7th Grade - Gateway 1

The instructional materials for Discovery Education Math Techbook Grade 7 Mathematics meet the expectation for assessing grade‐level content and, if applicable, content from earlier grades. The Unit Assessments that are included in the Teacher View were reviewed for Discovery Education Math Techbook Grade 7 Mathematics. Overall, there were no assessment questions addressing standards from above Grade 7.

Examples of grade-level assessment items include the following:

• Unit 4 question #12- Students demonstrate their knowledge of 7.RP.3 by solving a multi-step ratio and percent problem about an employer paying her employees a 25% commission.
• Unit 6 question #10- Students demonstrate their knowledge of 7.EE.4b by applying their understanding of inequalities to solve a real-world application problem based on mowing lawns to save money to buy an electronic tablet.

The instructional materials for Discovery Education Math Techbook Grade 7 Mathematics meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 72 percent of the instructional time is spent on major work of 7th grade.

To determine this, three perspectives were evaluated: 1) the number of Units devoted to major work, 2) the number of Instructional Periods/Sessions devoted to major work, and 3) the Time devoted to major work. Time devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts.

Evidence was collected from the Content Pages, Scope and Sequence, Table of Contents and the Course Overview.

• Units– Approximately 7 complete units out of 12 units, which is approximately 58 percent, is spent on major work.
• Sessions (excluding Extensions)– Approximately 79 sessions out of 110, which is approximately 72 percent, is spent on major work.
• Time (excluding Extensions)– Approximately 4,400 minutes out of 6,150 minutes, which is approximately 72 percent, is spent on major work.

The instructional materials reviewed for Discovery Education Math Techbook Grade 7 Mathematics meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Overall, many Concepts that address supporting work integrate with major work so that students are given more opportunities to engage with the major work of the grade.

The following examples demonstrate how the Concepts that address 7.SP.C integrate this supporting cluster with major work from 7.RP.A. In each of these examples, students get the opportunity to integrate statistical standards with the use of proportional relationships, 7.RP.2, to determine the number of outcomes in experiments where the sample sizes are different but the ratios of the outcomes are the same.

• In Concept 8.1 the materials present students with the opportunity to understand the probability of a chance event and how likely an event is to happen based on its probability, 7.SP.5, and this introduction is integrated with the use of proportional relationships, 7.RP.2.
• In Concept 8.2 students have the opportunity to approximate probabilities by collecting data on chance events, 7.SP.6, and develop probability models to find the probabilities of events, 7.SP.7. This opportunity integrates the use of proportional relationships, 7.RP.2.

Examples of how the Concepts that address 7.G.A and 7.G.B integrate these supporting clusters with major work from 7.RP.A, 7.NS.A, and 7.EE.B are as follows:

• In Concept 4.2 students have the opportunity to solve problems involving scale drawings of geometric figures, 7.G.1, which supports students computing unit rates, 7.RP.1, and using proportional relationships to solve multistep ratio problems, 7.RP.3.
• In Concepts 10.1 and 10.3 the materials give students the opportunity to solve problems involving angle measure, area, surface area, and volume, 7.G.5,6, and these Concepts support 7.EE.3,4 by having students solve and create simple equations from information they are provided in real-world problems that include rational numbers.
• In Concept 12.1 students have the opportunity to work with three-dimensional figures, 7.G.3, and find the surface area and volume of them, 7.G.6, which supports student's knowledge of positive and negative numbers, 7.NS.1; formulating equations, 7.EE.4; and using proportions, 7.RP.3.

The instructional materials reviewed for Discovery Education Math Techbook Grade 7 Mathematics 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 Scope and Sequence document states that one period is equivalent to approximately 50 instructional minutes. According to the times given in each of the Units, there are approximately 123 50-minute class periods without Extension Lessons. There are twelve Unit Assessments, bringing the total number of days to approximately 135 days if one day is allotted for each Unit Assessment. The Scope and Sequence document also states that “the instructional time does not include in-class time for the extensive, independent student work available in the Practice and Apply sections that many teachers may wish to incorporate as part of their daily instruction.”

There are 27 Practice and 27 Apply sections in the materials as each of the 27 Concepts in the materials has a Practice and Apply section. Adding one day to complete the Practice and Apply sections for each Concept brings the total number of instructional days to approximately 162 50-minute class periods. Overall, with 162 50-minute class periods, the instructional materials meet the expectations for this indicator.

The instructional materials reviewed for Discovery Education Math Techbook Grade 7 Mathematics meet the expectations for the material being consistent with the progressions in the Standards. The materials develop according to the grade-by-grade progressions in the Standards, and the content from prior or future grades is clearly identified and related to grade-level work.

At the beginning of each Concept, there is a section called Progressions and Standards, and in this section, there are three parts titled During Previous Instruction, Through The Investigations In This Concept, and During Subsequent Instruction.

• During Previous Instruction identifies content from previous grades and explains how previous content is related to grade-level work. For example, Concept 6.2 includes the following: "During Previous Instruction, students have learned to create and solve one-variable algebraic equations involving one operation (6.EE.7) and two operations (7.EE.4a). Students have developed the meaning of the solution to an inequality as a set of values that satisfies a given condition (6.EE.5). Students also have explored how simple inequalities of the form x>c or x<c represent a constraint in a mathematical problem and identified the graph of these inequalities on a number line (6.EE.8)."
• Through The Investigations In This Concept discusses grade-level content. For example, Concept 6.2 includes the following: "Through The Investigations In This Concept, students develop formal algebraic methods to solve inequalities with one variable and two operations using rational numbers (7.EE.1, 7.EE.4b). Students graph the solution set of an inequality on a number line and interpret the meaning of the solution set in context (7.EE.3). Students solve multi-step inequalities with both positive and negative coefficients, understanding how negative coefficients affect the relationship between the two expressions."
• During Subsequent Instruction describes how the grade-level content relates to content later in the current grade-level and future grade-levels. For example, Concept 3.2 includes the following: "During subsequent instruction in this unit, students will build upon their understanding of proportional reasoning... (7.RP.2c,d). Students will explore the slope of a line... (8.EE.5,6). In addition, students will use proportional reasoning to determine whether two figures are similar (G-SRT.2)."

The instructional materials give all students extensive work with grade-level problems. Each Concept has three sections- Discover, Practice, and Apply- which contain grade-level problems. The following are included in the three sections:

• In the Discover section, there are at least two Investigations that enable all students to work with grade-level problems. There are Extension Lessons that take grade-level work and enhance it by utilizing new contexts or different tools. For example, the Unit 7 Concept 7.2 Extension has students extending their on grade-level standards into working on a battery project using data analysis to discuss quality control with batteries. There is Additional Assistance in the Summary where there are math explanations and extra videos that provide more instruction to students who need it. Also, there are grade-level blackline masters available with this section. For example, the Unit 2 Concept 2.1 Summary has definitions of rational numbers and terminating decimals, videos to deepen understanding, and View Math Explanations that are on grade-level and offer extra practice.
• In the Practice section, there are the Coach and Play sections, and each of these include grade-level problems. The Coach section offers grade-level work that gives students guided practice and hints when needed. For example, the Unit 9 Concept 9.2 Practice Coach has ten grade-level questions with supports and feedback available as students work through compound probability problems.
• In the Apply section, there are two or three grade-level problems that offer real-world contexts in which students get to apply the content that has been learned in the current Concept. For example, Concept 5.3 has the following two problems in the Apply section: Will Your Investments Pay Off?, where students write and evaluate algebraic expressions with percents and use the properties of operations to determine if expressions are equivalent, and How Old Is a Dog in Dog Years?, where students apply their knowledge of algebraic expressions in a real-world context.

The instructional materials reviewed for Discovery Education Math Techbook Grade 7 Mathematics meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings and problems and activities that serve to connect two or more clusters in a domain or two or more domains in the grade.

Examples of how the learning objectives are visibly shaped by the CCSSM cluster headings include:

• In Concept 3.2 the objective states that students should "recognize proportional relationships between quantities in real-world contexts and identify the constant of proportionality (unit rate)," which is shaped by the cluster heading for 7.RP.A, "Analyze proportional relationships and use them to solve real-world and mathematical problems."
• In Concept 5.3 one objective states that students should "demonstrate the meaning of equivalent expressions," which is shaped by the cluster heading for 7.EE.A, "Use properties of operations to generate equivalent expressions."
• In Concept 7.1 one objective states that students should "use sample data to draw inferences about a population," which is shaped by the cluster heading for 7.SP.A, "Use random sampling to draw inferences about a population."

Examples of problems and activities that serve to connect two or more clusters in a domain or two or more domains in the grade include:

• In Units 5 and 6, Concepts 5.3 and 6.2 connect 7.EE.A with 7.EE.B as students use properties of operations to generate equivalent expressions and solve problems using numerical and algebraic expressions and equations.
• Unit 8 Concept 8.3 connects 7.SP.C with 7.RP.A as students develop and use probability models, along with analyzing and using proportional relationships, to solve problems.
• Unit 10 Concept 10.2 connects 7.G.A with 7.NS.A as students draw geometric shapes with given conditions and add and subtract rational numbers to determine what figures the given conditions yield.