7th Grade - Gateway 1

The materials reviewed for EdGems Math (2024) Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Within the materials, print-based and digital assessments are included. Each unit has the following assessment types: Assessments that are available in two forms (A and B), Tiered Assessments available in two forms (AT and BT), Online Assessments available in two forms (A and B), and a Performance Assessment.

Examples of grade-level assessments include: 

• Unit 1, Assessments, Form B, Problem 11, “A map has a rectangular pickleball court that has a scale of 2 inches: 7 feet. On the map, the pickleball court is 6 inches by 12 inches. What is the area of the actual pickleball court in square feet?” (7.G.1)

• Unit 4, Performance Assessment, Problem 2, “Alaina and Josue are avid hikers and love tracking how far they have walked, how much elevation they have gained and how long they have been hiking…Alaina and Josue’s second hiking destination is Badwater Basin. They start their hike 57\frac{1}{4} feet below sea level and reach the lowest point on the trail at 283\frac{1}{3} feet below sea level. a. What was their elevation change from their start to the lowest point? Use a number line to support your answer. b. From their starting point, how much elevation would they have to gain or lose to be at an elevation of 0 feet? Show all the work necessary to justify your answer. c. Josue said that they lost the same amount of elevation as they gained. Explain whether you agree or disagree. Justify your answer using words and mathematics.” (7.NS.1 and 7.NS.3)

• Unit 7, Tiered Assessments, Form BT, Problem 14, “Joe’s age is less than twice Jill’s age (j) plus four. Joe is 32 years old. Write a simplified inequality that represents Jill’s age.” (7.EE.4b)

There is an above grade-level assessment item that could be modified or omitted without impacting the underlying structure of the materials. An example:

• Unit 9, Assessments, Form A, Problem 9, “Find the volume of each solid.” There is an image of a pentagonal pyramid with a base area labeled as 71.8 m^{2} and a height labeled as 9.3m. (G.GMD.3)

The materials reviewed for EdGems Math (2024) Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each unit has a Storyboard that includes a Launch and a Finale. These tasks incorporate real-world applications and provide opportunities for students to apply unit concepts. Explore! activities provide students with an opportunity to discover mathematical concepts in a variety of methods. Teacher Gems are teacher-led activities that engage students with the main concepts of the lesson. Student lesson tasks fall into four categories (Practice My Skills, Reason and Communicate, Apply to the World Around Me and Spiral Review) in which students engage in grade-level content.

Materials engage all students in extensive work with grade-level problems to meet the full intent of grade-level standards. Examples include:

• In Unit 2, Lesson 2.4, students engage in extensive work with grade-level problems to meet the full intent of 7.RP.2 (Recognize and represent proportional relationships between quantities.). In the Starter Choice Board, Storyboard Starter, students decide whether ratios in a table are equivalent. “I would love to visit Kuwait one day. I looked up the average seasonal temperatures in Kuwait, but they were all listed in degrees Celsius. To imagine what the weather might feel like, I created a table to compare temperatures in both measurement systems. Could you use proportions to convert between Celcius and Fahrenheit? Why or why not?” A table is given with labels of “℃” and “℉” with values 0,1,2,3 under the ℃ column and 32, 33.8, 35.6, and 37.4 under the ℉ column. In Exit Card, Exercise 1, students complete a table and graph based on an equation. The problem states, “Complete the table and graph the equation y=2x.” A table is provided with x values of 0, 1, 2, 3, 4 and corresponding y values blank. A graph is provided with the x- and y- axes labeled from 1 to 10. In Exercise 2, students identify the constant of proportionality from a table and use it to write an equation. “The table below shows ordered pairs which represent a proportional relationship. Write an equation relating the x- and y- coordinates in the form y=rx. A table is given with x values of 0, 1, 2, 3, 4 and y values of 0, 3, 6, 9, 12. In Exercise 3, students identify the constant of proportionality from a given equation. “What is the constant of proportionality of the equation y=\frac{x}{6}?”

• In Unit 4, Lessons 4.1, 4.3, and 4.4, students engage in extensive work with grade-level problems to meet the full intent of 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.) In Lesson 4.1, Student Lesson, Exercises 4-6, students use a number line to find sums of numbers. “Use a number line to find each sum. -5+(-1) 5. 6+(-2) 6. -3+4”. In Lesson 4.3, Explore, Steps 1-3, students model and explain the subtraction of rational numbers using a number line. “One model that can be used to add and subtract integers is the number line. Use arrows on the number line to model each situation. Step 1: Use the number line to find the value of 5-4. Step 2: Use the number line to find the value of 5+(-4). Step 3: How are the expressions in Step 1 and Step 2 similar or different? How do the values of the expression compare?” In Lesson 4.4, Student Lesson, Exercise 9, students use a number line to find fractional distances between rational numbers. “ What two values are exactly \frac{7}{3} units from point J on the number line? Explain how you know.” A number line is shown extending from -3 to 3 with markings at each third and a point, J, marked at -\frac{2}{3}.

• In Unit 6, Lessons 6.3 and 6.4, students engage in extensive work with grade-level problems to meet the full intent of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.). In Lesson 6.3, Student Lesson, Exercises 10-12, students factor algebraic expressions. “Factor each expression using the greatest common factor. 10. 8x-20 11. 8x + 16y 12. 14x-21y+35d” In Student Lesson, Exercise 17, students expand an expression using the distributive property. One problem states, “A rectangular trampoline has a length of 5 feet and a width of x + 7 feet. a. What is the area of the trampoline as an expression with no parentheses? b. What is the area of the trampoline when x = 10.5 feet?” In Lesson 6.4, Student Lesson, Exercise 1, students add like terms to simplify an expression. “Examine the expression 6+5y+x-8y. a. Which terms are like terms? b. What is the coefficient of the x term? c. Write the expression in simplified form.”

• In Unit 10, Lesson 10.4, students engage in extensive work with grade-level problems to meet the full intent of 7.SP.1 (Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.) In Student Lesson, Exercise 4, students explain how a sample will give the best chance for an accurate prediction to a statistical question. “David wants to know which football team is the most popular in the country. Which sample will give him the best chance to make an accurate prediction? Explain your reasoning. A. A survey of 80 men walking into a stadium before the game. B. A survey of 80 men and women leaving a stadium after their game. C. A survey of 80 people randomly selected from a sporting goods company’s mailing list. D. A survey of 80 people randomly selected from a national phone directory.” In Student Lesson, Exercise 10, students use data to make inferences. “Two different students surveyed 90 random students at Eagle Middle School about their lunch preference. Use the information in the table below to make at least two inferences about the overall student population. Explain how you arrived at each inference using the information provided.” A table is provided with rows labeled Sample1 with the values 9, 21, 60, 90 and Sample 2 with the values 9, 18, 63, 90. Column headings of Salad, Hot Dogs, Pizza and Total are above the data values.

The materials reviewed for EdGems Math (2024) Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

When implemented as designed, the majority of the materials address the major clusters at least 65% of the time. Materials were considered from three perspectives; units, lessons, and instructional time (days).

• The approximate number of units devoted to major work of the grade is 7 out of 10, which is approximately 70%.

• The approximate number of lessons devoted to major work is 27 out of 43, which is approximately 63%.

• The approximate number of days devoted to instructional time, including assessments, of major work is 100.5 out of 146, which is approximately 69% of the time.

The lesson instructional time (days) are considered the best representation of the materials because these represent the time students are engaged with major work, supporting work connected to major work, and include assessment of major work. Based on this analysis, approximately 69% of the instructional materials focus on the major work of the grade.

The materials reviewed for EdGems Math (2024) Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Each unit contains a Unit Overview with information regarding standards correlation and how standards are connected in a unit. Specific examples are provided as well.

Materials connect supporting work to major work throughout the grade level, when appropriate, to enhance major grade-level work. Examples include:

• Unit 2, Lesson 2.2, Student Lesson, Exercise 3, connects the supporting work of 7.G.1 (Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale) to the major work of 7.RP.2 (Recognize and represent proportional relationships between quantities). Students solve a problem involving scale drawings of geometric figures in a proportional relationship. An example is as follows, “The pentagons below have a scale of 2 : 7. What are the values of x and y?” Two scaled pentagon images are given, one with two sides labeled y and 7 and corresponding sides on the second labeled 3 and x.

• Unit 3, Lesson 3.1, Student Lesson, Exercise 20, connects the supporting work of 7.SP.1 (Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.) to the major work of 7.NS.2 (Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers). Students calculate percentages using results from a sample population. An example is as follows, “Jake interviewed students in the cafeteria. He asked if they preferred pizza, tacos or hamburgers. He found that \frac{3}{5} of the students interviewed preferred pizza and 3 out of every 10 preferred tacos. What percent of the students preferred hamburgers?”

• Unit 8, Lesson 8.2, Student Lesson, Exercise 8, connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities). Students use their knowledge of angle relationships to write an equation to find each angle measure. An example provided is, “Find the value of x for each diagram.” Exercise 8 gives a diagram of an angle that has a ray splitting it into two adjacent angles. The two smaller angles are labeled as (5x-19)^{\circ} and (2x+5)^{\circ}. The whole angle is labeled 119° .

The materials reviewed for EdGems Math (2024) Grade 7 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Each unit contains a Unit Overview with a section titled, Connecting Content Standards where information regarding connections as well as specific examples is provided when applicable.

There are connections from supporting work to supporting work and/or major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Unit 5, Lesson 5.3, Student Lesson, Exercise 13 connects the major work of 7.RP.A (Analyze proportional relationships and use them to solve real-world mathematical problems) to the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions). Students solve a real-world problem involving rational numbers and rates: “Charlie had 6 bags of trail mix to serve at day camp. Each bag held 2.75 pounds of trail mix. If each camper gets \frac{3}{8} pound of trail mix, how many campers will get trail mix?”

• Unit 7, Lesson 7.3, Student Lesson, Exercise 10 connects the major work of 7.EE.A (Use properties of operations to generate equivalent expressions) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations). Students apply properties of operations to describe the steps for solving an algebraic equation: “In words, describe the steps you would take to solve the equation 5(x+2)+3x=82.”

• Unit 9, Lesson 9.1, Student Lesson, Exercise 19 connects the supporting work of 7.G.A (Draw, construct, and describe geometrical figures and describe the relationships between them) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume). Students calculate the area of the plane section of a three-dimensional figure: “A cylinder is 12 inches tall and has a diameter of 8 inches. a. A cut is made perpendicular to the base of the cylinder and through the center of the cylinder. What is the area of the surface created with the perpendicular cut? b. A cut is made parallel to the base of the cylinder and through the center of the cylinder. What is the area of the surface created with the parallel cut?”

The materials reviewed for EdGems Math (2024) Grade 7 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

EdGems Math provides teachers with evidence that the content addressed within each unit is related to both previous and future learning. This information is first outlined in the Content Analysis section of the Unit Overview. The Unit Overview then provides a Learning Progressions table for each unit, illustrating the vertical alignment of the topics and standards present in the unit. This vertical progression of mathematical concepts and standards is further elaborated throughout each unit. Each unit includes a Readiness Check and Starter Choice Boards that focus on prerequisite skills. Each Readiness Check reviews three to five skills from a previous grade level, which represent prerequisite skills for the unit. The Unit Overview outlines the skills targeted within the Readiness Checks. Starter Choice Boards offer three options: "Storyboard," "Building Blocks," and "Blast from the Past." The Building Blocks warm-up focuses on a prerequisite skill that directly relates to the current lesson. The standards alignment for Building Blocks is provided in the Teacher Guide for each lesson. Finally, "Explore!" activities build upon students' prior knowledge and experiences to scaffold the discovery of grade-level concepts or skills. The Teacher Guide provides an overview of the activity, including connections to previous grades.

Materials identify content from future grades and relate it to grade-level work. Examples include:

• Unit 3, Planning and Assessment, Unit Overview, Readiness Check & Learning Progression, “In this unit, students will… Convert a rational number to a decimal (7.NS.A.2d), solve multi-step percent problems (7.RP.A.3), and solve markup, discount, percent increase, percent decrease, and percent error problems (7.RP.A.3),” connecting it to, “In the future, students will… Construct and interpret two-way tables and use relative frequencies to describe possible associations between two variables (8.SP.A.4), and model situations using exponential functions involving percent growth or decay (HS.F-LE.A.1).” Examples are given for each skill.

• Unit 5, Planning and Assessment, Unit Overview, Readiness Check & Learning Progression, “In this unit, students will… Understand that multiplication is extended from fractions to rational numbers through the properties of operations (7.NS.A.2a), understand that integers can be divided as long as the divisor is not zero (7.NS.A.2b), and solve real-world problems involving multiplication and division with rational numbers (7.NS.A.2c, 7.NS.A.3),” connecting it to, “In the future, students will… Perform operations with numbers expressed in scientific notation (8.EE.A.4), and determine and explain the rationality of the sums and products of rational and irrational numbers (HSN.RN.B.3).” Examples are given for each skill.

• Unit 9, Planning and Assessment, Unit Overview, Content Analysis, “This unit also develops students’ understanding of the properties of solids by asking students to identify the two-dimensional figures formed by slicing solids parallel and perpendicular to their bases. Slicing solids will help students distinguish between prisms and pyramids as well as make sense of their nets. When a right prism is sliced parallel to its base, the resulting two-dimensional figure is a shape that is the exact same size and shape as the base… In future grades, students will explore congruence and similarity in two-dimensional figures, find the surface area and volume of right and non-right solids (including cylinders, cones, and spheres), and slice solids on an axis that is not parallel or perpendicular to the base.”

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include:

• Unit 2, Lesson 2.2, Teacher Guide, Starter Choice Board Overview identifies prior grade level skills with their standard. “Starter Choice Board Overview Storyboard: Storyboard: Solve a proportion (7.RP.A.3) Building Blocks: Solve one-step multiplication equations (6.EE.B.7) Blast from the Past: Compute a measurement conversion (4.MD.A.2, 6.RP.A.3) Fluency Board Skills: Solve one-step equations, add and subtract decimals, plot fractions and decimals on a number line.” The Lesson Planning Guidance: Day 1 supports teachers in choosing the activity that supports the needs of their students. An example is, “In this lesson, the “Building Blocks” task asks students to access background knowledge on solving one-step multiplication equations. Use this activity if many of your students need support in recalling this skill. Consider using Expert Crayons to have students move around the room supporting each other. Choose the Starter Choice Board’s “Blast from the Past” task to give students an opportunity to utilize problem solving skills involving computing a measurement conversion.”

• Unit 6, Planning and Assessment, Unit Overview, Standards Correlation, indicates that lesson 6.2 connects to 6.EE.A.2. “This unit includes Focus Content Standards across two domains and two grade levels. In the first lesson, students’ concentration on the Number System domain within the Grade 7 standards will conclude, though students will continually apply rational number operations in this course and beyond. The remainder of the unit transitions into the Expressions and Equations domain by revisiting prerequisite work from Grade 6 (6.EE.A.) and beginning investigations into the last two major clusters of the year. The Grade 7 standards in this unit are formatively assessed throughout the unit and summatively assessed in the unit’s Test Prep, Performance Assessment and Unit Assessments.”

• Unit 7, Planning and Assessment, Unit Overview, Content Analysis highlights prior grade-level skills, such as solving one-step equations and inequalities, aligned with standards 6.EE.B.7 and 6.EE.B.8. “This unit builds directly upon students’ work in Grade 6 with equations and inequalities. While the Grade 6 standards limited this work to one-step equations and inequalities, the Grade 7 standards focus on solving multi-step equations and inequalities, limited to equations in the forms px + q = r or p(x + q) = r and inequalities in the forms px + q < or > r.”