Warm Up:

1. Are you here? Warm Up: • Give examples and/or counterexamples to show whether each statement is true or false. • Let 0 < a < b < c. • a/b < b/c ? • a/c > c/a ? • c/b < b/a? • (ac)/b = (ab)/c ?

2. Agenda • Yamalet Video • Review Word Problems • Alexa Video • Review Pictorial Models • 3 Practice Problems • Assign homework

3. Yamalet Watch the video. On page 21, the follow-up questions ask us to use a pizza scenario to understand how 3/8 could be used as a ratio, an operator, and a quotient.

4. 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.

5. 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.

6. 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 : 3 or 2 : 1). • You try one.

7. 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.

8. 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.

9. 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

10. 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

11. 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.)

12. Alexa • We will watch Alexa in just a few moments. Look at her work on page 23 for the second problem. What do you think Alexa was doing in each diagram? • Now pick one. Can this picture be used to mean part-whole? Ratio? Operator? Quotient? If yes, say why. If no, say why not.

13. Now, we’ll watch Alexa • Complete parts 1, 2, and part a in your groups. • Now, try part c (skip b for just a moment). Once you found the value for 5, explain it in words so that someone else will understand.

14. Alexa • Now, let’s try part d. Same thing--once you get an answer, try to write it up in words so that someone else will understand.

15. Alexa • Now, let’s talk about how parts b and c are alike, and how they are different. • Do part b.