Download Day 20

March 31, 2009
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A mind once stretched by a new idea never
regains its original dimensions.
- Anonymous
March 31, 2009
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• Exploration 5.8 and 5.9
• Meanings for fractions
• Assign Homework
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Explorations 5.8 + 5.9
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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”
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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
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Meanings for fractions
Ex: 2/5
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Part-whole: subdivide the whole into 5 equal parts, then
consider 2 of the 5 parts.
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area
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discrete
Length (number line)
0 1/5 2/5 3/5 4/5 1
Sec 5.2 - (cont’d)
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Show 3/8 and 8/3 using an area model, a
discrete model and a number line.
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Sec 5.2 - (cont’d)
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Number line:
0
1/2
Discrete:
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3/2
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5/2
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Sec 5.2 - (cont’d)
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Area:
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Sec 5.2 – (cont’d)
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You try:
Show pictorial models for 1/10 and 5/3
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Sec 5.2 – (cont’d)
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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
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2 red : 2 non-red
Ratio is 2 : 3
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Sec 5.2 – (cont’d)
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Ex: Show a picture and a word problem for
4/9 as a ratio
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In a group of students, 8 are female and 10 are male. What is
the ratio of female to male students?
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Sec 5.2 – (cont’d)
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Meanings for fractions
Ex: 2/5
3. Operator: the fraction can operate on a set, telling us what
portion of the set to use.
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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.
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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.
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Sec 5.2 – (cont’d)
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Ex: Show a picture and a word problem
for 4/9 as an operator.
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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?
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Of the 54 circles, 4/9 are red. (4/9 • 54 = 24)
Sec 5.2 – (cont’d)
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Meanings for fractions
Ex: 2/5
Quotient: The result of a division.
There are two ways to think about this:
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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?
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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.
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Sec 5.2 – (cont’d)
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Ex: Show a word problem for 4/9 as a
quotient.
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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?
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Homework
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Due Thursday, 4/2
Link to online homework list:
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http://math.arizona.edu/~varecka/302AhomeworkS09.
htm
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