1. Chapter 7 Lesson 33 Divisibility WO.8 Know the basic multiplication facts (products of one-digit numbers) and the related division facts. WO.18 Find factors and multiples of whole numbers. WO.17 Use long division to determine if one number is divisible by another. WO.20 Find multiple factorizations for composite numbers (e.g., 30 = 3 × 10 = 5 × 6 ).

5. 6 ÷ 2 = 3 6 = 2 × 3

6. a = 2 × h Here a is divisible by 2 when h is a whole number. 2 = 2 × 1 4 = 2 × 2 6 = 2 × 3 8 = 2 × 4

9. Check for Understanding 1. Each of the following rectangles is made out of 7 unit squares. The widths are whole numbers but the heights are not. Express the height of each rectangle as a whole number plus a fraction. h = 3 + h = 2 + h = 1 +

10. Check for Understanding 2. If you make a rectangle out of 10 unit squares that has a width of 4, what will the height be? Draw a picture to show your answer. Express the height as a whole number plus a fraction. 3. Which of the following numbers are odd? Which are even? a. 5 b. 7 c. 8 d. 9 f. 0 e. 6 odd odd even odd even even The width is 4, the height is 2 + .

12. 2 = 2 2 + 2 = 4 2 + 2 + 2 = 6 2 + 2 + 2 + 2 = 8

13. Numbers divisible by 3: h × 3 h is a whole number

14. Check for Understanding 4. Name the first ten multiples of 7 as quickly as you can. 5. Name four multiples of 2 that are also multiples of 3. 6. Name three multiples of 4 that are also multiples of 5. 7. Name three multiples of 3 that are also multiples of 4. 8. What do we call the numbers that are multiples of 1? 0, 7, 14, 21, 28, 35, 42, 49, 56 and 63. The first four are 0, 6, 12 and 18. The first three are 0, 20, and 40. The first three 0, 12, and 24. Whole numbers

16. Is 133 divisible by 7? 133 = 7 × 19

19. Check for Understanding 9. Find the smallest whole number (other than 0) that is NOT a factor of 1260. 8 is the smallest whole number that is not a factor of 1260.

20. Multiple Choice Practice n is greater than d . n is a multiple of d . n is divisible by d . n is a factor of d . 1. Given the location of on the number line, which statement is true if n and d are whole numbers? n d

21. Multiple Choice Practice 2. If m and w are whole numbers and m is a multiple of w , which statement is NOT necessarily true?

22. A student drew a picture showing that 176 can be divided into 3 equal parts. From this the student claimed that 176 is divisible by 3. What does the student misunderstand about what it means to be divisible? Is 176 really divisible by 3? Find the Errors Any number can be broken down into 3 equal parts. To be divisible means that each of those equal parts is a whole number! 176 is not divisible by 3, because when you divide it by 3 you do not get a whole number.