7th Grade - Gateway 1

The instructional materials reviewed for EdGems Math Grade 7 meet expectations for assessing grade-level content.

Each unit includes Form A and Form B Assessments as well as Tiered Assessments Form AT and Form BT, all of which include selected response and constructed response sections. Performance Tasks are also included with each unit. In addition, Gem Challenges are online, standards-based items for use after a standard has been addressed and are located after certain lessons. 

Examples of grade-level assessments include:  

• Unit 2, Proportional Relationships, Form A, Part II, Problem 1: “Write two different ratios that would form a proportion with the ratio of 8/6.” (7.RP.1) 
• Unit 5, Products & Quotients of Rational Numbers, Form A, Part I, Problem 5: “What is the value of the expression below? 6(−1+5)−30; a. -66,  b. -54,  c. -6,  d. 6” (7.NS.2a)
• Unit 6, Algebraic Expressions, Form A, Part II, Problem 16: “Explain two different ways to simplify 3(1.2x − 6+2.1x). Show that both ways lead to the same simplified expression.” (7.EE.1)
• Lesson 10.1, Probability, Online Gem Challenge 1, Problem 3: “Students in a math class will be randomly assigned a polygon for a class project. The only types of polygons being assigned are quadrilaterals, pentagons, hexagons, octagons and decagons. If there is an equal number of each type of polygon, what is the probability that the first polygon assigned will be a hexagon?” (7.SP.7)

There are above grade-level assessment items that could be modified or omitted without impact on the underlying structure of the instructional materials. These items include:

• Unit 9, Part I, Problem 9: “The area of the base of a trapezoidal pyramid is $$34ft^2$$. The pyramid is 12 feet tall. What is the volume of the pyramid?” (8.G.9)
• Unit 9, Part 1, Problem 10: “The perimeter of the base of a square pyramid is 12 yards. The height of the pyramid is 13.5 yards. What is the volume of the pyramid?” (8.G.9)
• Unit 8, Part I, Problem 2: “What is the approximate area of the shaded sector? Use 3.14 for pi.” (G-C.5) Students are using a circle with a sector shaded. The angle within the sector is labeled as 100* and the radius is labeled as 3 cm.
• Unit 8, Part II, Form A, Problem 4: “Determine if the following pair of triangles must be the same shape or not. Explain your reasoning.” (8.G.4)

The instructional materials reviewed for EdGems Math Grade 7 meet expectations for spending a majority of instructional time on major work of the grade. 

• The number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6.5 out of 10, which is 65%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 27.5 out of 43, which is approximately 64%.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 102 out of 140, which is 73%. 

A day-level analysis is most representative of the instructional materials because this perspective includes all connections to major work and follows the recommended pacing suggestions for addressing major work. As a result, approximately 73% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for EdGems 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 and clusters are connected to major standards and clusters of the grade, and lessons address supporting standards while maintaining focus on the major work of the grade. Examples of supporting work being used to support the focus and coherence of the major work of the grade include:

• Lesson 2.2 connects 7.G.6 and 7.RP.3 as students use facts about polygons to solve proportions. An example is, “Two squares have a scale of 1 : 8 1/2 . The perimeter of the larger square is 170 units. What is the side length of the smaller square?”
• Lesson 8.4 connects 7.EE.3 and 7.G.6 as students write and solve equations to determine area and missing side lengths of polygons. An example is, “The length of a rectangle is 2.5 cm. The area is $$20 cm^2$$. What is the width of the rectangle?”
• Lesson 10.2 connects 7.RP.2c and 7.SP.7 as students use proportions to predict outcomes using probability. For example, Example 2 states, “Last week in practice, Lou had 12 hits in 40 at-bats. Use experimental probability to predict how many hits he will have next week if he gets 30 at-bats.” The worked-out example describes how to set up a proportion to solve.
• Lesson 10.3 connects 7.SP.8 and 7.NS.2 as students find the probability of events by multiplying rational numbers. An example is, “A shirt comes in three colors (blue, red and black) and can be either long-sleeved or short-sleeved. If you choose one shirt from a pile, what is the probability that it is a short-sleeved blue shirt?” 

The instructional materials for EdGems Math Grade 7 meet expectations for being consistent with the progressions in the Standards. In general, the instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. In addition, the instructional materials give all students extensive work with grade-level problems.

Each Unit Overview describes how the work of the unit is connected to previous grade level work, for example:

• The introductory paragraph of the Unit 7 Overview, Solving Equations and Inequalities, states, “In Grade 6 CCSS, students solved one-step equations. In this unit, students will apply their understanding of balancing an equation to solving two-step equations. They will also use their skills of simplifying expressions to solve equations that include like terms or the Distributive Property. Students have previously used the inequality symbols to compare numbers and graph solutions to an inequality. Students will also combine that knowledge with the equation-solving process to solve inequalities and graph their solutions on a number line.”

Each Unit Overview includes Learning Progression, and each Learning Progression includes statements identifying what students have learned in earlier grades and what students will learn in future grades, for example:

Unit 6: Algebraic Expressions, In earlier grades, students have…

• Evaluated expressions in which letters stand for numbers. (6.EE.2)
• Applied properties of operations to generate equivalent expressions. (6.EE.3-4)
• Used variables to represent numbers and write expressions for real-world problems. (6.EE.6)

In future grades, students will…

• Solve multi-step equations that require simplifying before solving. (8.EE.7)
• Add, subtract and multiply polynomials. (A-APR)
• Interpret expressions that represent a quantity in terms of its context. (A-SSE.1)

In some units, the Unit Overview references connections to current grade level work that was addressed in prior units. Examples include:

• Lesson 2.2, Problem Solving With Proportions, the Teaching Tips Section includes, “In this lesson, students utilize their knowledge of scale factors and scales from Lesson 1.4 and apply these scales using proportions.” 
• Lesson 5.3, Dividing Rational Numbers, “Students divided fractions when working with complex fractions in Unit 1. Make connections to that work to remind students about the process of dividing fractions by multiplying by the reciprocal.”

The instructional materials present opportunities for students to engage with work with grade-level problems within each Student Lesson, Explore activity, Student Gem (online activities to provide practice with the content), Online Practice & Gem Challenge (only in some lessons), Exit Card, and Performance Task. For example: 

• In Lesson 5.4, students solve problems by identifying where to put parentheses in numerical expressions (7.NS.3). For example, “Insert one set of parentheses to make the equation true: Problem 31. 5 + 3 + 9 ÷ 3 = 9.”  

The materials include one example of off grade-level content that is not identified that distracts students from engaging with the grade-level standards:

• In Lesson 8.6, students find the area of sectors of circles (G-C.5). Example 5 presents a diagram of a circle with a 115 degree shaded sector and states, “Find the area of the shaded sector in circle M. Round to the nearest hundredth.”

Each unit includes a Parent Guide with Connecting Math Concepts, which includes, “Past math topics your child has learned that will be activated in this unit and Future math this unit prepares your child for.” For example, in Unit 6, Algebraic Expressions, “Past math topics your child has learned that will be activated in this unit; evaluating expressions in which letters stand for numbers, applying properties of operations to generate equivalent expressions, and using variables to represent numbers and write expressions for real-world problems.” “Future math this unit prepares your child for; solving multi-step equations that require simplifying before solving, adding, subtracting and multiplying polynomials, and interpreting expressions that represent a quantity in terms of its context.”

Each Lesson Guide includes Teaching Tips, which often include connections from prior or future grades, for example:

• Lesson 2.4, Proportional Relationships Equations, “In later grades (starting in Grade 8), students begin calling the constant of proportionality the slope of the line. You may want to connect to the concept of slope in this lesson as students are solidifying the idea that the constant of proportionality is the rate at which the function is increasing or decreasing. The larger the absolute value of the constant of proportionality, the steeper the line.”

In each Lesson Guide, Warm Up includes problems noted with prior grade-level standards. For example:

• Lesson 3.2, Percent of a Number, Concepts and Procedure (5.NF.4), Question 36, Skill: Find the value of each expression:
• a. (0.05)(100) 
• b. (0.2)(48) 
• c. (35/100)(90)
• d. (3/100)(57) 
• e. (1.1)(14.5) 
• f. (125/100)(32)

The instructional materials for EdGems Grade 7 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards.

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

• The objective of Lesson 1.2, “I can calculate unit rates and use unit rates to solve problems,” is shaped by 7.RP.A, Analyze proportional relationships and use them to solve real-world and mathematical problems.
• The objective of Lesson 5.1, “I can find the value of multiplication and division expressions involving integers,” is shaped by 7.NS.A; Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• The objective of Lesson 6.2, “I can use the Distributive Property to write equivalent expressions,” is shaped by 7.EE.A, Use properties of operations to generate equivalent expressions.
• The objective of Lesson 9.2, “I can calculate the surface area of prisms,” is shaped by 7.G.B, Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

• Lesson 1.4 connects 7.G.A and 7.G.B as students use scale factor to find the base and height of a triangle and use them to find area.
• Lesson 2.1 connects 7.NS.A and 7.RP.A as students perform operations with rational numbers to solve multi-step problems involving percent of change. 
• Lesson 7.3 connects 7.EE.B and 7.NS.A as students solve multi-step, real-world problems by writing and solving equations and performing appropriate calculations while applying the properties of operations. 
• Lesson 6.3 connects 7.EE.A and 7.EE.B as students use properties of operations to create equivalent expressions and solve problems. 
• Lesson 10.5 connects 7.SP.B and 7.SP.C as students use random sampling to draw inferences about two populations using various measures of center.