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Rational Numbers (Grade 7)

Related Topics:
Common Core for Grade 7
Common Core for Mathematics
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 7

Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to 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.

Common Core: 7.NS.1ab

Suggested Learning Targets

  • I can add and subtract rational numbers (integers, fractions, and decimals).
  • I can explain that each rational number has an opposite that adds to zero.
  • I can describe real-world situations in which opposite quantities add together to equal zero. (James was overdrawn in his checking account by $25. He ran to the bank and deposited $25 into his account. Explain why James's balance is now $0.)
  • I can compute rational numbers
  • I can use a number line to show that the 1st addend (p) and the sum (p+q) represent location and the absolute value of the 2nd addend (q) represents distance traveled. (ex. Let p=7 & |q|=3 so 7 + 3= 10 and 7 + -3 = 4. The distance from 7 and 10 is 3 and the distance from 7 and 4 is 3.)
  • I can use a number line to demonstrate that the sum of a number and its opposite is zero (ex. p + -p = 0, the distance from p and 0 is |-p| or –p + p = 0, the distance from –p and 0 is the |p|).
  • I can use real-world context to describe the sums of rational numbers. (The result should indicate location and not the total distance. Ex. Sandy is 22 miles from home. She traveled 10 miles further from home. How far from home is she now? 22 + 10 = 32. 22 miles and 32 miles are the actual locations of Sandy and 10 miles is the distance traveled.)
  • I can create real-world context to explain that the distance between two numbers is the absolute value of the difference between those numbers.
Adding & Subtracting Rational Numbers (7.NS.1)
Thinking with the Number Line
Rule: When you add a positive, you move to the right on the number line. When you subtract a positive you move to the left.
Adding a Negative
Rule: Adding a negative number is just like subtracting a positive.
Subtracting a Negative
Rule: Subtracting a negative number is just like adding a positive.

Adding the Opposite Add Rational Numbers
The Common Core State Standards (CCSS) videos are designed to support states, schools, and teachers in the implementation of the CCSS. Each video is an audiovisual resource that focuses on one or more specific standards and usually includes examples/illustrations geared to enhancing understanding. The intent of each content-focused video is to clarify the meaning of the individual standard rather than to be a guide on how to teach each standard although the examples can be adapted for instructional use. Adding Integers
Grade 7 / Math / Engagement
CCSS: Math.7.NS.A.1c
Lesson Objective
Add and subtract integers using a number line and a song with motions

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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