Casey Runner: Adding and Subtracting Positive and Negative Numbers

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

7

Overview

In this free interactive math learning activity from Math is Fun, students gain an understanding of adding and subtracting positive and negative numbers by “playing” with an interactive tool. 

This activity results from the ALEX Resource Development Summit.

Phase

During/Explore/Explain
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.

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.

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.

Learning Objectives

Students will add and subtract rational numbers using number lines to show a connection to distance.

Activity Details

Provide the students with a link to the website How to Add and Subtract Positive and Negative Numbers from Math is Fun. The class will begin by reading the webpage aloud together from the website. Make sure to point out the two rules: (1) two like signs become addition and the sign stays the same, (2) two unlike signs become subtraction. After subtracting, take the sign of the larger number. 

Stop at the Now Play With It section and give the students time to “play” with the interactive Casey Runner by choosing either a positive or negative sign to solve the equation. The goal is to move the runner closer to the finish line. If students choose the correct sign, the runner will move closer to the finish line. If students choose incorrectly, the runner will run backward away from the finish line. The teacher should circulate around the room observing for struggling students. Allow students enough time to play with interactive.

Continue scrolling down and reading the webpage aloud with the students while working the examples given together to ensure understanding. Stop at the section, “YOOO TOOO”. Students will complete this ten-question quiz as their assessment.

Assessment Strategies

The ten questions in the section titled YOOO TOOO will be used as an assessment tool to check for mastery of the standard.

Variation Tips

Students who are struggling may need to be paired with stronger students.

This learning activity can be completed as a whole class activity or as an independent activity.

Background / Preparation

The teacher and students will need internet-connected devices.

https://www.mathsisfun.com/positive-negative-integers.html

Approved Date

Owner (Author)

morganboyd
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