Learning Activity

Bookstore Account: Adding and Subtracting Positive and Negative Numbers

Subject Area

Mathematics

Grade(s)

7

Overview

In this free learning activity from Illustrative Mathematics, students will be presented with a real-world problem involving Evan and his school bookstore account. Students will need to use the tricks they have learned about adding and subtracting positive and negative numbers to help Evan with his school bookstore account and justify their reasoning.

This activity was created as a result of the ALEX Resource Development Summit.

Mathematics (2019) Grade(s): 7

MA19.7.4

Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

Unpacked Content

UP:MA19.7.4

Vocabulary

  • Integers
  • Rational numbers
  • Additive inverses
  • opposite quantities
  • Absolute value
  • Terminating decimals
  • Repeating decimals

Knowledge

Students know:
  • a number and its opposite have a sum of 0.
  • A number and its opposite are called additive inverses.
  • Strategies for adding and subtracting two or more numbers.
  • Absolute value represents distance on a number line, therefore it is always non-negative.
  • Strategies for multiplying signed numbers.
  • Every quotient of integers (with non-zero divisor) is a rational number.
  • If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
  • The decimal form of a rational number terminates or eventually repeats.

Skills

Students are able to:
  • add rational numbers.
  • Subtract rational numbers.
  • Represent addition and subtraction on a number line diagram.
  • Describe situations in which opposite quantities combine to make 0.
  • Find the opposite of a number.
  • Interpret sums of rational numbers by describing real-world contexts.
  • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
  • Use absolute value in real-world contexts involving distances.
  • Multiply and divide rational numbers.
  • Convert a rational number to a decimal using long division.

Understanding

Students understand that:
  • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
  • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
  • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
  • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
  • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
  • Integers can be divided, provided that the divisor is not zero.
Mathematics (2019) Grade(s): 7

MA19.7.8

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

Unpacked Content

UP:MA19.7.8

Vocabulary

  • Rational numbers
  • Integers
  • Estimation

Knowledge

Students know:
  • techniques for converting between fractions, decimals, and percents.
  • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.

Skills

Students are able to:
  • convert between different forms of a rational number.
  • Add, subtract, multiply and divide rational numbers.-translate verbal forms of problems into algebraic symbols, expressions, and equations.
  • Use estimation and mental computation techniques to assess the reasonableness of their answers.

Understanding

Students understand that:
  • One form of a number may be more advantageous than another form, based on the problem context.
  • Using estimation strategies helps to determine the reasonableness of answers.

Phase

After/Explain/Elaborate
Learning Objectives

Learning Objectives

Students will be able to:
- apply their knowledge of addition and subtraction of rational numbers to describe real-world contexts.

Activity Details

Students should have been introduced to adding and subtracting positive and negative numbers and have had an opportunity to explore adding and subtracting them. The teacher may choose to review the rules for adding and subtracting positive and negative numbers as an introduction to this learning activity. This activity can be used to give students the chance to demonstrate their knowledge of adding and subtracting positive and negative numbers and explain their thinking.

The teacher should provide the students with a link to the website Bookstore Account or provide hard copies that can be downloaded and distributed (one per student).

The students should have discovered in class the following tricks for adding and subtracting positive and negative numbers:

The first number tells you where to start and in which way to look:

  • Negative – left
  • Positive – right

The second number tells you how far to move and in which direction to move:

  • Negative – backward
  • Positive – forwards

During this learning activity, students will demonstrate their understanding of adding and subtracting positive and negative numbers by helping Evan solve his real-world school bookstore problem. Students will then explain why it would make sense to use a negative number to represent Evan’s account.

The teacher should walk around the room and observe for any students who might be struggling.

Assessment Strategies

Assessment Strategies

The real-world Bookstore Account problem will be used to assess students’ mastery of adding and subtracting positive and negative numbers. There is a solution available on the website.

Variation Tips

Students who are struggling may need to be paired with stronger students. Struggling students may need to watch the video again.

Background and Preparation

Background / Preparation

The teacher needs an internet-connected device to present the problem on an interactive whiteboard if he/she chooses to present the problem to the whole class.

The hardcopy can be placed under a document camera and projected if no internet-connected device is available.

Copies will need to be made of the Bookstore Account problem and distributed if no internet-connected devices are available.

Digital Tools / Resources

http://tasks.illustrativemathematics.org/content-standards/7/NS/A/1/tasks/1475

Approved Date

Owner (Author)

morganboyd
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