Math 7 Unit 2

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

This chapter begins with a focus on conversions between fractions and decimals. Students look at how to represent a fraction and a decimal using division. Then they look at changing decimals to fractions, learning how to convert both terminating and repeating decimals.

In Section 2.2, students begin to work with integers. Students start by considering a linear model with directional movement as they represent the movement of an acrobat on a tightrope with diagrams and numeric expressions. Within this model, students compose and decompose integers and rational numbers as they find the sum of positive and negative numbers. They examine multiplication as repeated addition and then they depart from the linear model and transition to using manipulatives to help make sense of integer addition and multiplication. They continue to extend this understanding to signed rational numbers.

In the final section, students will review and extend their previous work with coordinate graphs. They will investigate the effect of changing the scale on a graph, both its appearance and usefulness. They will practice choosing a scale and creating their own axes. Students reinforce their understanding of partitioning numbers into parts as they plot integer, fractional, and decimal coordinates.

Throughout Chapter 2 students will continue to develop the practices introduced in Chapter 1. Remember, an overriding goal of every lesson is Standard 1: Make sense of problems and persevere in solving them. Even when not specifically mentioned, one of your goals while facilitating these lessons is to encourage understanding through the use of questioning strategies during whole class activities, while you circulate among teams, and during closure activities.

In the last section of this chapter you will have the opportunity to implicitly introduce the final mathematical practice standard: Standard 4: Model with Mathematics.

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.

a) Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b) Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

d) Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

a) Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

d) Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.RP.2.(Preparation for Section 4.2) Recognize and represent proportional relationships between quantities.

a) (Preparation for Section 4.2)Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b) (Preparation for Section 4.2)Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9