Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for alignment. The materials spend the majority of the time on the major work of the grade, and the assessments are focused on grade-level standards. Content is aligned to the standards and progresses coherently across the grades and within each grade. The lessons include conceptual understanding, fluency and procedures, and application. There is a balance of these aspects for rigor. The Standards for Mathematical Practice (MPs) are used to enrich the learning.

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Partially Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
30
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for being focused on and coherent with the Common Core State Standards in Mathematics. The Unit Assessments do not assess above grade-level topics, and the instructional materials devote over 65 percent of class time to major work. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and will foster coherence between the grades. The materials explicitly relate grade-level concepts to prior knowledge from earlier grades, and the materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The materials did not include any assessment questions that were above grade-level.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for focus within assessment. Overall, the instructional material does not assess content from future grades within the assessment sections of each unit.

There are multiple Self-Assessments within each unit. Each assessment includes a scoring rubric that helps students articulate their understanding of key concepts being assessed. All assessments have answer keys provided in the Teacher Workbook.

On grade-level examples include:

  • Chapter 4 Section 4.1- Students demonstrate their knowledge of 8.EE.8 by graphing or solving simultaneous, linear equations by substitution or elimination. Question 3 on the Self-Assessment states: “One equation in a system of linear equations is ???? = −2???? + 4. a. Write a second equation for the system so that the system has only one solution.”
  • Chapter 5 Section 5.3- Students demonstrate their knowledge of 8.F.5 by analyzing and then describing a graph. Question 1 Concept 3 on the Self-Assessment states: “Below are two graphs that look the same. Note that the first graph shows the distance of a car from home as a function of time and the second graph shows the speed of a different car as a function of time. Describe what someone who observes the car’s movement would see in each case.”
  • Chapter 8 Section 8.2- Students demonstrate their knowledge of 8.EE.4 by subtracting, adding, multiplying, and dividing numbers in scientific notation and then converting the answer to standard form. Question 2a on the Self-Assessment states: “Change the numbers below into scientific notation. 3,450,000,000.” Question 2c states: “Change the number given below into standard form. 6.03 x 108.”

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for having students and teachers using the materials as designed, devoting the large majority of class time to the major work of the grade. Overall, the materials devote approximately 80 percent of class time to major work.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for focus by spending a majority of class time on the major clusters of the grade including all clusters in 8.EE, 8.F, 8.GA, and 8.G.b. To determine this, three perspectives were evaluated: 1) the number of chapters devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of weeks devoted to major work. Of the three perspectives, the number of lessons is most representative and was used to determine the score for this indicator.

Overall, the materials spend approximately 80 percent of instructional time on the major clusters of the grade. The Grade 8 materials have 10 chapters that contain 164 lessons, which accounts for a total 33 weeks of class time including Anchor Problems and Self-Assessments.

  • Grade 8 instruction is divided into 10 chapters. Approximately 8 out of 10 chapters (80 percent) focus exclusively on the major clusters of Grade 8, while the other 2 chapters focus primarily on supporting work that does not often support major work.
  • Grade 8 instruction consists of 139 lessons. Approximately 131 out of 164 lessons (80 percent) focus on the major clusters of the grade.
  • Grade 8 instruction is divided into 33 weeks. Approximately 24.5 out of 33 weeks (74 percent) focus exclusively on the major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for being coherent and consistent with the standards. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and fosters coherence between the grades. Content from prior or future grades is clearly identified, and the materials explicitly relate grade-level concepts to prior knowledge from earlier grades. The objectives for the materials are shaped by the CCSSM cluster headings, and they also incorporate natural connections that will prepare a student for upcoming grades.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The Instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the lessons that focus on supporting content also engage students in major work where natural and appropriate.

The following examples demonstrate where the supporting work enhances understanding of the major work of Grade 8.

  • Chapter 6: Section 6.1 focuses on fitting a straight line to the scatter plot. Students then write a prediction function for the line of best fit and explain the meaning of the slope and y-intercept of the function in context. This work uses 8.SP.A to support 8.F.A and 8.F.B.
  • Chapter 6: Section 6.2a and 6.2b uses 8.SP.A to support 8.EE through the use of trend lines and finding the line of best fit.
  • Chapter 7: In Activity 7.1a 8.NS.A supports 8.G.B. Through creating squares of different areas, the idea of the Pythagorean Theorem emerges as the sides of a right triangle form three squares and the two sides of a right triangle place together equals the longest side square.
  • Chapter 7: Activity 7.2a uses 8.NS.A to support 8.EE through students creating and solving expressions and equations based on powers and roots.
  • Chapter 7: Section 7.3 8.NS.A is used to support major work as it focuses on rational and irrational numbers. Under Concepts and Skills to be Mastered, it lists, “Know that the square root of a non-perfect square is an irrational number,” which is a part of 8.EE.2.
  • Chapter 10: This chapter links geometry with both number system and expressions and equations, 7.EE.4, as students write and solve Pythagorean Theorem equations where solutions are approximated.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The instructional materials are designed to take approximately 165 days. According to the publisher, completing the work would take a total of 33 weeks. (There is some discrepancy in the material regarding Chapter 3. The Chapter overview states that the Chapter is designed for 4 weeks, but the title of the Chapter folder indicates 3 weeks.) Completing the work includes days for Anchor Problems, Class Activities, and Homework. According to the Preface, “Each lesson covers classroom activity and homework for a 50-minute class. Sometimes the demands of the material exceed this limitation; when we recognize this, we say so; but some teachers may see different time constraints, and we defer to the teacher to decide how much time to devote to a lesson, how much of it is essential to the demands of the relevant standard. What is important are the proportions dedicated to the various divisions, so that it all fits into a year’s work. Within a lesson, the activities for the students are graduated, so that, in working the problems, students can arrive at an understanding of a concept or procedure. In most cases there is an abundance of problems, providing the teacher with an opportunity to adapt to specific needs.” The number of weeks was converted to days for this review. Each chapter has built-in days for Self Assessments. Overall, the amount of content that is designated for this grade level is viable for one school year.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
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Indicator Rating Details

The materials reviewed for The Utah Middle School Math Project Grade 8 meet the criteria for consistency with the progressions in the Standards. In general, materials develop according to the grade-by-grade progressions in the Standards and provide extensive work with grade-level problems. Materials consistently relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior and future grade levels is identified in Connections to Content at the beginning of each student and teacher workbook chapter. Chapter overviews/summaries, as well as section overviews, include written explanations of what students will be doing throughout the chapter. Summaries explain what students will learn and how they will use this knowledge in future learning.

  • Chapter 1: The Section 1.1 Overview explains that Section 1.1 “involves a review of algebraic expressions.” The teacher notes emphasize this further, telling teachers that the first section is 7th grade material and to work through it faster with an honors class or assign it as homework. (page 8WB1 - 8)
  • Chapter 2: “Students begin this chapter by reviewing proportional relationships from 6th and 7th grade, recognizing, representing, and comparing proportional relationships. In 8th grade, a shift takes place as students move from proportional linear relationships, a special case of linear relationships, to the study of linear relationships in general.” (page 8WB2 – 2)
  • Chapter 3: “In Chapter 5 students will solidify the concept of function, construct functions to model linear relationships between two quantities, and interpret key features of a linear function. This work will provide students with the foundational understanding and skills needed to work with other types of functions in future courses.” (page 8WB3 - 2)
  • Chapter 5: “This chapter builds an understanding of what a function is and gives students the opportunity to interpret functions represented in different ways, identify the key features of functions, and construct functions for quantities that are linearly related. This work is fundamental to future coursework where students will apply these concepts, skills, and understandings to additional families of functions.” (page 8WB5 – 2)

Materials consistently relate grade-level concepts explicitly to prior knowledge from earlier grades. Connections between concepts are addressed in the Connections to Content, chapter overviews/summaries, and Math Textbook. Examples of these explicit connections include:

  • Chapter 1, Math Textbook: “The first three chapters of grade 8 form a unit that completes the discussion of linear equations started in 6th grade and their solution by graphical and algebraic techniques.” (page 8MF1 - 1)
  • Chapter 6, Class Activity 6.1a: “Problems 1 and 2 provide students with an opportunity to connect what they have learned in 6th/7th grade with what they will learn in 8th grade. Problem 1 is a review of 6th and 7th grade content where students learned to display and analyze univariate data. Students have learned…In 8th grade, students connect this learning with bivariate data.” (page 8WB6 - 10)

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

In the teacher's workbook, the CCSSM are identified on the introduction page of each chapter. Each chapter correlates to a Grade 8 domain, with sections within the chapter focused on standards within the domain. There is a section titled “Concepts and Skills to Master" which identifies specific learning objectives for each section in the teacher, parent, and student workbooks.

  • The Chapter 4 Overview reflects 8.EE.C (Analyze and solve linear equations and pairs of simultaneous linear equations) as students work with and “discuss intuitive, graphical, and algebraic methods of solving simultaneous linear equations; that is, finding all pairs (if any) of numbers (x, y) that are solutions of both equations.” (page 8WB4 - 2)
  • In Chapter 5 Cluster 8.F.A students work with functions (define, evaluate, and compare functions). In Section 5.2 Explore Linear and Nonlinear Functions, students distinguish between linear and nonlinear functions given a context, table, graph, or equation. In Section 5.3 Model and Analyze Functional Relationships, the objective is to analyze functional relationships between two quantities given different representations.

The materials include problems and activities that serve to connect two or more clusters in a domain where connections are natural and important.

  • Chapter 3 Section 3.1 Classroom Activity 3.1f problems 1-6 include content from both 8.F.A and 8.F.B as students review the slope-intercept form of a linear equation and then use their understanding to model relationships between quantities. (page 8WB3 – 49)
  • Chapter 5 Section 5.3 Classroom Activity 5.3a connects 8.F.A and 8.F.B. Students construct functions to model linear relationships while they are comparing properties of functions that are represented in different ways. (page 8WB5 - 76)

The materials include problems and activities that serve to connect two more domains in a grade where connections are natural and important.

  • Chapter 2 Section 2.3d-g connects 8.EE.5 and 8.F.A as students determine the rate of change from graphs. Students compare the rates of graphs, compare the steepness of several lines on the same graph, and relate the steepness of the lines to their rates of change. (pages 8WB2 - 84, 8WB2 - 85 & 8WB2 - 126)
  • Chapter 8 Section 8.3 connects 8.EE.A and 8.G.C as students use square root and cube root symbols and evaluate square roots and cube roots while solving problems involving the volume of cylinders, cones, and spheres. (page 8WB8 - 72)

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for rigor and mathematical practices. The materials meet the expectations for rigor as they balance and help students develop conceptual understanding and procedural skill and fluency. The materials meet the expectations for mathematical practices as they identify and use each of the MPs and support the Standards' emphasis on mathematical reasoning.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 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 in all three aspects of rigor.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

Each chapter/section starts with an Anchor Problem which poses a mathematical situation that students will learn to solve. Many of these are conceptual in nature and also provide explicit connections to prior knowledge. For example, Chapter 3 Anchor Problem 3.0: Solutions to a Linear Equation specifically refer to prior learning from Chapter 1 involving writing and solving linear equations with one variable. Students then move on to more complex linear equations as the activity guides them toward problems with infinite solutions and plotting ordered pairs on the coordinate plane. The Teacher Notes say, “Project the grid on the board and ask students to come up and plot an ordered pair that is a solution to the equation. They will soon see that the ordered pairs follow a pattern. Some students may even come up with solutions that include fractions. If not, ask them if there are solutions that fall between integer ordered pairs. Begin filling in all of these solutions as well. Soon a line will start to appear because all of the fractional solutions will start to 'merge' together.” The Teacher Notes emphasize developing understanding.

Many Class Activity problems involve hands-on activities or models. In Chapter 10 Homework 10.2a students use grid paper to draw squares adjacent to the given triangle sides showing a proof of the Pythagorean theorem.

The Teacher Notes for each lesson describe the purpose of the lesson and how to guide students to develop their understanding of a concept. The notes include prompts and questions during instruction that lead to conceptual understanding.

Chapter 2 addresses 8.EE.B as students make the connection between proportional relationships, lines, and linear equations. Students explain, generalize, and connect ideas using supporting evidence; make and justify conjectures; compare information within or across data sets; and generalize patterns. Chapter 2 builds conceptual development as students make the connection between proportional relationships, lines and linear equations.

  • The Section 2.1 Concepts and Skills to Master lists conceptual objectives for the students.
    • "Graph and write equations for a proportional relationship and identify the proportional constant or unit rate given a table, graph, equation, or context."
    • "Compare proportional relationships represented in different ways."
  • Throughout Chapter 2 Class Activities and Homework, students are asked to identify correspondences between contexts, tables, graphs, and equations. Students explain, generalize, and connect ideas using supporting evidence (Question 10a, page 8WB2 - 13 and Question 2e-f, page 8WB2 - 46); compare information within or across data sets (Question 7, page 8WB2 - 19), and generalize patterns (2.2a Class Activity & Homework).
  • A Teacher Note provides the following directive and explanation to assist teachers in engaging students in the conceptual understanding of the work: “Please refer to the Mathematical Textbook for Chapter 2, as this will help the teacher understand why it is important to approach Standard 8.EE.6 from the perspective that the slope is the same between any two distinct points on a line because of dilations. Transformational geometry is integrated with slope by understanding that a dilation produces figures with proportional parts. Right triangles that are formed from any two distinct points on a line are dilations of one another. Since they are dilations of one another they have corresponding parts that are proportional and parallel. This is why the rise/run ratio is the same from any of these triangles and thus the slope is the same between any two distinct points.” (page 8WB2 - 85)

Chapter 9 addresses 8.G.A.: Lessons develop conceptual understanding of translations, reflections, rotations, dilations, their properties, as well as their roles in determining if/when two figures are congruent, and if/when they are similar. Students examine preimages and images, use patty paper to perform reflections and rotations, use tables to record coordinates of images and preimages, describe transformations, draw figures congruent and/or similar to ones shown, and write coordinate rules for transformations shown. Properties of translations, reflections, rotations, and dilations are experimentally verified and compared/contrasted.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, when the intention is that procedural skill and fluency be developed, the materials offer opportunities for their development.

There are examples and repetition in practice in each lesson and homework.

  • 8.EE.7: In Lessons 1.1a, 1.2a, 1.2b, and 1.2d students have opportunities to develop procedural skill and fluency in solving linear equations. Students work with rational numbers throughout. In the Homework students are tasked with problems that promote fluency, including being able to identify common mistakes (pages 8WB1 - 35 and 36). Throughout Chapter 1 and in other chapters in the grade (Chapters 3, 4, and 6), students are solving linear equations in one variable that includes rational coefficients. This leads them to fluency by the end of the year.
  • 8.G.9: In the student content in Chapter 8, students are introduced to volume in a conceptual way, as they are asked to describe what volume is and its importance. Attention is given to 8.G.9 in Section 8.3. In Lessons 8.3b, 8.3c, and 8.3d, students find the volume of spheres, cones, and cylinders using the correct formulas. Students derive the equations for the volume of cones, cylinders, and spheres and practice problems related to them in Section 8.3. In Class Activity 8.3b Questions 7-12 and Homework Questions 1-6, students find the volume and/or missing measurement of each cylinder. In Class Activity 8.3c Questions 7-12 and Homework Questions 1-6, students find the volume and/or missing measurement of each cone. In Class Activity 8.3d8 - 13 and Homework 1-6 students are given the directions to find the volume and/or missing measurement of each sphere.

Note that there are no spiral reviews in Grade 8 to provide additional procedural skill and fluency practice.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation that teachers and students spend sufficient time working with engaging applications of mathematics, without losing focus on the major work of the grade. Overall, the materials have multiple opportunities for application.

The materials incorporate Anchor Problems at the beginning of each chapter which provide students multi-step questions where they solve problems by using a variety of paths.

  • In Anchor Problem 1.0 students use their own assumptions to model several situations mathematically. Students are directed to “(c)onsider the following situations. Then answer the questions below. Include any pictures, models, or equations you used to solve the problem and clearly explain the strategy you used.” For example, students explore the following situation: “Two students, Theo and Lance, each have some chocolates. They know that they have the same number of chocolates. Theo has four full bags of chocolates and five loose chocolates. Lance has two full bags of chocolates and twenty-nine loose chocolates. Determine the number of chocolates in a bag. Determine the number of chocolates each child has.” (page 8WB1 - 7)
  • Chapter 4’s Anchor Problem, “Chickens and Pigs,” has multiple ways to solve (trial and error, a table, pictures or symbolic representations, and equations and graphs). There is flexibility for students in this contextual problem to apply their mathematical understanding. “A farmer saw some chickens and pigs in a field. He counted 30 heads and 84 legs. Determine exactly how many chickens and pigs he saw. There are many different ways to solve this problem, and several strategies have been listed below. Solve the problem in as many different ways as you can and show your strategies below.“ (page 8WB4 – 6)

In Grade 8, a specific standard and cluster that include application are 8.EE.8c and 8.F.B. Examples of problems that address these standards include:

  • Chapter 4 "Who will win the race?" Class Activity and Homework is a multi-step problem leading to two linear equations in two variables that encourage students to use their own methods of problem solving so that there are multiple paths of entry. (8.EE.8c)
  • In Chapter 4 Section 4.2 students solve simultaneous linear equations that have one, no, or infinitely many solutions using algebraic methods. For example, Homework 4.2e Question 4 asks the following: “Sarah has $400 in her savings account, and she has to pay $15 each month to her parents for her cellphone. Darius has $50, and he saves $20 each month from his job walking dogs for his neighbor. At this rate, when will Sarah and Darius have the same amount of money? How much money will they each have?” (8.EE.8c)
  • In Chapter 2 students calculate the cost for attending the state fair and riding various rides given the costs for the fair and each ride. Students determine the total number of rides that can be be purchased, given a specific amount, and create a table and graph to represent the situation. (8.F.B)
  • Chapter 5 Section 5.3 includes real-world contexts such as a height vs. time function, pennies earned per day, and the half-life of Carbon-14. (8.F.B)

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation that the materials balance all three aspects of rigor with the three aspects not always combined together nor are they always separate. Every chapter includes all three aspects of rigor. In some lessons the aspects of rigor are addressed separately, and in some lessons multiple aspects of rigor are addressed. Overall, the three aspects of rigor are balanced in this program.

There are lessons where the aspects of rigor are not combined.

  • Homework 3.1a provides a variety of problems for students to practice their procedural skill of writing equations in slope-intercept form.
  • In Class Activity 9.1a students develop their conceptual understanding of translations by answering a variety of questions designed to illicit similarities and differences between the properties of translations.

There are multiple lessons where two or all three of the aspects are interwoven.

  • In Class Activity 4.2c (page 8WB4 - 44) students are first asked to solve, in any way they choose, a couple of contextual problems that can be modeled and solved using systems of linear equations. For example, “Carter and Sani each have the same number of marbles. Sani’s little sister comes in and takes some of Carter’s marbles and gives them to Sani. After she has done this, Sani has 18 marbles and Carter has 10 marbles. How many marbles did each of the boys start with? How many marbles did Sani’s sister take from Carter and give to Sani?” Students then determine the values of "shape-addends" that form two shape equation systems designed to match the contextual problems. This work is followed by more shape equation systems for students to represent algebraically and to solve using the elimination method. Students apply their understanding of the elimination method and develop procedural skills as they solve several systems of linear equations. In the final task students create a context for a given system, solve the system, and write the solution in a complete sentence.
  • In Class Activity 1.1c students use models to solve linear equations by combining like terms. Students develop an understanding of like terms through the models leading to development of procedural skill. By the end of the lesson, students are asked to solve equations and verify their solutions.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectations for practice–content connections. The materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialized language of mathematics. The instructional materials also support the Standards' emphasis on mathematical reasoning.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade.

The Standards for Mathematical Practices are identified in both the Teacher and Student Workbooks in most lessons. The MPs are listed in the beginning of the chapter and are also identified using an icon within the lessons where they occur.

Overall, the materials clearly identify the MPs and incorporate them into the lessons. All of the MPs are represented and attended to multiple times throughout the year, and MPs are used to enrich the content and are not taught as a separate lesson.

  • Chapter 3 Homework 3.1g Questions 1-4 ask students to "reason quantitatively" as they write equations from graphs of linear representations and then tell the story that relates to the equation (MP2). For example, “The graph below shows a trip taken by a car where x is time (in hours) the car has driven and y is the distance (in miles) from Salt Lake City. Label the axes of the graph. Use your graph and equation to tell the story of this trip taken by the car.”
  • Chapter 4 Class Activity 4.2c highlights MP1 as students make sense of problems. The problem states: “Ariana and Emily are both standing in line at Papa Joe’s Pizza. Ariana orders 4 large cheese pizzas and 1 order of breadsticks. Her total before tax is $34.46. Emily orders 2 large cheese pizzas and 1 order of breadsticks. Her total before tax is $18.48. Determine the cost of 1 large cheese pizza and 1 order of breadsticks. Explain the method you used for solving this problem..” The Teacher Note also emphasizes that “there are a variety of ways to solve this problem” and gives examples of methods which reinforce the goal of students making sense and persevering in solving the problem as students can solve the problem many different ways.
  • Chapter 5 Class Activity 5.1b, “The Function Machine,” asks students to “attend to precision” by figuring out the rule from a table of values. Students rely upon accurately calculating the values to figure out the rules (MP6).

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 partially meet the expectations for attending to the full meaning of each Mathematical Practice Standard. The MPs are most frequently identified in Teacher Notes where they are aligned to a particular practice activity or question. Many times the note is guidance on what the teacher does or says rather than engaging students in the practice.

The intent of the MPs is often not met since teachers engage in the MPs as they demonstrate to students how to solve the problems.

  • Many problems marked MP1 do not ensure that students have to make sense of problems and persevere in solving them. For example, in Chapter 4 Class Activity 4.2b and Homework, problems are heavily scaffolded and centered around using systems of equations. This does not give students an opportunity to engage in making sense of the problem or persevering in solving them.
  • MP4 is identified throughout the program; however, it is rarely identified in situations where students are modeling a mathematical problem and making choices about that process. In many situations, it is labeled when directions are provided for how the teacher models. For example, in Chapter 6 Class Activity 6.1a: “In 10-13 above the adjacent angle pairs are also examples of supplementary angles. Are adjacent angles always supplementary? Why or why not?” The Teacher Notes add: “No, have students draw a counterexample.” “Also, begin to talk about simple equations. For example, #12 can be written as: B + 123 = 180 or 180 – 123 = B. In other words, you’re beginning to discuss modeling with mathematics.”
  • Where MP5 is labeled, the materials suggest a specific tool for students to use which does not lead students to develop the full intent of MP5. For example, in Chapter 3 Class Activity 3.1c students are told to graph each equation by hand and then use a graphing calculator to check their line.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for prompting students to construct viable arguments concerning grade-level mathematics detailed in the content standards.

In many cases, students are asked to construct arguments and justify their thinking,

  • Throughout the materials students are asked to justify their thinking. For example, in Class Activity 1.2c Questions 9-13 students are asked to “plot each fraction on the number line. Fill in the blank with < , > or = . How do you know your answer is correct? Justify your answer.”
  • There are instances where students are asked to make conjectures. For example, in Chapter 5 Class Activity 5.1a Questions 1-3 the directions state: “Make a conjecture (an educated guess) about what kind of relationship makes a function and what disqualifies a relation from being a function.”
  • Students are asked to engage in Error Analysis in some of the lessons. For example, in Chapter 10 Homework 10.2c Question 15 students identify the error in using the Pythagorean Theorem Formula to calculate the leg between hypotenuse and other leg. In the given solution, the error was in subtracting, instead of adding the area of the squares before finding the square root.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Many of the directions for MP3 are the same as those found written in the Student Workbook. Guidance is given on how to assist students in expressing arguments.

A few examples of guidance provided for teachers include:

  • There is assistance for the teacher in engaging students in constructing viable arguments. Chapter 6 Class Activity 6.1a Question 1a asks students to “make some observations about the data shown in the dot plot.” The Teacher Notes state the following: “Listen to what students say. They may say things like, the average amount she makes is around $100. The data does not appear to be very spread out. The point 55 appears to be an outlier and may pull the average down. What could have caused this outlier? She can usually expect to make between $75 and $120 a day.”
  • There is assistance for the teacher in engaging students in analyzing the arguments of others. For example, in Chapter 8 Class Activity 8.1d the Teacher Notes say,When they are finished have them discuss their answers with a neighbor before moving on to a group discussion. Ask for people to come to the board to show and justify how they fixed the mistake in each statement.”
  • There are some prompts for the teacher in the form of questions to ask or problems to present. For example, in Chapter 5 Class Activity 5.2b students are prompted to determine if given situations can be modeled with linear functions and to provide evidence to back their claim. Teachers are given this guidance in the notes: “For the answers below, students can provide various pieces of evidence (constant/changing rate of change; first difference is the table is constant/not constant; graph is/is not a line; form of the equation). Accept all valid explanations.”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 meet the expectation for attending to the specialized language of mathematics. Overall, the materials provide explicit instruction on how to communicate mathematical thinking using words, diagrams, and symbols. When students are introduced to new mathematical vocabulary, it is explained, and teachers are encouraged to tell students to use the new terms.

  • Each chapter in the workbook begins with a vocabulary list of words used in the chapter that includes words from previous learning as well as new terms.
  • Throughout the chapter, new terms are used in context during Class Activities, Homework, and Self-Assessments.
  • Vocabulary is bold in the context of the lesson.
  • Vocabulary is presented throughout the textbook, Mathematical Foundations, along with accurate definitions. For example, on page 8MF2 - 3: “Given two quantities x and y, they are said to be proportional if, whenever we multiply one by a factor r, the other is multiplied by the same factor, r. For example, if we double the variable x, then y also doubles.”
  • Students are encouraged to use vocabulary appropriately. For example, Chapter 9 Class Activity 9.1 introduces the terms: translation, pre-image, image, and corresponding vertices. These terms are introduced, defined, and taught to the students. They are used throughout the chapter.
  • At times the Teacher Notes give suggestions for using vocabulary in a lesson. For example, Chapter 5 Class Activity 5.1a says, “Talk to the students about the term unique and how it is used in mathematics, as they will see it in many definitions in the future.”
  • The terminology that is used in the course is consistent with the terms in the standards.

Gateway Three

Usability

Partially Meets Expectations

Criterion 3a - 3e

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

The instructional materials for The Utah Middle School Math Project Grade 8 meet the expectations for use and design. Materials are well-designed, and lessons are intentionally sequenced. Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter. Students produce a variety of types of answers including both verbal and written answers. Manipulatives are used in the instructional materials as mathematical representations and to build conceptual understanding.

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 for Grade 8 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

The chapters begin with a non-routine problem that introduces new concepts and is labeled as an Anchor Problem. The chapters are subsequently sectioned into Class Activities, Homework, and Assessments.

Generally, each Class Activity has problems to solve together as a class with instructor guidance. Occasionally, they are intended to review previous grades concepts in order to connect them to eighth grade concepts. Most often, the Class Activities are for the students to apply what they have already learned.

The mathematics taught in each Class Activity is reinforced by an accompanying Homework component.

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 for Grade 8 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.

Students are presented with an Anchor Problem at the beginning of each chapter to introduce new concepts. Anchor Problems are sometimes referenced throughout the chapter.

Within each chapter, concept development is sequential. During Class Activities, the teacher introduces new concepts or builds upon prior knowledge. Students work individually or as a whole class when engaged in the Class Activities. The Homework component reinforces the mathematical concepts taught during the previous Class Activity. Spiral Reviews are used to provide continued practice of newly learned mathematical concepts throughout the year.

The progression of lessons taught is intentional and assists students in building their mathematical understanding and skill. Students begin with activities to build conceptual understanding and procedural skill, and progress to applying the mathematics with more complex problems and procedures.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

The instructional materials for Grade 8 meet the expectation for the variety in what students are asked to produce.

Throughout the Class Activities, students are asked to produce answers and solutions, discuss ideas, make conjectures, explain solutions and justify reasoning, make sketches and diagrams, and use appropriate models. These aspects are found individually within problems as well as in combination with others, such as provide an explanation of a solution and include a diagram.

  • Chapter 1 Class Activity 1.1a: Students examine the models and write the simplified form of the expressions. Subsequent tasks require students to evaluate expressions and produce a model for a given expression.
  • Chapter 1 Homework 1.1a: Students are asked to “identify the mistake, explain it, and simplify the expression correctly.”
  • Chapter 1 Class Activity 1.1c: Students are asked to “model and solve the following equations. Show the solving action, and verify your solution.”

Indicator 3d

Manipulatives 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 for Grade 8 meet the expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models.

Algebra tiles are used to model and simplify linear expressions. In Class Activity 1.1a, Question 5 reads, “Using your tiles, model the expression 2(2???? − 1). a. Write the simplified form of this expression. b. Evaluate this expression when ???? = 0.”

Number lines are used to model the approximate location of irrational numbers. In Class Activity 7.3d, Question 1 reads, “Between which two integers does the square root of 5 lie? a. Which integer is it closest to? b. Show its approximate location on the number line below. c. Now find the square root of 5 accurate to one decimal place. Show its approximate location on the number line below.”

Indicator 3e

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

The instructional materials for Grade 8 meet the expectation that the visual design is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

  • The student materials are clear and consistent between investigations within a grade-level as well as across grade-levels.
  • Each Class Activity and Homework is clearly labeled and provides consistent numbering for each investigation and problem set with both a lesson number and page number.
  • The examples shown in the Textbook: Mathematical Foundation are consistently labeled and numbered within each section.

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 for The Utah Middle School Math Project Grade 8 meet the expectations for supporting teachers’ learning and understanding of the standards. The instructional materials provide questions that support teachers in delivering quality instruction. The teacher’s edition is easy to use and consistently organized and annotated. The teacher’s edition explains the mathematics in each unit as well as the role of the grade-level mathematics within the program as a whole. The instructional materials are all aligned to the standards, and the instructional approaches and philosophy of the program are clearly explained.

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 for Grade 8 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

  • Anchor Problem 2.0 focuses on proportionality and unit rate as students connect prior learning from 6th and 7th grade. The teacher notes guide the students’ mathematical development for question 5 by stating, “At this point have students divide these quantities to see that they are proportional to the unit rate.”
  • Class Activities are the guided lessons where a teacher facilitates students through conceptual, procedural, and application work. In Class Activity 2.2d, “Rate of Change in a Linear Relationship,” teachers are prompted to, “ask students to interpret what it means if the line is going up and if the line is going down. Also discuss the possibility of a negative rate of change.”

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 materials for Grade 8 meet expectations for containing a Teacher Workbook that has ample and useful annotations and includes 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.

  • The Teacher Workbook offers suggestions and annotations, labeled in red, on how to present the content.
    • Section 3.0 Anchor Problem: Suggestions on how to present finding solutions to a linear equation include, “It might be helpful to demonstrate how the line is formed by the solutions to the equation above. Project the grid on the board and ask students to come up and plot an ordered pair that is a solution to the equation. They will soon see that the ordered pairs follow a pattern. Some students may even come up with solutions that include fractions. If not, ask them if there are solutions that fall between integer ordered pairs. Begin filling in all of these solutions as well. Soon a line will start to appear because all of the fractional solutions will start to “merge” together. You could have this discussion either before or after students do problems #21-23.”
  • There are suggestions occasionally placed as to common student mistakes and misconceptions that teachers could expect. In Chapter 4 Class Activity 4.1b, the teacher notes read, “A common mistake here is for students to neglect the scales on the axes. You may want to remind students to take note of the scales.”
  • Scaffolding is provided as, "remind students that...” or “probe students to think..."
  • A small number of links are embedded to assist in presenting the material. However, geometry software and graphing calculators are mentioned for students to use.

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons 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 for Grade 8 meet expectations for containing a Teacher Workbook that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

  • Mathematical Foundations, written for each chapter, is a resource for teachers to understand the mathematics of the chapter and for teachers to expand their understanding of the mathematical concepts.
  • Each Mathematical Foundations includes problems, explanations of problems, examples, and connections to CCSSM.
  • The Teacher Workbook provides clear, step-by-step solutions.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
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Indicator Rating Details

The instructional materials for Grade 8 meet expectations for containing a teacher edition (in print or clearly distinguished and accessible as such in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.

  • Each chapter contains an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Knowledge required from prior modules and/or grades is explicitly called out in this section. The Prior Knowledge section for chapter 7 states, “Students have worked a great deal with rational numbers up to this point. They have defined and worked with the subsets of rational numbers. They have represented rational numbers on a number line, expressed rational numbers in different but equivalent forms, and operated with rational numbers.”
  • The teacher edition connects the learning from previous grade levels and explains how standards build on one another throughout the program. The chapter overview for chapter 1 states, “Later in this book, students will analyze and solve pairs of simultaneous linear equations. They will also create and solve linear equations in two-variables to solve real-world problems. A student’s understanding of how to solve a linear equation using inverse operations sets the foundation for understanding how to solve simple quadratic equations later in this course and additional types of equations in subsequent coursework.”

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered 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 for Grade 8 meet expectations for providing a list of lessons in the teacher edition (in print or clearly distinguished/accessible as such in digital materials), cross-referencing the standards covered, and providing a pacing guide on the estimated instructional time for each chapter.

  • The materials provide an overview for each chapter that specifies the standards addressed in each chapter.
  • Each chapter contains a Table of Contents that organizes the lessons into topics but does not state which lesson(s) align to each standard.
  • Each chapter overview identifies the number of weeks for instruction.

Indicator 3k

Materials contain strategies for informing 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 for Grade 8 contain strategies for informing parents or caregivers about the mathematics program and give suggestions for how they can help support student progress and achievement.

The parent manual for each chapter is available in PDF and Word files that can be downloaded. The manual contains general course information, questioning suggestions, keys for student success, content explanations, examples, and practice problems with answers aligned by topic and chapter.

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 materials for Grade 8 do not contain explanations of the instructional approaches of the program and identification of the research-based strategies within the teaching materials.

There are no connections to research-based strategies within the lessons. There are chapter overviews and connections to content listed at the beginning of each chapter; however, these do not explain the program’s instructional approaches. They list what the students will be learning through the chapter.

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
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Criterion Rating Details

The instructional materials for The Utah Middle School Math Project Grade 8 partially meet expectations for providing teachers resources and tools to collect ongoing data about student progress. There are no assessments that purposely identify prior knowledge within and across grade levels. There are some suggestions in the teacher materials that identify common misconceptions and errors, but there are no specific strategies to address these when they arise. Opportunities for ongoing review, practice, and feedback occur in various forms. Standards are identified that align to the section, and there is mapping of Standards to items for the Self-Assessments. There are opportunities for students to monitor their own progress.

Indicator 3m

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

The instructional materials for Grade 8 partially meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. While no explicit method for assessing student’s prior knowledge is used, there are some ways that the materials lead to gathering this information.

The materials provide teachers with strategies on how to use the Self-Assessment for Section 2.1 as a formative assessment. The description on page (8WB2 - 37) states, “This self-assessment is meant to be used as a formative assessment and is one way to assess how students are doing toward mastery of the skills and concepts in a particular section. Teachers should guide students through this self-assessment by asking probing questions of the students. This is also a resource for teachers to analyze, to assess whether the class as a whole is ready to move on or not. There are many ways that you can use this self-assessment. For example, you could have students complete each example problem and use it as a quiz. Tell your students to read each Skill or Concept and answer the corresponding problem that relates to the skill. Then grade the quiz together as a class. At this point, have students rate their mastery level based off of how they performed on the quiz, using the rubric. Come up with the criteria for the rubric together as a class. Some sample criteria are provided.”

The teacher notes give suggestions on how to proceed with instruction when students may or may not have demonstrated mastery of a topic, however, there is no guidance on how to gather the information needed to determine mastery.

Chapter 1, Chapter Overview (8WB1 - 2) states, “It is encouraged that you move on from chapter 1 after the recommended time frame even if students have not demonstrated mastery of this topic. Students will likely require additional practice throughout the year in order to master the skill of solving complicated linear equations. We have incorporated this practice in spiral reviews, and we encourage you to continue to practice this skill throughout the year.”

Chapter 2, Section 2.1a Overview (8WB2 - 9) states, “Section 2.1a is a review of proportional relationships from 7th grade. Depending on the background knowledge of your students you may decide to skip some of the problems in this section. Be sure to assess the needs of your students as you decide which problems you are going to have them do. In addition, look at Chapter 4 in the 7th grade textbook and workbook to see examples of the foundation of which understanding is built for proportional relationships.”

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
1/2
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Indicator Rating Details

The instructional materials for Grade 8 partially meet expectations for identifying and addressing common student errors and misconceptions. Materials provide occasional suggestions for teachers to identify and address common student errors and misconceptions.

Student misconceptions are often identified for the teachers, however, instructional plans to address these misconceptions are not detailed. The suggestions to address misconceptions consist of phrases such as, “Remind the students…, Discuss with students…, Point out that…..”

Chapter 2, Class Activity 2.2b, Representations of a Linear Pattern: “Many students will draw a continuous graph, even though this is a discrete situation. This is not the focus of this lesson, but you can discuss this if you feel it is appropriate. Students will expand their understanding of discrete functions when they study sequences in Secondary I.”

Chapter 6, Class Activity 6.2b, Fit a Linear Model to Bivariate Data: “You may want to point out to students that the plot shows a positive association, and the slope is also positive.”

Indicator 3o

Materials provide opportunities 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 for Grade 8 meet expectations for providing opportunities for ongoing review and practice for students in learning both concepts and skills.

Over the course of each chapter, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support within the Class Activities to independent problem solving within the Homework. The Anchor Problems at the beginning of each chapter incorporate review and practice of previously taught standards.

  • Chapter 1. Class Activity 1.2b, Teacher Note: “Again, there are many different ways to solve the given equation and arrive at the correct solution; however some solution pathways are easier than others. Practice develops a sense of the solving sequence that is the easiest and most direct path to the solution.”
  • Chapter 2, Section 2.1a, Overview contains a teacher note that states, “Section 2.1a is a review of proportional relationships from 7th grade.”
  • Anchor Problems engage students in both previously-taught standards as well as standards that are to be covered in the chapter. The Anchor Problems often guide the teacher to return to the problem while working through the concepts in the chapter. Anchor Problem 5.0: Waiting at the DMV reads, “This anchor problem can be done intermittently throughout the chapter. You may choose to have students work on pieces of the problem and then return to the problem throughout the chapter. This problem could also be used as a culminating task.” The Anchor Problems are also embedded with the review of previously taught standards. Anchor Problem 7.0: Zooming in on the Number Line, states, “The problems below are a review of skills learned in 6th and 7th grade. In 6th and 7th grade, students used the number line as a model for thinking about numbers.”
  • Mathematical concepts are reinforced by an accompanying Homework component for each Class Activity that is designed for individual practice.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

The instructional materials for Grade 8 partially meet expectations for offering summative Self-Assessments for the students denoting which standards are being emphasized.

  • Each standard that is being emphasized is noted within the “Concepts and Skills to be Mastered” at the beginning of each section.
  • There are no summative assessments provided within the instructional materials. The assessments for this program consist solely of each section's Self-Assessment.
  • Self-Assessments are developed to assess particular standards, and the scoring guidelines specifically use the wording of these standards.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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Indicator Rating Details

The instructional materials for Grade 8 partially meet expectations for assessments including scoring guidelines that provide sufficient guidance to teachers in interpreting student performance but do not include suggestions for follow-up.

  • Each Self-Assessment includes a scoring guideline as well as worked-out solutions for correct responses.
  • The scoring guidelines are easy to understand and interpret.
  • Self-Assessment scoring guides are provided, but follow-up suggestions based on scoring criteria are not provided.

Indicator 3q

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

The instructional materials for Grade 8 encourage students to monitor their own progress.

There is a Self-Assessment for students at the end of every section within each chapter. The directions to students are: “Consider the following skills/concepts. Rate your comfort level with each skill/concept by checking the box that best describes your progress in mastering each skill/concept. Corresponding sample problems, referenced in brackets, can be found on the following page.”.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
8/12
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Criterion Rating Details

The instructional materials for The Utah Middle School Math Project Grade 8 partially meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. Activities provide students with multiple entry points and a variety of solution strategies and representations. However, the materials provide few strategies for ELL students, special populations, or to challenge advanced students to deepen their understanding of the mathematics.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
1/2
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Indicator Rating Details

The instructional materials for Grade 8 partially meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The sequencing and scaffolding are built into lesson development so that teachers pose problems as they progress through more rigorous processes or skills. However, if students need additional support, the guidance is not explicit.

The scaffolding guidance for Chapter 10, Class Activity 10.1b, “Special Angles Formed by Transversals,” reads, “Before you begin the activity below you might find it helpful to review the words in the table below with your class. Ask them, 'When you hear the following words, what do you think of? What key words or ideas will help you remember what these words mean?' Write the graphic organizer below together as a class on the board for students to refer to as they complete the activity.” There are no strategies provided for students who may still need additional support after the activity is complete.

Advanced students have “Honor” class extensions that involve more rigorous topics from later grades that can be used at teacher discretion, such as Class Activity 5.2a, question 4. The teacher notes state, “The equation that models this relationship is y = x^2 + x + 4. It is not expected that students will be able to come up with this equation in Grade 8; however, you may challenge your honors students to try to do this. One equation that models this situation is shown below. It has been color-coded to show how the equation connects to the geometric model.” Writing a quadratic equation is a high school standard.

Indicator 3s

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

The instructional materials for Grade 8 partially meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The Teacher Workbook includes limited notes providing some strategies to help teachers sequence or scaffold lessons. The notes are concise, such as, "ask students," "remind students of a definition," or “point out to students.”

Chapter 5, Class Activity 5.1e, “More About Functions” contains a teacher note that reads, “This is a good time to point out to students that the independent variable is graphed on the x-axis and the dependent variable is graphed on the y-axis.”

Chapter 9, Class Activity 9.1f, “Congruence cont.” provides the following teacher note at the end of the activity: “Review with students the definition of congruence – a figure is congruent to another if the second can be obtained from the first by a sequence of rigid motions (rotations, reflections, and translations). It will help with the corresponding homework.”

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 for Grade 8 partially meet expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

Tasks allow students to use multiple entry points and to solve problems using a variety of strategies, paths, and/or models. In the Chapter 5 Anchor Problem, “Waiting at the DMV,” students are asked to find an estimated time that Nazhomi will make it to the front of the line by analyzing the given information of times that others were called to the desk, time when employees are at lunch, and when Nazhomi needs to leave. This problem requires students to make their own assumptions and simplifications.

Teachers are asked to model various solution strategies and to lead students through finding a solution path.

Indicator 3u

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

The instructional materials for Grade 8 partially meet expectations for suggesting options for 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). Materials provide some strategies to help teachers sequence or scaffold lessons so that the content is accessible to a range of learners. The notes in the Teacher Workbook use suggestions like, "give students time to analyze..." or "remind students of a definition." The suggestions are not specific to the content being taught.

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
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Indicator Rating Details

The instructional materials for Grade 8 partially meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

  • Extension problems are placed sporadically throughout the materials, however, it is unclear if extension problems are optional for the entire class, scaffolded for the class, or explicitly for students who need advanced mathematics. Chapter 2, Homework Activity 2.2a, “Connect the Rule to the Pattern” (page 8WB2 - 44): “Extension: Compare this pattern to pattern 2 in class. How are the patterns the same, and how are they different? How is the difference reflected in the rules? Will the two patterns ever have the same number of tiles?”

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The instructional materials for Grade 8 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.

  • No examples of bias were found.
  • Pictures, names, and situations present a variety of ethnicities and interests. Chapter 4, Class Activity 4.2b questions 19 and 20, “Nettie’s Bargain Clothing is having a huge sale. All shirts are $3 each, and all pants are $5 each. You go to the sale and buy twice as many shirts as pants and spend $66,” and “Xavier and Carlos have a bet to see who can get more 'friends' on a social media site after 1 month. Carlos has 5 more friends than Xavier when they start the competition. After much work, Carlos doubles his amount of friends and Xavier triples his. In the end they have a total of 160 friends together.”

Indicator 3x

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

The instructional materials for Grade 8 provide limited opportunities for teachers to use a variety of grouping strategies.

  • Some Class Activities and Anchor Problems are intended for cooperative learning groups, though there are no recommendations for forming groups or mention of why students work within a certain group size.

Indicator 3y

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

The instructional materials for Grade 8 do not encourage teachers to draw upon home language and culture to facilitate learning.

  • There is no evidence of teachers needing to draw upon home language and culture to facilitate learning.

Criterion 3aa - 3z

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

The instructional materials for The Utah Middle School Math Project Grade 8 provide limited support for the effective use of technology to enhance student learning. The materials are available for download online using Microsoft Word which would allow access from multiple operating systems. The suggested (optional) technology is intended to be used for students developing an understanding of the mathematical content. The technology provides limited opportunities to personalize instruction, and suggestions for customization are not provided. The technology is not used to foster communications between students, with the teacher, or for teachers to collaborate with one another.

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 Apple 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 for Grade 8 are available for download online using Microsoft Word which would allow access from multiple operating systems. There are no web-based portions in the core materials.

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 for Grade 8 are all paper and pencil based. The suggested (optional) technology is intended to be used for students developing an understanding of the mathematical content.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. 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 The Utah Middle School Math Project Grade 8 are not easily customizable for individual learners or users. Suggestions and methods of customization are not provided.

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.).
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Indicator Rating Details

The instructional materials reviewed for The Utah Middle School Math Project Grade 8 do not include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

Indicator 3z

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 for Grade 8 do not generally integrate technology, such as interactive tools or virtual manipulatives. Technology suggestions occur in conjunction with Proportional Relationship and Geometry standards.

In Chapter 2, Class Activity 2.3j, “Use Dilations and Proportionality to Derive the Equation y = mx + b” includes a Teacher Note at the end of the activity that reads, “Interactive lesson similar to the ones in derivations in this activity can be found at: http://learnzillion.com/lessons/1472-derive-ymx-using-similar-triangles http://learnzillion.com/lessons/1473-derive-ymxb-using-similar-triangles”

In Chapter 3, teachers are encouraged to allow students to use on-line graphing calculators to check their work with graphs.

In Chapter 9, the Teacher’s Notes explain that the chapter was written so that they could use pencil and paper, but that they could “choose” to use Geometer’s Sketchpad or GeoGebra.

Additional Publication Details

Report Published Date: Wed Aug 30 00:00:00 UTC 2017

Report Edition: 2017

About Publishers Responses

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

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

The publisher has not submitted a response.

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.

Math K-8 Rubric and Evidence Guides

The K-8 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 K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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