Warm Up:

1. Are you here? Warm Up: List all the factors of p2q (assume p, q are prime!) Think About: Can 1/2 = 1/4?

2. Agenda • Explorations and other items • Unit/Whole Take 2! • Meanings for fractions: part-whole, ratio, operator, quotient

3. Homework • Complete the explorations. Use your manipulative packs! These are due on Friday. • Read section 5.2 carefully in your textbook. • Bring your class notes on Monday!

4. Unit/Whole • If = 1 1/3 what is 1/4?

5. Unit/Whole • If = 1 1/3 then = 1 • So = and = 1/4

6. The “whole” is the given object or amount • We measure the value of the whole with respect to the “unit”

7. discrete area Length (number line) 0 1/5 2/5 3/5 4/5 1 Meanings for fraction: 2/5 • Part-whole: subdivide the whole into 5 equal parts, then consider 2 of the 5 parts.

8. Show 3/8 and 8/3

9. 0 1/2 1 3/2 2 5/2 Show 3/8 and 8/3

10. Now you try… • Show pictorial models for 1/10 and 5/3.

11. Meanings for fraction: 2/5 • Ratio: a comparison two quantities. In this case, the first quantity is the number of parts/pieces/things that have a certain quality, and the second quantity is the number of parts/pieces/things that do not share that quality. 2 purple : 3 non-purple2 : 3

12. Show a picture and a word problem for 4/9 as a ratio. • In a group of students, 8 are female and 10 are male. What is the ratio of female to male students?

13. Meanings for fraction: 2/5 • Operator: instead of counting, the operator can be thought of as part of a set, or a change (stretch/shrink) of a given amount. • If the fraction is less than one, then the operator shrinks the given amount. If the fraction is greater than one, then the operator stretches the given amount. • 2/5 of a set might mean take 2 out of every 5 elements of a set. It might also mean 2/5 as large as the original.

14. Of the 54 circles, 4/9 are red. (4/9 • 54 = 24) Show a picture and a word problem for 4/9 as an operator. • When I made 54 cookies for the party last year, over half were uneaten. This year, I plan to make 4/9 as many. How many should I make?

15. Meanings for fraction: 2/5 • Quotient: The result of a division. • There are two ways to think about this. • We can think of 2/5 as 2 ÷ 5: I have 2 candy bars to share among 5 people; each person gets 2/5 of the candy bars. • We can also think of this as the result of a division: I have 16 candy bars to share among 40 people: 16/40 = 2/5.

16. Show a word problem for 4/9 as a quotient. • I have 4 minutes left on my exam to solve 9 problems. How long should I spend on each problem? • 45 people want to eat some of the 20 pizzas I ordered. To be fair, how much should each person eat? • Fix this problem so it is correct! If I have 9 yards of material to make 4 dresses, how much material should I use per dress?

17. More Examples

18. Word Problems • Write word problems for 2/5 and 5/2 for each: • Part of a whole • Ratio • Operator • Quotient We will look at some examples then take some time to write our own.

19. Word Problems • Part of a whole: The question must state what the whole is, and the parts must all be the same size. • Ex: I have 4 marbles, but 3 of them are scratched. What fraction describes the scratched marbles? (3/4) • Ex: I have 14 plates, but four are covered with grease. What fraction describes the clean plates? (10/14 or 5/7) • You try one.

20. Word Problems • Ratio: The question must describe the comparison between 2 quantities. • Ex: I have 20 socks, and 8 are red. Write a ratio describing the red and not red socks. (8 : 12 or 2 : 3) • Ex: On my homework, I got 6 out of 9 problems correct. Write a ratio comparing the correct and incorrect answers. (6 : 9 or 2 : 3). • You try one.

21. Word Problems • Operator: This question asks how a quantity has changed. If the initial amount has increased, then the operator is greater than one. • Ex: This year, I have 25 students in Math 302A. Next year, I hope to have 20. What fraction of my current class is this? (4/5) • Ex: Last year, 100 students passed Math 302A. This year, I hope 6/5 as many pass. How many students do I hope pass? • You try one.

22. Word Problems • Quotient: Either, the answer to the question is the fraction, or the question describes the dividend (numerator) and divisor (denominator). • Ex of 5/30: If a family of 30 equally shares 5 pizzas, how much pizza should each person eat? (5/30 or 1/6) • Ex of 5/30: If 300 people share 50 pans of brownies, how much should each person eat? (50/300 = 5/30 = 1/6) • You try one.

23. Word Problems • Label each problem as (a) part-whole, (b) ratio, (c) operator, or (d) quotient. If you are not sure, write not sure. • Marci had 15 marbles. But she lost 2/3 of them. How many does she have? • operator • Jeremy comes from a large family: there were 2 boys for every 1 girl. Could he have 12 kids in his family? Could he have 13? • ratio

24. Word Problems • Beatriz walks 3/8 of a mile. • Part of a whole (the mile is the whole). • Kevin planted 16 tomato plants last year. “I’m gonna plant 2 times as many this year.” How many tomato plants will Kevin need? • Operator (the fraction is 2/1) • At the dog park, 8 dogs had outfits on and 16 did not. • Ratio

25. Word Problems •Mom made 3 pans of brownies to share equally among 36 kids. How much does each kid get? Quotient Dad has $90 to share equally with 12 grandchildren. How much does each grandchild get? Quotient A certain company has 300 workers, and 4/5 of them make minimum wage. How many workers earn minimum wage? Operator (note: if the problem said 300 workers and 40 of them made minimum wage, then it is part of a whole.)