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.
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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.
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.
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
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.
Editor's Notes
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Page 18 -The Greeks were fascinated with repeating patterns. -We can specify the repeating pattern with this notation:
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Page 19 c . iv. We only have one pattern. d. ii. We have no patterns
Page 19 -What will repeat? +b -How many times will it repeat? 4 times -This shows a jump of distance + b repeated 4 times.
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Page 20 -b + b + b + b is a multiple of b . -What if n = 0? -What if n = 2? What if n = 1?
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Page 20 -4 is a whole number because it equals 1 + 1 + 1 + 1. -Why is 4 a whole number?
Page 20 -Why is zero defined as a whole number? -What would the diagram mean if w = 0?
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Page 21 -What will it look like on the number line?
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Page 21 - 22 -Let’s use the definition of addition and whole numbers to find out. -Therefore we can draw the following equation: