7th Grade - Gateway 1

The materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The assessments are aligned to grade-level standards. The instructional materials reviewed for this indicator were the Post-Tests, which are the same assessments as the Pre-Tests, both Form A and Form B End of Topic Tests, Standardized Practice Test, and the Topic Level Performance Task. Examples include: 

• Module 1, Topic 3, End of Topic Test-Form A, 7.RP.2b,2c: Students represent a proportional relationship in an equation. Question 13  presents a table with in-store and online prices for three items.  The item asks, “ Does the online price vary directly with the in-store price? Explain your reasoning. Define the variables and write an equation to represent the relationship between the in-store price and the online price. What is the constant of proportionality? Interpret the constant of proportionality for this problem situation. What is the online price for a product that costs $92 in the store? What is the percent markup for in-store products from online products?” 

• Module 3, Topic 1, End of Topic Post-test Form B, 7.EE.3: Students solve multi-step equations. Question 2 states, “A theater charges a service fee of $4.50 plus a ticket fee based on the section of the theater.” A table is provided with only part of the information given. Students fill in the missing information; “Write an algebraic expression to represent the cost of x number of Orchestra tickets; Can the same algebraic expression be used for tickets in the Mezzanine and tickets in the Second Balcony? Explain your reasoning. If a group buys 4 Mezzanine tickets and 2 Orchestra tickets, what will be the total cost of the tickets? Explain your reasoning.” 

• Module 4, Topic 1, Standardized Test, 7.SP.5: Students express the likelihood of a random event. Question 3 states, “Ilana drew a marble at random from a bag containing 4 blue, 3 red, 2 yellow, and 5 green marbles. What is the probability that she picked a marble that is not red?” 

• Module 3, Topic 2, End of Topic Test Form B, 7.EE.4a: Students solve a word problem in the form px+q=r. Question 23 states, “Veronica is an English tutor. She charges $60 for each tutoring session plus $0.75 per mile that she has to drive to and from the session. Write an equation to represent this situation. Define the variables.” 

• Module 5, Topic 1 Performance Task, 7.G.5: Students use facts about angles to write multi-step problems to solve for unknown angle measures in a figure. In X Marks the Spot, given pairs of intersecting lines, students reason to “Explain how you could determine the measure of each of the marked angles made by the X; Calculate the measures of the marked angles; For the third drawing shown, show two different ways to determine the unknown values. Write equations and determine the measures of all four angles.”

The materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The design of the materials concentrates on the mathematics of the grade. Each lesson has three sections (Engage, Develop, and Demonstrate) which contain grade-level problems. Each topic also includes a performance task. 

• In the Engage section, students complete activities that will “activate student thinking by tapping into prior knowledge and real world experiences and provide an introduction that generates curiosity and plants the seeds for deeper learning.” An example of this is Module 1, Topic 3, Lesson 4 (169), students are presented with a table that  lists the products from the All that Glitters Jewelry Store and the fact that the store marks up its prices so it can maximize its profits. Given the cost and the customer price students are asked the following: “What is the percent increase for each item? Use the formula shown to complete the table. (7.RP.3)

• In the Develop section, students do multiple activities that “build a deep understanding of mathematics through a variety of activities —real-world problems, sorting activities, worked examples, and peer analysis—in an environment where collaboration, conversations, and questioning are routine practices.” For example, Module 2, Topic 2, Lesson 2, Activity 2 (271) has students write equivalent fractional representation and write equivalent decimal representation to demonstrate the understanding that if the quotient of two integers is negative, the negative sign can be placed in front of the representative fraction, in the numerator of the fraction, or in the denominator of the fraction and in front of the decimal notation. (7.NS.2b,d) 

• In the Demonstrate section, students “reflect on and evaluate what was learned.” An example of this is Module 3, Topic 1, Lesson 1 (291k), where “ Students write an expression and substitute values in the expression to solve problems.” (7.EE.1 and 3) 

The end of each lesson in the student book includes Practice, Stretch, and Review problems. These problems engage students with grade level content. Practice problems address the lesson goals. Stretch problems expand and deepen student thinking. Review problems connect to specific, previously-learned standards. All problems, especially Practice and Review, are expected be assigned to all students. 

After the lessons are complete, the students work individually with the MATHia software and/or on Skills Practice that is included. 

• MATHia - Module 4, Topic 3 (533b): Students spend approximately 65 minutes in MATHia software comparing the characteristics of data displays, specifying which numerical characteristics can be determined from each display, then using data displays to compare populations by determining the visual overlap and describing the difference between the measures of centers in terms of measures of variability. 

• Skills Practice - Module 5, Topic 1 ( 593 b and c): Students can be assigned 5 problem sets for additional practice of the lesson skills such as: Constructing Segments and Angles, Classifying Angles, Solving for Unknown Angle, The Triangle Inequality Theorem, Identifying Unique Triangles.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days were also included in the evidence. 

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 8 ¾  out of 12, which is approximately 73 percent. 

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is is 39 out of 52, which is approximately 75 percent. 

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 114 out of 143, which is approximately 80 percent. 

The approximate number of days is most representative of the instructional materials because it most closely reflects the actual amount of time that students are interacting with major work of the grade. As a result, approximately 80 percent of the instructional materials focus on major work of the grade.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations that supporting content 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. Examples include: 

• In Module 1, Topic 1, Lesson 2, Activity 2.3: That’s a Spicy Pizza-Unit Rates and Circle Areas: Students use their knowledge of circles (7.G.4) and unit rates (7.RP.1) to determine which pizza is the better buy. 

• In Module 1, Topic 2, Lesson 3, Tagging Sharks – Solving Proportions Using Formal Strategies.  Students solve several proportions embedded in real-world situations. They use inverse operations to solve for unknown values in proportional relationships. The In Activity 3 students use proportions to solve scale problems, linking major cluster standards 7.RP.2c and 7.RP.3 to 7.G.1.

• In Module 4, Topic 3, Lesson 4, students use random samples from two populations to draw conclusions (7.SP.1-4) and solve real world problems involving the four operations with rational numbers (7.NS.3). Students create graphic displays to answer questions regarding means, medians, ranges, mean absolute deviation, and interquartile ranges. 

• In Module 5, Topic 1, Lesson 2, Special Delivery – Special Angle Relationships. Students use protractors and patty paper to explore special angle pairs formed when two lines intersect. (7.G.5) They calculate the supplement and complement of angles and classify adjacent angles, linear pairs, and vertical angles (7.NS.3)

The materials for Carnegie Learning Middle School Math Solution Course 2 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.

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: 

• In Module 1, Topic 3, Lesson 4, clusters 7.G. and 7.RP are connected, the Lesson Overview states,  “Students apply the percent increase and percent decrease formulas and then investigate a situation with a percent increase, followed by the same percent decrease. They calculate a depreciation rate to a car’s value over several years and recognize that the relationship is not proportional through their tabular and graphical models. Students also investigate percent increase in geometric contexts.”

• In Module 2, Topic 2, Lesson 2, clusters 7.NS and 7.RP are connected, the Lesson Overview states “Students divide integers and classify the quotients; they learn that the terminating and repeating decimal results are rational numbers. Students perform operations with positive and negative rational numbers as they calculate percent error and solve real-world problems. Students express rational numbers written as negative fractions in equivalent forms by changing the negative sign’s position.”

• In Module 4, Topic 1, Lesson 1, clusters 7.SP. and 7.NS are connected when students utilize knowledge of rational numbers to represent probability as a value between zero and one. The Lesson Overview states,  “Students learn vocabulary related to probability. They calculate the probability of simple events and their complements and express the results as fractions, decimals, and percents. Students also estimate probabilities using the benchmarks 0, \frac{1}{2}, and 1 on a number line. They realize that the sum of the probabilities for all outcomes of any experiment will always be 1.”

• Module 5, Topic 1, Lesson 5 connects 7.NS, 7.G, and 7.EE as students calculate the measure of angles in special angle pairs and write equations to solve problems involving unknown angles.  The Lesson Overview states, “Students use protractors and patty paper to explore special angle pairs formed when two lines intersect. They calculate the supplement and complement of angles and classify adjacent angles, linear pairs, and vertical angles. Students then use these special angle pairs in multi-step problems to write and solve equations for unknown angles.”

The materials for Carnegie Learning Middle School Math Solution Course 2 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. 

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 content is explicitly related to prior knowledge to help students scaffold new concepts. Content from other grade levels is clearly identified in multiple places throughout the materials. Examples include: 

• A chart in the Overview shows the sequence of concepts taught within the three grade levels of the series (FM-15). 

• The Family Guide (included in the student book) presents an overview of each Module with sections that look at “Where have we been?" and "Where are we going?” which address the progression of knowledge. 

• The Teacher Guide provides a detailed Module Overview which includes two sections titled, “How is ____ connected to prior learning?” and “When will students use knowledge from ___ in future learning?” 

  • Module 2 Overview- How is Operating with Signed Numbers connected to prior learning? (182C): “Operating with Signed Numbers draws on students’ fluency with adding, subtracting, multiplying, and dividing whole numbers, decimals, and fractions. They continue working on fluency in these operations when operating with signed rational numbers. This module also builds on students’ experiences with signed numbers on the number line and four quadrants of the coordinate plane. They use their knowledge of absolute value when they revisit distance on a number line in terms of magnitude, model operations on the number line, and connect the model to an algorithm. See Math Representation. Finally, Operating with Signed Numbers applies the properties of numbers students formalized in grade 6.” 

  • Module 3 Overview- When will students use knowledge from Reasoning Algebraically in future learning? (290D) “This module strengthens students’ reasoning and fluency in solving equations. In grade 8, students analyze and solve systems of linear equations, which involve equations with variables on both sides and rational coefficients. Using a double number line provides the underpinnings for geometric and algebraic transformations of objects and equations. In grade 8 and high school, students will transform geometric objects and conjecture about the effects on the coordinates of the figures. They will also transform linear functions, recognizing that the graph of y = mx 1 b is a translation of y = x.” 

• At the beginning of each Topic in a Module, there is a Topic Overview which includes sections entitled “What is the entry point for students?” and “Why is ____ important?” 

  • Module 1, Topic 1- Circles and Ratio (3D) - What is the entry point for students?: “Students are familiar with circles from elementary school. They have determined the perimeters of shapes and the areas of rectangles, parallelograms, and trapezoids. In grade 6, students reasoned extensively with ratios. They used various tools to write equivalent ratios: tape diagrams, double number lines, ratio tables, and graphs. Students know how to scale ratios up and down to solve real-world and mathematical problems. To begin Circles and Ratio, students draw on these experiences using physical tools to investigate the constant ratio pi and review basic ideas of ratios and proportional relationships." 

  • Module 1, Topic 3- Proportionality (129D) - Why is Proportionality important?: “Proportional Relationships provides students with opportunities to recognize proportional relationships in real-world situations and to solve related problems. Students learn financial literacy skills related to taxes and fees, commissions, markups and markdowns, tips, and percent increase and decrease, including depreciation. They will continue to use proportional reasoning to solve problems for everyday percent problems that they will encounter throughout their lives. In the Introduction to Probability, students will use ratios and percents to analyze probabilistic events. ” 

• The Topic Overview also contains a table called “ How does a student demonstrate understanding?” There is a checklist of what Students will demonstrate by the end of the Module.” 

• Each “Topic Lesson Resource” has Mixed Practice at the end of each topic. The Mixed Practice worksheet provides practice with skills from previous topics and the current topic, paced review fluency, problem solving from previous topics, and end of topic review problems from current topic.