7th Grade - Gateway 1

The instructional materials reviewed for enVision Mathematics Common Core Grade 7 meet expectations that they assess grade-level content.

Each Topic contains diagnostic, formative, and summative assessments. Summative assessments provided by the program include: Topic Assessments Forms A and B, Topic Performance Tasks Forms A and B, and Cumulative/Benchmark Assessments. Assessments can be administered online or printed for paper/pencil format. No above grade-level assessment questions are present. Examples of grade-level assessment aligned to standards include: 

• Topic 1, Assessment Form A, Question 2, “Four out of nine dogs weigh less than 20 pounds. What is the decimal equivalent for the number of dogs weighing under 20 pounds? A) 0.$$\overline{2}$$ B) 0.24 C) 0.$$\overline{4}$$  D) 0.49. (7.NS.2)
• Topic 2, Assessment Form A, Question 3, “The graph shows how many bottles a machine fills in a certain number of seconds. Part A: What is the constant of proportionality, and what does it mean in this situation? Part B: Choose one ordered pair on the graph. What does it represent in this situation?” (7.RP.2)
• Topic 3, Performance Task Form A, Question 6, “The sanctuary takes out a $12,500 loan to renovate its gift shop. At 5% simple interest, how much would the sanctuary need to pay back in total after 10 years?” (7.RP.3)
• Topics 1-4, Cumulative/Benchmark Assessment, Question 20, “The temperature of chicken soup is 192.7° F. As it cools, the temperature of the soup decreases 23° F per minute. Part A: What is the temperature of the soup after 25 minutes? Part B: How many minutes will it take for the soup to cool to 100.7° F?” (7.EE.3)
• Topic 8, Performance Task Form A, Question 3, “Dave decides to add a strip of wood diagonally in each frame for extra support. The wood is sold in lengths of 10 feet, 15 feet, or 20 feet. If Dave wants to use one strip for each diagonal with the least amount of waste, which length of wood should he buy? Explain.” (7.G.2)

The instructional materials reviewed for enVision Mathematics Common Core Grade 7 meet expectations for spending a majority of instructional time on major work of the grade. 

• The approximate number of Topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5.5 out of 8, which is approximately 69%.
• The number of lessons (content-focused lessons, 3-Act Mathematical Modeling tasks, projects, Topic Reviews, and assessments) devoted to major work of the grade (including supporting work connected to the major work) is 67 out of 89, which is approximately 75%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 144 out of 186, which is approximately 77%.

A lesson- level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each Topic. As a result, approximately 75% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. Examples from the Teacher Resource include:

• Lesson 6-2, Draw Inferences from Data, Visual Learning, Do You Know How?, Item 6, students use proportional relationships and equations to make predictions based on given data, “In the dot plot above, 3 of 20 players made all 5 baskets. Based on this data, how many players out of 300 players will make all 5 baskets.” This question connects the supporting work of 7.SP.2, use data from a random sample to draw inferences about a population with an unknown characteristic of interest to the major work of 7.RP.2, recognize and represent proportional relationships between quantities and 7.EE.3, solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
• Lesson 6-3, Make Comparative Inferences about Populations, Visual Learning, Example 3, students calculate measures of center and measures of variability to compare two data representations, “Mr. Bunsen had students grow the same type of plant in two different rooms to test the growing conditions. The box plots show the heights of all the plants after 3 weeks. How do the two populations compare? What inferences can be drawn?” This example connects the supporting work of 7.SP.3, informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability to the major work of 7.EE.3, solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.
• Lesson 7-3, Understand Experimental Probability, Visual Learning, Example 2, students use ratios and percents to make predictions using experimental probability while analyzing proportional relationships, “Joaquin also kept track of players and winners for his game during the fair. Based on the results shown in the table, how many winners should he expect if 300 people play his game?” This example connects the supporting work of 7.SP.6 supports approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency and predict the approximate relative frequency given the probability to the major work of 7.RP.3, use proportional relationships to solve multistep ratio and percent problems.
• Lesson 8-1, Solve Problems Involving Scale Drawings, Visual Learning, Example 1, students use proportional relationships to solve problems involving scale drawings, “The island in the blueprint is 6 inches long. What is the actual length of the island in the diagram?” This example 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.
• Lesson 8-4, Solve Problems Using Angle Relationships, Visual Learning, Example 1, students find the measure of angles using angle relationships and recognize the relationship between different angles formed by intersecting lines and rays, “Why might a civil engineer be concerned if the intersection of roads is skewed?” This example connects the supporting work of the 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.3, solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form.

The instructional materials reviewed for enVision Mathematics Common Core Grade 7 meet expectations that the amount of content designated for one grade-level is viable for one year. As designed, the instructional materials can be completed in 162-186 days.

According to the Pacing Guide in the Teacher Resource, Program Overview, “enVision Mathematics 6-8 was designed to provide students rich opportunities to build understanding of important new mathematical concepts, develop fluency with key skills necessary for success in algebra, and to gain proficiency with the habits of mind and thinking dispositions of proficient mathematical students. To achieve these goals, the program includes content-focused lessons, 3-Act Mathematical Modeling lessons, STEM projects, and Pick a Project. All of these instructional activities are integral to helping students achieve success, and the pacing of the program reflects this. Teachers are encouraged to spend 2 days on each content-focused lesson, giving students time to build deep understanding of the concepts presented, 1 to 2 days for the 3-Act Mathematical Modeling lesson, and 1 day for the enVisions STEM project and/or Pick a Project. This pacing allows for 2 days for each Topic Review and Topic Assessment, plus an additional 2 to 4 days per topic to be spent on remediation, fluency practice, differentiation, and other assessment.” For example:

• There are 8 Topics with 57 content-focused lessons for a total of 114 instructional days.
• Each of the 8 Topics contains a 3-Act Mathematical Modeling Lesson for a total of 8-16 instructional days.
• Each of the 8 Topics contains a STEM Project/Pick a Project for a total of 8 instruction days.
• Each of the 8 Topics contains a Topic Review and Topic Assessment for a total of 16 instructional days. 
• Materials allow 16-32 additional instructional days for remediation, fluency practice, differentiation, and other assessments.

The instructional materials reviewed for enVision Mathematics Common Core Grade 7 meet expectations for the materials 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. According to the Teacher Resource, Program Overview, “Connections to content in previous grades and in future grades are highlighted in the Coherence page of the Topic Overview in the Teacher’s Edition.” These sections are labeled Look Back and Look Ahead. Examples from the Teacher Resource include:

• Topic 1 Overview, Rational Number Operations, Math Background, Coherence, “In Grade 6 students graphed integers and their opposites on a number line to understand their equal distances from zero. Students examined positive and negative numbers in real world contexts and related the meaning of the distance from the number to zero. Students began exploration into the concept of the opposite of the opposite of a number as being the number itself. In Grade 6, students performed operations with decimals and fractions by following an algorithm or utilizing a number line. Students recognized that opposite signs in rational numbers indicated locations on opposite sides of zero on the number line. In Grade 8, students will continue to use operations with positive and negative integers and rational numbers to solve equations by using inverse relationships and operation rules. In Grade 8, students will use operations with positive and negative integers and rational numbers to find solutions for a system of linear equations using algebraic methods. In Grade 8, students will begin to examine the use of square and cube roots and will discover that square roots of negative numbers cannot be found in the real number system.” 
• Topic 2 Overview, Analyze and Use Proportional Relationships, Math Background, Coherence, “In Grade 6 students learned to reason about ratios by using equivalent ratios, tables of equivalent ratios, bar diagrams, and double-number-line diagrams. In Topic 6, they used what they learned about ratios to work with a special type of ratio called a percent. In Topic 5, students learned about a special type of ratio called a rate. In Grade 8, students will understand the connections among proportional relationships, lines, and linear equations. Students will also graph proportional relationships and compare proportional relationships represented in different ways. In Grade 8, students will use similar triangles to investigate slope, and they will derive the equations y = mx and y = mx + b for lines.”
• Topic 5 Overview, Solve Problems Using Equations, Math Background, Coherence, “In Grade 6, students learned to evaluate expressions, and then applied this knowledge to write and solve one-step equations and inequalities. Students represented and analyzed the quantitative relationship between dependent and independent variables and established an understanding that a change to one quantity directly affects the other. In Grade 6, students learned to use graphs, tables, and number lines. They analyzed solutions and related mathematical models to expressions, equations, and inequalities. In Grade 8, students will extend their understanding of expressions, equations, and inequalities to more complex versions. They begin to explore equations that contain two variables. In Grade 8, students continue to make connections between models and equations including proportional relationships, lines, and linear equations.” 

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The Solve & Discuss It! section presents students with high-interest problems that embed new math ideas, connect prior knowledge to new learning and provide multiple entry points. Example problems are highly visual, provide guided instruction and formalize the mathematics of the lesson. Try It! provides problems that can be used as formative assessment following Example problems and Convince Me! provides problems that connect back to the Essential Understanding of the lesson. Do You Understand?/Do You Know How? problems have students answer the Essential Question and determine students’ understanding of the concept and skill application. Examples from the Teacher Resource include:

• Lesson 1-5, Add and Subtract Rational Numbers, Solve & Discuss It!, students extend their knowledge of positive and negative rational numbers to adding and subtracting with rational numbers and apply their knowledge to solve real-world problems, “Malik hikes Castle Trail from point A to point B. The elevation at Point A is below sea level. What are the possible beginning and ending elevations of Malik’s hike?” (7.NS.1)
• Lesson 3-6, Solve Simple Interest Problems, Visual Learning, Example 1, students understand what simple interest is and how it is calculated, “Victoria opens a savings account with a deposit of $300. She will earn 1.6% simple interest each year on her money. How much interest will she earn over 5 years (assuming she does not add or take out any money?).” (7.RP.3)
• Lesson 4-5, Factor Expressions, Do You Know How?, Item 3, students find common factors of linear expressions using the distributive property and recognize factoring is the opposite of expanding expressions, “Sahil is putting together supply kits and has 36 packs of x pencils, 12 packs of y crayons, and 24 erasers. a. Write an expression to show the total number of items. b. Use factoring to show how many kits Sahil can make while putting every type of item in each kit. c. Use the factored expression to find the number of each item in each kit.” (7.EE.1, 7.EE.2) 
• Lesson 6-4, Make More Comparative Inferences About Populations, Visual Learning, Example 1, students use center and variability to compare populations, “Quinn collects data from a random sample of 20 seventh grade students who participate in a youth fitness program. She compares the number of curl-ups each student completed in thirty seconds last year and this year. What can Quinn infer from her comparison of the data sets?” (7.SP.3, 7.SP.4)
• Lesson 5-1, Write Two-Step Equations, Visual Learning, Example 2, Try It!, students use a variable to represent an unknown in a real-world context and construct an equation, “Marcia and Tamara are running a race. Marcia has run 4 kilometers. Tamara has completed $$\frac{3}{4}$$ of the race and is 2.5 kilometers ahead of Marcia. Write an equation that represents the relationship between the distances each girl has run. Let k represent the total length of the race in kilometers.” (7.EE.4)
• Lesson 8-5, Solve Problems Involving Circumference of a Circle, Visual Learning, Example 1, Convince Me!, students use given information about diameter to make deductions about circumference, “If the diameter is doubled, what happens to the circumference? Explain.” (7.G.4) 

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each Lesson Overview contains a Coherence section that connects learning to prior grades. Examples from the Teacher Resource include:

• Lesson 2-1, Connect Ratios, Rates, and Unit Rates, Lesson Overview, Coherence, “Students will be able to use ratios and rates to describe the relationship between two quantities. Students find equivalent ratios and use unit rates to solve multi-step problems.” (7.RP.1, 7.RP.3) “In Grade 6, students learned the concepts of ratios and rates and used math models and ratio reasoning to solve problems.”
• Lesson 6-1, Population and Samples, Lesson Overview, Coherence, “Students will be able to understand the difference between a population and a sample. Students establish whether a sample is representative of a population. Students will be able to generate random samples that represent the entire population.” (7.SP.1). “In Grade 6, students learned that statistical questions include, and account for variability in the data as part of the answers.”
• Lesson 8-2, Draw Geometric Figures, Lesson Overview, Coherence, “Students will be able to draw geometric shapes with given conditions. Students name and classify quadrilaterals according to their properties.” (7.G.2) “In Grade 6, students drew polygons in the coordinate plane using given conditions. Students found the area of special quadrilaterals and applied this understanding to solve real-world problems.”

The instructional materials reviewed for enVision Mathematics Common Core Grade 7 meet expectations that materials foster 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. Topics are divided into Lessons focused on domains. Grade 7 standards are clearly identified in each Topic Planner found in the Topic Overview. Additionally, each lesson identifies the Content Standards in the Mathematics Overview. Examples from the Teacher Resource include:

• Lesson 1-6, Multiply Integers, Lesson Overview, Mathematics Objective, “Multiply positive and negative integers. Use models and mathematical properties to develop a deep understanding of and fluency with multiplying integers.” (7.NS.2a, 7.NS.2c) 
• Lesson 2-2, Determine Unit Rates with Ratios of Fractions, Lesson Overview, Mathematics Objective, “Find unit rates with ratios of fractions. Use unit rates to solve multi-step problems.” (7.RP.1, 7.RP.3)
• Lesson 4-7, Subtract Expressions, Lesson Overview, Mathematics Objective, “Identify the similarity of the procedure between subtracting integers and subtracting linear expressions. Simplify linear expressions involving subtraction.” (7.EE.1, 7.EE.2)
• Lesson 6-1, Populations and Samples, Lesson Overview, Mathematics Objective, “Understand the difference between a population and a sample. Establish whether a sample is representative of a population. Generate random samples that represent the entire population.” (7.SP.1) 
• Lesson 8-7, Describe Cross Sections, Lesson Overview, Mathematics Objective, “Describe and sketch cross sections of right rectangular prisms and right rectangular pyramids. Solve problems involving cross sections.” (6.G.A.3) 

Materials 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. Examples include:

• Lesson 2-5, Graph Proportional Relationships, Visual Learning, Example 2, students solve real-world problems involving the four operations with rational numbers, “The graph shows a proportional relationship between the distance and the amount of time Mr. Brown drives. a. What does each of these points represent in this situation: (0, 0), (1, 55), and (5, 275)? b. What is the constant of proportionality? c. What equation relates the distance, y, and the time, x?” This example connects the work of 7.RP to the work of 7.NS. 
• Lesson 3-2, Connect Percent and Proportions, Visual Learning, Example 1, students use their understanding of proportional relationships to solve equations with percentages from a diagram (shown are 9 blue dots representing shots made and 3 purple dots representing shots missed), “The basketball team statistician tracked the shots Emily made and the shots she missed during the last game. What percent of attempted shots did she make? Draw a bar diagram and write a proportion to represent the number of shots made and the total number of shots. Solve the proportion to find the percent of shots made during the last game.” This example connects the work of 7.RP to the work of 7.EE. 
• Lesson 4-4, Expand Expressions, Practice & Problem Solving, Item 15, students generate equivalent expressions as they use properties of operations to add, subtract, multiply, or divide rational numbers, “A grocery store has 13%-off sale on all bread. You decided to purchase 6 loaves of bread. Let b be the original price of a loaf of bread. Expand the expression 6(b - 0.13b). Once the expression is expanded, what do the terms represent?” This example connects the work of 7.EE.A, use properties of operations to generate equivalent expressions to the work of 7.NS.A, apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 
• Lesson 5-1, Write Two-Step Equations, Practice and Problem Solving, Item 7, students use the full range of rational numbers as they work with algebraic expressions and equations, “A farmer ships oranges in wooden crates. Suppose each orange weighs the same amount. The total weight of the crate with g oranges is 24.5 pounds. Write an equation that represents the relationship between the weight of the crate and the number of oranges it contains.” Students are provided a diagram that shows the weight of the crate itself as 15 pounds. This question connects the work of 7.NS to the work of 7.EE.
• Lesson 8-3, Draw Triangles with Given Conditions, Visual Learning, Example 3, students draw triangles with a combination of given side lengths and angle measures, “Can more than one triangle be drawn with the following conditions? a. side lengths of 5 inches and 6 inches with an angle of 45°. b. a side length of 6 inches with angles at each end measuring 40° and 60°.” This example connects the work of 7.G.A, draw, construct, and describe geometrical figures and describe the relationships between them to the work of 7.G.B, solve real-life and mathematical problems involving angle measure, area, surface area, and volume.