1. March 31, 2009 A mind once stretched by a new idea never regains its original dimensions. - Anonymous

2. March 31, 2009 Exploration 5.8 and 5.9 Meanings for fractions Assign Homework

3. Explorations 5.8 + 5.9 Exploration 5.8: answer Part 1 #1 – 5, 7 Pay extra attention to answering the questions like: Write directions for solving “if [blank] = 1, then sketch a/b” Exploration 5.9: answer Part 1 #1, 2, 4 – 7 (skip 5c); Part 2 #1, 2; Part 3 #1

4. Sec 5.2 – Fractions and Rational Numbers Meanings for fractions Ex: 2/5 1.Part-whole: subdivide the whole into 5 equal parts, then consider 2 of the 5 parts. 0 1/5 2/5 3/5 4/5 1 discrete area Length (number line)

5. Sec 5.2 - (cont’d) Show 3/8 and 8/3 using an area model, a discrete model and a number line.

6. Sec 5.2 - (cont’d) Number line: Discrete: 0 1/2 1 3/2 2 5/2

7. Sec 5.2 - (cont’d) Area:

8. Sec 5.2 – (cont’d) You try: Show pictorial models for 1/10 and 5/3

9. Sec 5.2 – (cont’d) Meanings for fractions Ex: 2/5 2.Ratio: a comparison of 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 red : 2 non-red Ratio is 2 : 3

10. Sec 5.2 – (cont’d) Ex: 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?

11. Sec 5.2 – (cont’d) Meanings for fractions Ex: 2/5 3. Operator: the fraction can operate on a set, telling us what portion of the set to use. If the fraction is less than one, then the operator shrinks the original set. If the fraction is greater than one, then the operator stretches the original set. 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.

12. Sec 5.2 – (cont’d) Ex: Show a picture and a word problem for 4/9 as an operator. When I made 54 cookies last time, over half were uneaten. This time, I plan to make 4/9 as many. How many should I make? Of the 54 circles, 4/9 are red. (4/9 54 = 24)

13. Sec 5.2 – (cont’d) Meanings for fractions Ex: 2/5 4. 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 bar. If students do not understand this model, then much of algebra will be less meaningful. What is π / 6? How do you solve x/3 = 12? We can also think of this as the simplified result of a division: I have 16 candy bars to share among 40 people: 16/40 = 2/5.

14. Sec 5.2 – (cont’d) Ex: 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?

15. Homework Due Thursday, 4/2 Link to online homework list: http://math.arizona.edu/~varecka/302AhomeworkS09. htm