanding and Practice and Problem Solving, most of the problems develop procedural skills and there are a few, real-world applications. The corresponding ISG lesson, Exponential Functions, states the objectives are “creating exponential functions to model relationships between quantities” and “graph exponential equations on a coordinate plane.” Students develop conceptual understanding in the ISG lesson by writing exponential equations, interpreting different parts of the equation, using data in real-world context to explain why an exponential equation should be used, graphing exponential equations, and interpreting parts of the graphs in context.
  • In Geometry, Lesson 3-1, and the ISG, Reflections, students draw and identify reflections (G-CO.4,5). In the lesson, there are five examples, four of which emphasize procedural skills. Example 2 uses real-world context to minimize distance using a reflection. In the Check Your Understanding and Practice and Problem Solving, procedural skills are utilized in the majority of the problems. In the ISG, students develop the definition of reflection and the rules for mapping reflections through conceptual understanding and students construct arguments while identifying transformations that are reflections. The Practice in the ISG emphasizes conceptual understanding as students describe, critique, and construct arguments.
  • In Geometry, Lesson 7-6, and the ISG, Parts of Similar Triangles, students prove theorems about triangles, use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures (G-SRT.4,5). In the lesson, two of the three examples emphasize procedural skills and the third example is an application. The example problems address finding side lengths with one correct solution and answer. In Check Your Understanding and Practice and Problem solving, students utilize procedural skills to find the value of a variable (side length) in the majority of the problems. In the ISG, students utilize Geometer’s Sketchpad to investigate parts of similar triangles and find patterns, make conjectures, describe steps to be used in a proof, calculate, and explain their solutions.
  • In Algebra 2, Lesson 4-6, students solve polynomial equations (A-CED.1) using procedural skills. Five of the six examples emphasize procedural skills and the sixth example is an application. In Check Your Understanding and Practice and Problem Solving, the majority of the problems require a numerical answer. As with each lesson, there are HOT Problems with five questions. In the ISG lesson, Solving Polynomial Equations, students examine a polynomial function in a real-world context, graph the function, and explain various aspects of the polynomial. Students use a graphing calculator to graph polynomials in order to approximate solutions. Also in the ISG lesson, students “explain the algebraic significance of a point of intersection on the graphs of f(x) and g(x)” and relate that to solving the equation f(x) = g(x). In Practice for the ISG lesson, students explain their reasoning, explain different methods for solving polynomials, and find two different equations given a graph.

Criterion 2e - 2h

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/8
+
-
Criterion Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for Practice-Content Connections. The materials intentionally develop the following mathematical practices to their full intent: make sense of problems and persevere in solving them (MP1), reason abstractly and quantitatively (MP2), construct viable arguments and critique the reasoning of others (MP3), model with mathematics (MP4), attend to precision (MP6), look for and make use of structure (MP7), and look for and express regularity in repeated reasoning (MP8). The materials do not intentionally develop MP5, use appropriate tools strategically, to its full intent.

The materials also contain misleading identifications of the MPs across the series, and due to these, 1 point is deducted from the scoring of indicator 2e. Examples of the misleading identifications include:

  • MP1: In Algebra 1, Lesson 8-5, students factor polynomials, but they do not persevere, check answers with different methods, or determine if their answers make sense.
  • MP2: In Geometry, Lesson 2-6, students identify which terms are accepted without proof. Students need to know definitions in order to answer the problem, but they do not reason abstractly or quantitatively.
  • MP3: In Algebra 2, Lesson 2-1, students create graphs that represent scenarios such as the height of a baseball, the speed of a car, the height of a person, or the temperature on a typical day. Students do not construct viable arguments or critique the reasoning of others.
  • MP4: In Algebra 1, Lesson 9-4, students use the equation h=-16t$$^2$$+24t, which represents the height of a soccer ball, to determine the possible answers for t if h=0. Students do not make assumptions or create a model for mathematics as they are given the equation and solve it. In Algebra 1, Lesson 10-2, students create dot plots, bar graphs, or histograms based on a given data set. Students do not analyze the relationships within the models or solve problems based on the models.
  • MP6: In Geometry, Lesson 3-1, the materials state, “The image of a point reflected in a line is always, sometimes, or never located on the other side of the line of reflection.” Students do not attend to precision as they choose the correct word to complete the statement.
  • MP7: In Geometry, Lesson 2-9, students calculate the value of x when given expressions of two corresponding angles. Students identify the angles as acute, right, obtuse, or not enough information. Students do not look for and make use of structure. 
  • MP8: In Algebra 1, Lesson 9-8, students select tables of data to best model exponential equations. Students select appropriate models instead of evaluating the reasonableness of their results.

Indicator 2e

The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for supporting the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards. The majority of the time MP1 and MP6 are used to enrich the mathematical content and are intentionally developed to reach the full intent of the MPs.

Throughout the materials, the MPs are identified in multiple places, but there are examples of misleading identifications for each MP across the courses of the series. Examples of the misleading identifications are listed in the criterion report for Practice-Content Connections, and as a result of those, 1 point is deducted from the scoring of this indicator.

Examples of MP1 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

  • In Algebra 1, Lesson 6-4, students make sense of problems by writing a system of linear equations given a verbal description. Students persevere in order to solve the system of linear equations using elimination.
  • In Geometry, Lesson 2-8, students make sense of problems and persevere by determining alternate ways for creating an equation of a line. Students calculate the slope of a line given points or a graph and students must determine if lines are parallel, perpendicular, or neither.
  • In Algebra 2, Lesson 3-4, students make sense of problems to determine dimensions of different shapes. Teachers encourage students to check their solutions using different methods and determine if their answers make sense.

Examples of MP6 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

  • In the Geometry ISG, Symmetry, students determine which tiles have symmetry. Students communicate precisely by justifying answers using definitions of symmetry and students describe reflectional and rotational symmetry of figures. Students also attend to precision by using correct terminology to communicate the types of symmetry.
  • In the Geometry ISG, Congruence, students determine if figures are congruent. Students “use precise language to justify your answer.”
  • In the Algebra 2 ISG, Distribution of Data, students draw a histogram to represent data on the wingspan of insects. Students describe the shape of the data set and what it means for the data to be skewed. Students also communicate precisely to explain what the data shows about the wingspan.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe 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. The majority of the time MP2 and MP3 are used to enrich the mathematical content and are intentionally developed to reach the full intent of the MPs. 

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

  • In Algebra 1, Chapter 8 Performance Task, students write expressions to represent different perimeters and areas of swimming pools, hot tubs, and lap pools. Students reason abstractly and quantitatively while computing both perimeters and areas.
  • In the Geometry ISG, Dilations, students use a figure representing an architect’s plan for a bedroom where one unit is equal to one foot. Students enlarge or reduce the size of the bedroom based on given perimeters. Students also “write an equation that can be used to find the scale factor (x) of a dilation given any perimeter (y).” Students reason and make connections between the drawing and the physical dilation that will occur.
  • In Algebra 2, Lesson 6-1, students reason to write functions representing situations. Students determine if the function represents exponential growth or an exponential decay, identify the growth factor, and graph the function.

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

  • In Algebra 1, Lesson 2-5, students perform an error analysis on the work of fictional students. Students determine if the fictional students are correct and explain any error in their reasoning.
  • In the Geometry ISG, Proving Triangles Congruent ASA, AAS, the materials state, “Raj says that he can draw two triangles that have two sides and a nonincluded angle congruent and that the two triangles are congruent.” Students agree or disagree with Raj justifying his claim with the SSA Congruence Theorem and provide a counterexample to disprove Raj’s claim.
  • In the Algebra 2 ISG, Designing a Study, students analyze a study on cat food and weight gain. Students calculate the mean weight of the cats and determine if the difference in weights is significant or not. Students construct an argument to explain their reasoning.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe Traditional series partially meet expectations for supporting the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards. The majority of the time MP4 is used to enrich the mathematical content and is intentionally developed to reach the full intent of the MP, but the materials do not not develop MP5 to its full intent as students do not choose appropriate tools strategically.

Examples of MP4 being used to enrich the mathematical content and intentionally developed to reach the full intent of the MP include:

  • In Algebra 1, Lesson 9-5, students determine the dimensions of a painting after it is increased in size. The materials state, “the increase in the length is 10 times the increase in the width.” Students draw a model or use an algebraic model to calculate the new dimensions of the painting.
  • In Geometry, Lesson 9-7, students write the equation of a circle to represent different scenarios.
  • In Algebra 2, Lesson 1-7, students model systems of inequalities by graphing in order to calculate multiple possible solutions.

Examples where the materials do not develop MP5 to its full intent include:

  • In Algebra 1, Extend 3-7, students graph piecewise linear functions. Students do not choose a tool as they are instructed to graph the function using a calculator.
  • In Geometry, Lesson 3-1, students “draw the reflected image in this line using a ruler.” Students do not choose a tool to draw the line.
  • In the Algebra 2 ISG, Graphing Exponential Functions, students determine the year a painting would be worth $750,000. Students do not choose a tool as they are instructed to use a calculator to determine the solution.

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
+
-
Indicator Rating Details

The instructional materials reviewed for the Glencoe 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. The majority of the time MP7 and MP8 are used to enrich the mathematical content and are intentionally developed to reach the full intent of the MPs.

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

  • In the Algebra 1 ISG, Solving Systems by Elimination, students explain two different pathways to solve a system of equations using elimination. Then students use one of the pathways described to calculate a solution to the system. In order to identify multiple solution pathways, students make use of structure to analyze the task.
  • In the Geometry ISG, Dilations, students dilate a triangle using different scale factors. Students make use of structure to find patterns when dilating with a scale factor less than 1, equal to 1, or greater than 1.
  • In the Algebra 2 ISG, Properties of Logarithms, students make use of structure to approximate solutions of $$log_{10}a=0.903$$ and $$log_{10}b=2.477$$ when given $$log_{10}2\approx0.301$$ and $$log_{10}3\approx0.477$$. Students approximate the solutions without the use of technology.

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

  • In the Geometry ISG, Angles and Arcs, students investigate the proportionality between arc length and the radius of a circle. Students calculate arc lengths for circles of different radii in order to generalize the relationship between arc length and radius.
  • In the Geometry ISG, Similar Triangles, students solve equations for the scale factor in order to write equal ratios. Students “state a generalization based on your findings.”
  • In the Algebra 2 ISG, Real and Complex Numbers, students use a calculator to find the values of (1+i)$$^2$$(1+i)$$^4$$, (1+i)$$^6$$(1+i)$$^8$$, (1+i)$$^10$$,(1+i)$$^12$$. Students also calculate the solution of (1+i)(1+iwithout using a calculator. Students use repeated reasoning to generalize a solution pathway of (1+i)$$^4$$ without using a calculator.

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

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.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

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.
N/A

Indicator 3d

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

Indicator 3e

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

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

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.
N/A

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.
N/A

Indicator 3i

Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.
N/A

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).
N/A

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.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.
N/A

Indicator 3n

Materials provide support for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

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).
N/A

Indicator 3v

Materials provide support for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

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

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

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

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.
N/A

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.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners.
N/A

Indicator 3ac.i

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
N/A

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.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
abc123

Additional Publication Details

Report Published Date: 10/22/2020

Report Edition: 2018

Title ISBN Edition Publisher Year
Glencoe Algebra 1 Student Print/Digital Bundle 9780078978791 McGraw-Hill Education 2018
Glencoe Algebra 2 Student Print/Digital Bundle 9780078978807 McGraw-Hill Education 2018
Glencoe Geometry Student Print/Digital Bundle 9780078978814 McGraw-Hill Education 2018
Glencoe Algebra 1 Guide Teacher Print/Digital Bundle 9780079056771 McGraw-Hill Education 2018
Glencoe Geometry Guide Teacher Print/Digital Bundle 9780079057532 McGraw-Hill Education 2018
Glencoe Algebra 2 Guide Teacher Print/Digital Bundle 9780079061492 McGraw-Hill Education 2018

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

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math HS Rubric and Evidence Guides

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

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

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

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.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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