7th Grade - Gateway 2

The instructional materials for Ready Grade 7 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill.

The instructional materials attend to procedural skills in the following ways: lessons that address specific standards, activities, and problem sets. Many of these opportunities are provided by the Additional Fluency Practice book for Grade 7. In the Practice and Problem Solving book, the development of procedural skills happen daily. In addition, the resources include math games for centers, unit practice, skills practice, and fluency repeated reasoning practice are included in the units.

• In Unit 3 Lesson 15 Writing Linear Expressions, students write linear expressions and apply operations to generate equivalent expressions (7.EE.1).

• In Unit 4 Lesson 18 Problem Solving with Angles, students write equations to find unknown angle measures using properties of supplementary, complementary, vertical, and adjacent angles (7.EE.4a).

• In Unit 1 Lesson 5 (7.NS.2d) Terminating and Repeating Decimals, there are problems included in the guided and independent practice that develop procedural skill. In these problems, students convert between decimals, fractions, and decimals and fractions.

The instructional materials reviewed for Ready Mathematics Grade 7 meet the expectation that teachers and students spend sufficient time working with engaging applications of mathematics without losing focus on the major work of the grade. Overall, the materials have opportunities for students to apply mathematical knowledge and/or skills in a real-world context.

During Independent Practice students often engage with problems that include real-world context and present opportunities for application. The Practice and Problem Solving workbook contains additional routine application problems, and Mid-Unit, Interim, and Unit Assessments often include problems that are contextual. For example:

• In Unit 1 Lesson 8 Independent Practice Problem 4 states, “Ally, Barbara, and Katherine will share the cost of a vacation rental for a week. Ally agrees to pay 30 percent of the cost. Barbara agrees to pay 0.45 of the cost. Katherine will pay the remaining balance. If the rental cost is $960, how much will Ally, Barbara, and Katherine each pay towards the week’s rent?” Students apply their knowledge of rational numbers to find the amount each person will pay of the total.

• Unit 4 Lesson 20 Practice and Problem Solving Book Problem 6 presents a flag in a geometric pattern of triangles and rectangles in three colors. The problem states, “What percentage of the total area of the flag is white?” Students apply both geometric and ratio reasoning to find a solution to the problem.

• The Unit 2 Performance Task begins, “You have been asked to make snack mix for a school event. Below are the main ingredients for two popular recipes. The amounts are for one serving.” Students are given two recipes and information on the cost of ingredients with several constraints. The task continues, “The total number of guests has not been determined, but you need to get some estimates of what the costs might be.” Students are given instruction on what to do, including choosing a recipe and explaining why it was chosen, finding the amounts of ingredients for different numbers of people, and making a shopping list for the maximum amount of people. Students are provided with some guidance to Reflect on Mathematical Practice, a Word Bank, and some Models.

The instructional materials reviewed for Ready Mathematics Grade 7 meet the expectations for balance. Overall, the three aspects of rigor are not always treated together and are not always treated separately.

In the Teacher Resource Book Program Overview Built for Rigor and Engagement outlines how the materials balance conceptual understanding, procedural skills and fluency, and application. The consistent structure of the lessons presents opportunities to “Understand,” where they develop conceptual understanding, followed by the sections Think It Through, Connect, and Apply, where they explore different procedural skills and application of the mathematics of the lesson. In addition, the Practice and Problem Solving book includes problems that present further opportunities to engage with the three aspects of rigor.

Students engage in the three aspects of rigor independent of each other. For example:

• Unit 2 Lesson 10 Understand Proportional Relationships is designed to develop conceptual understanding. Lesson 10 develops this understanding by having students connect tables and graphs to proportional relationships.

• In Unit 3 Lesson 15 Practice and Problem Solving Problem 3, students select all equivalent expressions to a given expression. Students use their understanding of equivalence and procedural skill to find all possible equivalent expressions.

• Unit 5 Lesson 26 Practice and Problem Solving Problem 6 states: “Evan surveyed his classmates to make a prediction about seventh-grade students. Look at his results in the table. Write two statistical questions that Evan could have asked to get his survey results. Then explain why Evan could not have asked a non-statistical question to get his results.” Students apply their understanding of statistics and relationships between variables in a table to identify plausible questions that are answered by the data in the table.

Balance is displayed in each unit with multiple lessons where two or three aspects of rigor are interwoven.

• In Unit 1 Lesson 3, students make connections between addition and subtraction of integers. Students solve contextual problems. At the end of this lesson, there is an opportunity for students to build fluency with integer operations as well as engage in contextual problems with integers.

• Unit 3 Lesson Practice Problem 15 states: “Market and More is having a cereal sale. Every box of cereal is $0.60 off the regular price. Jane has $10, and she wants to buy four boxes of the same cereal. She uses the inequality below to determine the regular price of cereal that she can afford. Solve the inequality and explain what the solution means. 4(r - 0.6) ≤10.”

• In Unit 4 Lesson 22, students apply their understanding of proportional relationships and scale drawings to determine the length of a boat. “Justin made a scale drawing of a sailboat he saw at a harbor. The length of the actual boat is 24 feet, and the mast is 20 feet high. In Justin’s sketch, the boat is 2 centimeters longer than the mast. What is the length of his sketch?”

The instructional materials reviewed for Ready Grade 7 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade level.

The Teacher Resource Book identifies MPs the for each lesson in the Table of Contents and in the CCSS Focus section as part of the Lesson Overview. SMP TIPs are found in the Teacher Resource Book throughout the lessons, and these tips highlight the integration of particular MPs within the lessons. Some examples of where the MPs are identified and used to enrich the mathematics content include:

• Unit 2 Lesson 9 Overview identifies MP 7. The SMP Tip for MP 7 states, “Students use structure when they explain how dividing 1 ½ by 2 is the same as multiplying 1 ½ by ½, because division by a number and multiplication by its reciprocal are equivalent operations.”

• Unit 3 Lesson 20 Area of Composite Figures. The SMP Tip for MP 1 states, “The Try It problem provides an opportunity for students to persevere in solving a problem and to reason abstractly. They will need to use the given measures to establish the length and width of the rectangle and the base and height of the triangle. They will then need to decide how to use those measures to find the area of the figure. (SMP 1)"

• In the Unit 1 End-of-Unit Performance Task, students model the mathematics of the task by using a number line to solve a multi-step problem that involves addition and subtraction of positive and negative numbers. (MP 4)

There are some instances where the MPs are overidentified. Unit 5 Lesson 29 Overview notes that MPs 1-7 are all present in the lesson. SMP2- Reason Abstractly and Quantitatively is identified in this lesson, but it is not evident where this practice occurs in the lesson. MP5 - Use appropriate tools strategically is also identified as being in the lesson, but there is no mention of mathematical tools in the lesson, and students are not directed to use or discuss them throughout the lesson.

The Mathematical Practices Handbook describes each of the MPs for students and provides students with questions to elicit thinking and discuss with a partner.

The instructional materials reviewed for Ready Grade 7 meet the expectation for prompting students to construct viable arguments and analyze the arguments of others. Overall, the materials offer students multiple opportunities to construct viable arguments and/or analyze the arguments of others.

Examples where students are prompted to construct viable arguments and analyze the arguments of others include:

• In the Unit 2 Performance Task, students are shown the work of another student in order to identify the mistake made in the work. Later, students reflect on the mathematical practices: “Argue and Critique - How did you discover and explain Raj’s mistake?”

• In Unit 3 Lesson 16, students construct viable arguments by refining a set of directions for solving two-step equations. The prompt states, “Talk about how you would find the correct answer, and then identify what Lonnie might have done incorrectly.”

• In Unit 5 Lesson 26, students compare sampling methods, and create a plan of their own to gather a random sample. Students critique the reasoning of others as they note the good ideas as well as the problems with each plan presented. Students construct arguments as they defend their own plan for creating a random sample.

The instructional materials reviewed for Ready Grade 7 meet the expectation for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. The materials provide teachers with SMP TIPs to help facilitate students to construct arguments and/or analyze the arguments of others.

Examples where teachers are supported to help students construct viable arguments and analyze the arguments of others include:

• In Unit 1 Lesson 1, teachers are directed to have students explain solutions to problems. The SMP Tip states: “Asking students to share their thinking provides them with an opportunity to practice critiquing the reasoning of others by rephrasing, asking for clarification, or identifying misconceptions.”

• In the Unit 4 Performance Task, teachers invite students to present solutions and choose a Reflect on Mathematical Practices question to answer. Teachers encourage students to explain how their solution is alike or different from other students’ solutions.

• In Unit 5 Lesson 29, students compare two companies' data shown in both dot and box plots. Students give an explanation of which brand seems to be more consistent in its performance. The SMP Tip states, “Asking students to reason inductively about the data and make plausible arguments that take into account the context from which the data arose develops their ability to justify conclusions, communicate them to others, and respond to the arguments of others. (SMP 3)”

The instructional materials reviewed for Ready Grade 7 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics.

• Lesson Vocabulary is identified at at the beginning of every lesson and used correctly to refer to mathematical terms and topics. For example, Unit 2 Lesson 9 includes a definition of a complex fraction in the teacher materials as well as the student materials. Complex fractions are defined as “a fraction where the numerator is a fraction, the denominator is a fraction, or both the numerator and the denominator are fractions.”

• Each lesson has an English Language Learners section in the Teacher Resource Book that contains some ways to support vocabulary development for all students. Some examples are:
  • Unit 1 Lesson 1 directs teachers to use the number line to review and reinforce the meaning of the phrases, "opposite sides of the number line" and "distance from 0." Teachers review the meaning of "integer" and have students locate 3 to 4 integers and name their absolute values.
  • In Lesson 5, teachers discuss the meanings of terminating decimals and repeating decimals. Students describe the meaning of each term in their own words.

• Teachers pose questions to students and attend to precision using appropriate terminology. For example, Unit 4 Lesson 22 teachers pose the following question, “Why do you multiply the numerator and denominator by 5?”

• In the Teacher Instruction Book, mathematical vocabulary is defined in the Find Out More section.

• Teachers are prompted in the Teacher Resource Book to have students use precise mathematical language. For example, in Lesson 17, the materials state, “In words, describe what the solution set is and what it means in context of the problem.”

• In the Student Practice and Problem Solving Book, mathematical terms are defined, along with a picture example in small square sections labeled “Vocabulary."