Transcript 6th Grade Math Focus 2: Rates, including percents

Standards: 6.RP.2, 6.RP.3b, 6.RP.3c
Resource: Connected Math Program 2
Bits and Pieces I, Investigation 4.1

Introduce percents as a part-whole relationship where the whole is not out of 100 but scaled to be “out
of 100” (4.1)

Use fraction partitioning and fraction benchmarks to make sense of percents (4.1)

Develop strategies, including percents, to use in comparisons where the whole is less than 100 (4.2)

Understand that comparing situations with different numbers of trials is difficult unless we use percents
or some other form of equivalent representation (4.2)

Work with situations where the whole is sometimes greater than 100 and sometimes less than 100 (4.3)

Develop connections between fractions, decimals, and percents (4.3)

Develop strategies for expressing data in percent form (4.3)

Relate fractions, decimals, and percents (4.4)

To move from percents to other representations and from other representations to percents (4.4)
Students will be able to work with percents by
understanding and completing the following:
1.
2.
An introduction of percents as a part-whole
relationship where the whole is not out of 100
but scaled to be “out of 100”
Use fraction partitioning and fraction
benchmarks to make sense of percents
Whitehills
Yes + No = 100 people
31 “out of 100” = 31% vote Yes
69 “out of 100” = 69% vote No
Bailey
Yes + No = 50 people
What would the numbers be like if 100
people were surveyed?
What are the percentages of Yes to No?
Percents are Part-to-Whole comparisons!
For example when the fraction total is out of 100:
31 (𝑌𝐸𝑆 𝑣𝑜𝑡𝑒𝑠−𝑃𝐴𝑅𝑇)
100 (𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑡𝑒𝑠−𝑊𝐻𝑂𝐿𝐸)
= Read as “31 out of 100” same as
31%
The percent sign, %, means “out of 100.”
For example when the fraction total is NOT out of 100:
17 (𝑌𝐸𝑆 𝑣𝑜𝑡𝑒𝑠−𝑃𝐴𝑅𝑇)
50 (𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑡𝑒𝑠−𝑊𝐻𝑂𝐿𝐸)
×
2
2
=
34
100
= Read as “34 out of 100” same as 34%
The fraction total (whole) does not have to be
out of 100.
17 YES
votes
25
votes
50
votes
50%
34%
A Percent Bar works like TWO number lines!
• Across the TOP of the bar is the RAW data (17/50)
• Across the BOTTOM of the bar the raw data is being scaled to
represent the data as percent “out of 100.”
Let’s see how fractions and decimals relate to percents!
1.
If this were a FRACTION BAR, what number would be
at the left end of the bar?
2.
What number would be here at the right end of the
bar?
3.
What fraction would belong here at the middle of the
bar?
4.
What decimals would go in each of these spots?
5.
What percent would go in each of these places?
How do
𝟏
,
𝟐
0.5, and 50% relate?
This is where Will got stuck and we are going to try to help him out.
Look at Will’s percent bar for Yao. Yao made 301 out of 371 free-throw
attemps. He has 371 labeled at the whole mark.
•
Why is it there?
•
If Yao made all those free throws, how much of the bar would I want to color in?
•
•
What percent would that be?
How much of the bar would I color in if he didn’t make any of his 371 attempted
free throws?
•
What percent would that be?
•
If I colored the bar halfway, about how many free throws would he make? Why?
•
What percent would that be?
Will also made a Percent Bar for Shaquille. He made 451 out of 725
attempts.
•
What does the 725 on his percent bar represent?
•
What does it say 100% by the 725?
COPY Will’s Percent Bars into your math workbook
so you’re ready for Problem 4.1, Part A.
Students will be able to work with percents by
understanding and completing the following:
1.
2.
3.
4.
5.
6.
What type of a ratio is a percent?
What type of a ratio is a fraction?
What type of a ratio is a decimal?
When would you use RAW data?
What does this sign, %, mean?
How do fractions and decimals help you make
sense of percents?
Bits & Pieces 1
ACE
#1, 2, 26-31