Transcript Day 20
March 31, 2009 0011 0010 1010 1101 0001 0100 1011 1 2 4 A mind once stretched by a new idea never regains its original dimensions. - Anonymous March 31, 2009 0011 0010 1010 1101 0001 0100 1011 • Exploration 5.8 and 5.9 • Meanings for fractions • Assign Homework 1 2 4 Explorations 5.8 + 5.9 0011 0010 1010 1101 0001 0100 1011 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” 1 2 4 Exploration 5.9: answer Part 1 #1, 2, 4 – 7 (skip 5c); Part 2 #1, 2; Part 3 #1 Sec 5.2 – Fractions and Rational Numbers 0011 0010 1010 1101 0001 0100 1011 Meanings for fractions Ex: 2/5 1. Part-whole: subdivide the whole into 5 equal parts, then consider 2 of the 5 parts. 1 area 2 4 discrete Length (number line) 0 1/5 2/5 3/5 4/5 1 Sec 5.2 - (cont’d) 0011 0010 1010 1101 0001 0100 1011 Show 3/8 and 8/3 using an area model, a discrete model and a number line. 1 2 4 Sec 5.2 - (cont’d) 0011 0010 1010 1101 0001 0100 1011 Number line: 0 1/2 Discrete: 1 3/2 2 5/2 1 2 4 Sec 5.2 - (cont’d) 0011 0010 1010 1101 0001 0100 1011 Area: 1 2 4 Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 You try: Show pictorial models for 1/10 and 5/3 1 2 4 Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 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 1 2 red : 2 non-red Ratio is 2 : 3 2 4 Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 Ex: Show a picture and a word problem for 4/9 as a ratio 1 2 In a group of students, 8 are female and 10 are male. What is the ratio of female to male students? 4 Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 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. 1 2 4 Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 Ex: Show a picture and a word problem for 4/9 as an operator. 2 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? 1 4 Of the 54 circles, 4/9 are red. (4/9 • 54 = 24) Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 Meanings for fractions Ex: 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 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. 4. 1 2 4 Sec 5.2 – (cont’d) 0011 0010 1010 1101 0001 0100 1011 Ex: Show a word problem for 4/9 as a quotient. • • • 1 2 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? 4 Homework 0011 0010 1010 1101 0001 0100 1011 Due Thursday, 4/2 Link to online homework list: 1 2 http://math.arizona.edu/~varecka/302AhomeworkS09. htm 4