CCB Mathematics pages 108 - 113
Apply and extend previous understandings of numbers to the system of rational numbers.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Use a number line to find the sum of two integers
Use integer addition rules to find the sum of two integers
Two ways to find the sum of two integers include using a number line and using a sequence of rules
Draw or have volunteers draw number lines from 0 to positive 25 on the board. Ask students to use the number lines to add positive whole numbers. Observe their work, intervening if necessary.
Remind students that a number line continues infinitely in opposite directions, representing both negative and positive integers. Also remind them that absolute value is the distance between 0 and a number on the number line, whether positive or negative.
- Use A Number Line to Add Integers
- Use Rules to Add Integers
Reason Abstractly: Allow students time to read and think about the sidebar. Ask if they can think of other math examples that are abstract. One example is a number line. It is an abstraction that students can use to manipulate numbers, but it doesn’t really exist as an object. Ask students to brainstorm other examples of abstractions they can use to work with numbers and values. Students may say, for example, that coordinate grids don’t really exist, but they are abstractions that show the relationships between pairs of numbers.
Perform Operations: Have students read the sidebar independently. Remind them to refer to the number line in Example 3 as they read, to help them understand the text. After students have written their explanations, ask them to share their ideas.
For students who need an alternative to a number line to illustrate integer addition, give students counters in two colors. Let one color represent positive numbers and the other color represent negative numbers. Have students use the counters to practice finding zero sums. You can use small objects such as paper clips and erasers if counters are not available.
Build Vocabulary: Invite students to play a game. Use tape to draw a number line along one edge of a table. Mark the center of the tape 0. Mark numbers to the right as positive integers and numbers to the left as negative integers. Have a volunteer stand in front of the 0 and push a paper clip or counter in a positive direction. Ask the student to announce the distance the counter moved. Then have the volunteer push it back in the opposite direction, again announcing how far the counter moved. Have a volunteer record the measurements on the board. Then ask the player to determine how far the counter moved in all while explaining the problem solving process using the vocabulary words. Invite other students to play.
Classify Concepts: Have students research the use of submersibles to explore the layers or zones of the ocean, from the surface, or Sunlight Zone, to the trenches, or Hadalpelagic Zone. Have students use their research to explain the concept of positive and negative integers.