This document discusses representing whole numbers and addition on a number line. It provides examples of using number lines to show repeated addition and multiples. Students are asked to write expressions for repeated addition diagrams, identify values on sample number lines, and write equations corresponding to diagrams. The objectives are to represent repeated addition on the number line, represent whole numbers on the number line, and add whole numbers on the number line.

1. Where are the Whole Numbers? Chapter 1 Lesson 2 Copyright 2010 MIND Research Institute For use only by licensed users WN.1 Represent whole numbers as points on a number line. WO.1 Represent the addition of whole numbers on a number line. EE.4 Represent expressions and equations with number line diagrams. Translate number line representations of expressions and equations into symbolic notation. EE.5 Represent the addition of numbers, variables, and expressions symbolically and with number line diagrams. EE.6 Represent repeated addition of the same term symbolically and with number line diagrams.

2. Objectives Represent repeated addition on the number line. Represent whole numbers on the number line. Add whole numbers on the number line.

3. Remember from Before What is a whole? How is addition defined on the number line?

4. Get Your Brain in Gear 1. Count backwards from 10 to 0. 2. Count by 5’s from 0 to 40. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 0, 5, 10, 15, 20, 25, 30, 35, 40

5. If we repeat this pattern 6 times, it will look like this: This means there are 6 copies of the image. The two images here represents the start and the end of the sequence.

6. What pattern does this diagram produce?

7. 1. Match the diagrams on the left with the patterns on the right. Check for Understanding What might some people find tricky about diagrams c and d ? a. iii b. i c. iv d. ii

8. These diagrams can also represent repeated jumps on the number line. We can write the expression as repeated addition .

9. 2. For the following diagrams, use symbols to write the corresponding repeated addition: Check for Understanding k + k + k y + y

10. A multiple of b is a point on the number line we can get to by repeated addition of b . This is a variable . It expresses all the multiples of b . If n = 5, what would the diagram mean?

11. 3. What would the diagram mean if n = 7? What about n = 4? Check for Understanding b + b + b + b b + b + b + b + b + b + b

12. A whole number is a multiple of 1. All whole numbers are obtained by repeated addition of +1.

13. Whole numbers in general can be illustrated by this diagram:

14. 4. The diagram below shows the locations of the first 10 whole numbers. What are the values of points a , b , c , and d ? Check for Understanding a = 5 c = 9 d = 8 b = 3

15. This equation shows the meaning of 5:

16. 5. Write the equations for the following diagrams: Check for Understanding 1 + 1 + 1 = 3 1 + 1 + 1 + 1 = 4

17. What is the value of y ? What does 2 mean? What does 3 mean? y = 1 + 1 + 1 + 1 + 1, which is the definition of 5.

18. 6. What are the values of the variables ( t , z and h ) in the following equations? Check for Understanding t = 4 z = 4 h = 6

19. Multiple Choice Practice 1. When w is a whole number, the value of the expression w + w + w + w is: a whole a positive w a variable w a multiple of w

20. Find the Errors The numbers are not evenly spaced apart from each other. All whole numbers are a distance of a whole away from the next whole number.