A Trick for Adding and Subtracting Negative Numbers

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

7

Overview

In this learning activity, students are introduced to the concept of adding and subtracting positive and negative numbers through an animated free math video from GCFLearnFree.org. In the video, a bird demonstrates how to move up and down the number line based on the operation and integers in the equation. It is a clever way to remember which direction to move based on the positive and negative numbers in the equation. Students then practice the tricks they learned using an interactive game.

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

Phase

Before/Engage
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 be able to:
- apply their knowledge of addition and subtraction of rational numbers to describe real-world contexts.
- add and subtract rational numbers using number lines to show the connection to distance.

Activity Details

Show the students the video A Trick for Adding and Subtracting Negative Numbers from GCFLearnFree.org. 

Have students write the tricks they learn down in their math journals.

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:

  • Negative – backward
  • Positive - forwards

Then, the teacher will provide students with the link for the interactive game, Math Dog Integer Addition from Math Nook. In this interactive game, students will help Math Dog, AKA Math Pup, catch the robber using the tricks to adding and subtracting negative numbers they have just learned. The robber is hiding behind the correct answer to the integer addition problem containing both negative and positive numbers. Students will just tap/click the correct answer to find and catch the robber. The game has 3 skill levels to choose from and students can choose to play timed or untimed. 

Assessment Strategies

While students explore the game, the teacher should circulate around the room to observe for struggling students. Allow students enough time to play and explore the concept. This can be an informal assessment as a check for struggling students early in the learning of this concept.

Variation Tips

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

Background / Preparation

The teacher and students will need internet-connected devices. The teacher will need a projector with sound capabilities to play the video. 

https://youtu.be/DBSviXhkubg

Approved Date

Owner (Author)

morganboyd
ALSDE LOGO

This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Alabama Learning Exchange © 2002-2023 by Alabama State Department of Education is licensed under Attribution-NonCommercial-ShareAlike 4.0 International

Design by Adaptive Theme