7th Grade - Gateway 1

The instructional materials reviewed for LearnZillion Illustrative Mathematics 6-8 Math, Grade 7 meet expectations for assessing grade-level content. The assessments are aligned to grade-level standards. Examples include:

• In Unit 3, End-of-Unit Assessment, Problem 4, students decide if the circumference and radius (7.G.4) are proportional based on the given graph and ordered pairs (7.RP.2): “A class measured the radius and circumference of various circular objects. The results are plotted on the graph. 1) Does there appear to be a proportional relationship between the radius and circumference of a circle? Explain or show your reasoning. 2) Why might the measured radii and circumferences not be exactly proportional?”
• In Unit 5, End-of-Unit Assessment, Problem 6 assesses student understanding of adding and subtracting rational numbers (7.NS.1,3) by presenting a scenario that describes a bank account in which students must calculate the balances and transaction amounts. Problems are presented with a relevant context for standards that require a real-world context.
• In Unit 8, Mid-Unit Assessment, Problem 7 assesses 7.SP.8a by presenting a game using a special deck of cards with 40 cards numbered from 1 to 40. Students find the probability for three different situations; drawing a card divisible by 2, 5, and 10 and explaining their reasoning. 

Assessments are located on the first page of each unit in Lessons & Assessments, which is below Unit Overview, for each of the first eight units. Unit 9 is an optional unit and has no assessments. Assessments are limited to seven problems but are often broken into multiple prompts and assess numerous standards. Units 6 and 8 contain Mid-Unit Assessments for a total of 10 assessments.

The instructional materials reviewed for LearnZillion Illustrative Mathematics 6-8 Math, Grade 7 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of units devoted to major work of the grade, including assessments and supporting work, is 5 out of 8, which is approximately 63 percent.
• The number of non-optional lessons devoted to major work of the grade, including assessments and supporting work, is 82 out of 124 total non-optional lessons, or approximately 66 percent.
• The number of days devoted to major work, including assessments and supporting work, is 93 out of 163 days, which is approximately 57 percent.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in. As a result, approximately 66 percent of the instructional materials focus on major work of the grade. An analysis of days devoted to major work includes 17 days for review and assessment, but the materials do not indicate which items to use for the review.

The instructional materials reviewed for LearnZillion Illustrative Mathematics 6-8 Math, Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade. Multiple lessons in the Grade 7 curriculum incorporate supporting standards in ways that support and/or maintain the focus on major work standards. Examples of the connections between supporting work and major work include the following:

• In Unit 2, Lesson 8, Activity 3, students analyze relationships between side length and total edge length, volume, and surface area (7.G.6) and determine if they are proportional or non-proportional (7.RP.2). Students also practice calculating volume and surface area of three-dimensional figures (7.G.6) while exploring, discussing, and proving whether relationships are proportional.
• In Unit 3, Lesson 3, Activities 1 and 2, students measure and plot the diameter and circumference of circles (7.G.4), determine if they are in a proportional relationship, and find the constant of proportionality (7.RP.2). In Activity 2, students are provided one measurement (diameter or circumference) and use the derived constant of proportionality to determine the other.
• In Unit 3, Lesson 5 (optional), 7.G.4 is connected to 7.RP.2,3. The Activities include contexts in which students use diameter and circumference relationships to calculate how far wheels (circles) can roll to reach certain distances and explore rotations per second and time traveled. In Unit 3, Lesson 7, students explore the proportionality between diameter and area to determine that they are not proportional.
• In Unit 7, Lesson 16, the Activities provide students with complex surface area and volume contexts in which students use proportional relationships situated in real-world problems (7.G.6, 7.RP.A). In Activity 2, students are given some dimensions and the area of a base of a hexagonal prism. Students find the total number of bags of sand that were poured into the prism to reach a certain height. Students use concepts related to surface area, volume, and proportional reasoning to answer subsequent questions, including determining how many more bags would be necessary to fill the prism (sandbox) an additional 3 inches.
• In Unit 8, Lessons 4, 7, 16 and 20, statistical work with simulations and populations is used in coordination with proportional reasoning as students explore experimental probability and statistical sampling (7.SP.C, 7.RP.A).
• In Unit 7, Lesson 5, Activities involve students using equations to represent angle relationships and solve for unknown angles. Angle relationships involve setting up simple and multi-step equations (7.EE.4, 7.G.5).

The instructional materials for LearnZillion Illustrative Mathematics 6-8 Math, Grade 7 meet expectations that the amount of content designated for one grade level is viable for one year.

The suggested amount of time and expectations of the materials for teachers and students are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in a school year.

• The provided scope and sequence found in the Grade 7 Course Guide includes materials for 163 instructional days. There are 124 non-optional lessons, 18 assessment days (10 summative), and 21 optional lessons.
• 121 of the non-optional lessons are designed to address grade-level standards. 3 non-optional lessons provide problem contexts and activities that prepare students for the unit.
• 8 of the optional lessons are present throughout the first eight units, and Unit 9 is an optional unit which includes 13 lessons.
• Units 1-8 are comprised of 11 to 22 lessons, and each lesson is designed for 45-50 minutes.  Within each unit, lessons contain a Warm-Up, two or three Activities, a Lesson Synthesis, and a Cool-Down. Guidance regarding the number of minutes needed to complete each component of the lesson is provided in the teacher edition.

The instructional materials for LearnZillion Illustrative Mathematics 6-8 Math, Grade 7 meet expectations for being consistent with the progressions in the standards. The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. The instructional materials also relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials are intentionally designed to address the standards the way they are laid out in the progressions, and the full unit narrative in the Unit Overview describes how the standards and progressions are connected. Units begin with lessons connected to the standards from prior grades that are relevant to the current topic. Standards from the grade level and prior grades and standards that will be addressed later in the year are identified in the sections as “addressing,” “building on,” and “building towards,” respectively. For example:

• In the Full unit narrative, Unit 1 is connected to geometry and geometric measurement found in earlier grades. The tasks in the unit are built upon work “composing, decomposing, and identifying shapes” in Grades 1 and 2, “distinguishing area and perimeter” from Grade 3, “[applying] area and perimeter formulas” in Grade 4, “[extending] the formula for the area of a rectangle to include rectangles with fractional side lengths” in Grade 5, and finally, generating formulas for the area of parallelograms and triangles in Grade 6. The unit addresses Grade 7 work with scale drawings as students “reason about the scaled copies of figures” leading to work with proportions in Unit 4 and extends this knowledge in Grade 8 when they will work with transformations.
• In Unit 5, Lesson 5 identifies 1.OA.4 as the standard that the lesson is “building on,” the standard the lesson is “addressing” is 7.NS.1c, and the standard the lesson is “building toward” is 7.NS.1. The lesson builds on Grade 1 understanding of subtraction and extends it to adding and subtracting rational numbers in the first lessons in the unit. By Lesson 15, rational numbers are embedded in expressions and equations. The following explanation is provided for teachers: “The purpose of this lesson is to get students thinking about how to solve equations involving rational numbers. In Grade 6, students solved equations of the form px=q and x+p=q and saw that additive and multiplicative inverses (opposites and reciprocals) were useful for solving them. However, that work in Grade 6 did not include equations with negative values of p or q or with negative solutions. This lesson builds on the ideas of the last lesson and brings together the work on equations in Grade 6 with the work on operations on rational numbers from earlier in Grade 7.”

The Warm-Ups in lessons frequently work with prior-grade standards in ways that support learning of grade-level problems and make connections to progressions from previous grades. For example:

• The Unit 2, Lesson 7 Warm-Up includes equivalent ratio context (6.RP.3) that builds to an expectation of students using proportional relationship language in context (7.RP.2). These precede two lessons where students explore the difference between proportional and nonproportional relationships.
• The Unit 5, Lesson 9 Warm-Up uses an image of a woman in stride and asks students to estimate where the woman will be in five seconds and where she was five seconds before. This activity builds off constant speed contexts in Grade 6 (6.RP.3b) and primes students for considering negative time and velocity (7.NS.3 and 7.RP.2).

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

In the Course Guide under Course Information and Scope and Sequence, there is a chart which accurately reflects the mathematics in the materials. All grade-level standards are represented across the 9 units. Tasks are aligned to grade-level work and are connected to prior-grade knowledge. For example:

• Unit 2 introduces proportional relationships and is strategically divided into sections that explore conceptual understanding through comparing proportional and non-proportional relationships, tabular and graphic representations, as well as equations in the form of y = kx. The Lesson 1 through 3 Warm-Ups explore ratios and patterns in tables and are connected to 6.RP.A. Lessons 4 through 6 focus on representing proportional relationships with equations with different contexts.
• In Unit 7, the first five lessons focus on angle relationships. The first two lessons focus on making connections to the additive nature of angle measures found in 4.MD.6 and 4.MD.7. Lesson 1 in this unit states, “Students were introduced to angles in Grade 4, when they drew angles, measured angles, identified angles as acute, right, or obtuse, and worked with adding and subtracting angles. Earlier in Grade 7, students also studied angles briefly in their work with scale drawings. Now they begin a more detailed study of angles. In this lesson, students gain hands-on experience composing, decomposing, and measuring angles. They refresh their memory about the relationship between right angles, straight angles (180 degrees), and ‘all the way around’ angles (360 degrees), and they fit pattern blocks around a point to find out the angles at their vertices.” The lessons then explore the properties of angles including solving for unknown angles. According to the CCSS Progressions for Grade 7, students build on earlier experiences with angle measurement to solve problems that involve supplementary angles, complementary angles, vertical angles, and adjacent angles.

A typical lesson has a Warm-Up, one or more Activities, and a Cool-Down. Additionally, every lesson provides practice problems that can be used as independent or group work. Some lessons also provide an “Are you ready for more?” question. These problems are an opportunity for students to explore grade-level mathematics in more depth and often make connections between the topic in the lesson and other concepts at grade level. They are intended to be used on an opt-in basis by students if they finish the main class activity early or want to do more mathematics on their own.

The instructional materials for LearnZillion Illustrative Mathematics 6-8 Math, Grade 7 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings, including:

7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.

• The Unit 2 Overview includes unit goals to understand terms and concepts related to proportionality and to recognize relationships that are proportional. Specific types of real-world situations that are used in the unit (constant speed, unit pricing, and measurement conversion) are also described. Lesson 1 begins with tasks from Grade 6 that involve analyzing differences between situations that require equivalent ratios and those that do not; in Lessons 2 and 3, students explore proportional relationships and develop formal terminology; in Lessons 7 through 9 students analyze aspects of proportional relationships as they compare to non-examples of proportional relationships; and Lessons 10 through 13 continue the work of representing and analyzing proportional relationships by comparing graphs and equations of proportional relationships.
• In Unit 2, Lesson 9, the learning targets are visibly shaped by the cluster heading and state, “I can solve all kinds of problems involving proportional relationships,” and “I can ask questions about a situation to determine whether two quantities are in a proportional relationship.”

7.EE.A Use properties of operations to generate equivalent expressions.

• Learning goals for Unit 6, Lessons 18 through 22 are developed from the cluster heading, including: “Use a graphic organizer for work with the distributive property.” “Understand how to rewrite subtraction as adding the opposite in order to use the commutative property.” “Apply the distributive property to expand and factor linear expressions with rational coefficients.” “Apply properties of operations to generate an equivalent expression with fewer terms.” “Identify and correct errors made when applying properties of operations.” and “Generate a variety of expressions by positioning parentheses in different places in a given expression; apply properties to write the expressions with fewer terms.”

7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

• In Unit 6, Lesson 11, the learning target is shaped by the cluster heading, stating, “I can solve story problems by drawing and reasoning about a tape diagram or by writing and solving an equation.”

The materials consistently include problems and activities that 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. Multiple examples of tasks connecting standards within and across clusters and domains are present.

• Unit 1, Lesson 6, Activities 1, 2, and Lesson Cool-down connect 7.G.A and 7.G.B when students use scale drawings to compute actual lengths and area to solve real-world problems involving geometric figures.
• In Unit 5, Lesson 12, Activities 3 and 4, students apply proportional reasoning when using equations including a negative constant of proportionality (7.EE.B and 7.RP.A) and solve real-world problems using all four operations which include rational values (7.NS.A) as they solve problems in the context of submarines. Lessons 14 through 17 include varying scenarios that involve interpreting rational values in the context of the given problem and operations with rational values.
• In Unit 6, Lesson 18, Activities 1 and 2 connect 7.NS.A and 7.EE.B. In Activity 1, students recall that subtracting a rational number or expression is the same as adding its additive inverse, and Activity 2 builds understanding of creating equivalent expressions by applying properties of operations.