Fractions “the whole story”

1. Dr. Rena Gibbs Amy Edmundson Fractions “the whole story”

2. What does it mean to “invert and multiply”?

3. Let’s say we want to divide a whole number by a fraction. For example… ÷

4. ÷ This is a visual representation of the first part of our equation “seven wholes”.

5. ÷ This is a visual representation of the number 7 divided by .

6. ÷ So this division problem is really asking us “How many ‘1/3rds’ can we ‘fit’ into the seven wholes?”

7. Three “thirds” fit in one.

8. Six “thirds” fit in two.

9. Nine “thirds” fit in three.

10. Twelve “thirds” fit in four.

11. Fifteen “thirds” fit in five.

12. Eighteen “thirds” fit in six.

13. Twenty-one “thirds” fit in seven.

14. ÷ = 21 So because twenty-one “1/3rds” fit into seven wholes.

15. We can verify this result in many ways, but the most common way taught in schools is to “invert and multiply”: ÷ is equivalent to x = 21 Because fits in each “whole” three times. We have seven “wholes” that we multiply by the three that fit into each whole x = 21 and 7 times 3 is 21, therefore

16. ÷ = ● • “Copy, dot, flip” OR “there are three rds in each whole”. • So how do we build this conceptual understanding? • By starting at the beginning… Memorization vs. conceptualization

17. Let’s say we want to do this math problem Using a 100’s Chart to combine unlike units(finding common denominators) +

38. + = or 1 +

39. > This same data can be used to determine that