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6 th Grade Math Focus 2: Rates, including percents

6 th 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. Bits and Pieces 1- Investigation 4: Working with Percents Mathematical Learning and Problem-Solving Goals.

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6 th Grade Math Focus 2: Rates, including percents

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  1. 6th Grade MathFocus 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

  2. Bits and Pieces 1- Investigation 4: Working with PercentsMathematical Learning and Problem-Solving Goals • 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)

  3. Bits and Pieces 1, Investigation 4.1Mathematical Learning Target Students will be able to work with percents by understanding and completing the following: • 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

  4. Getting Ready for Problem 4.1

  5. 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?

  6. Part-to-Whole Comparisons Percents are Part-to-Whole comparisons! For example when the fraction total is out of 100: = 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: = Read as “34 out of 100” same as 34% The fraction total (whole) does not have to be out of 100.

  7. How to Use PERCENT Bars 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.”

  8. Draw a Percent Bar in your workbook Let’s see how fractions and decimals relate to percents! • If this were a FRACTION BAR, what number would be at the left end of the bar? • What number would be here at the right end of the bar? • What fraction would belong here at the middle of the bar? • What decimals would go in each of these spots? • What percent would go in each of these places? How do , 0.5, and 50% relate?

  9. Problem 4.1- Who’s the Best?

  10. 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?

  11. 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.

  12. Problem 4.1, Part A

  13. TEACHER ONLY!

  14. Problem 4.1, Part B

  15. TEACHER ONLY!

  16. Bits and Pieces 1, Investigation 4.1Mathematical Learning Target Review Students will be able to work with percents by understanding and completing the following: • 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?

  17. 6th Grade Math Homework Bits & Pieces 1 ACE #1, 2, 26-31

  18. TEACHER ONLY!

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