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Focused Problem Solving Tasks that address selected Arizona High School Math Standards

Focused Problem Solving Tasks that address selected Arizona High School Math Standards. August 5, 2011 Steve Leinwand American Institutes for Research. Today’s focus:. Proportional Reasoning and Measurement in Problem Solving Contexts (as a model for other topics).

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Focused Problem Solving Tasks that address selected Arizona High School Math Standards

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  1. Focused Problem Solving Tasks that address selected Arizona High School Math Standards August 5, 2011 Steve Leinwand American Institutes for Research

  2. Today’s focus: Proportional Reasoning and Measurement in Problem Solving Contexts (as a model for other topics)

  3. CCSSM Mathematical Practices • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics.

  4. Just for fun 1/3 of a number is equal to 2/5 of another number. The sum of the two numbers is 88. What are the two numbers? Show your work.

  5. Which give biggest and which gives smallest price reduction? Explain.

  6. Gain or loss? Last year, it was bad news: the value of your savings plunged by 50%! This year was much better: the value of your savings increased by 75%! Are you ahead or behind? By what percent?

  7. What’s the story? No record for 9.96 in the 99.96 Meters

  8. What if the track was 100 m? 9.96? 9.97? 9.98? 9.99? 10.00? 9.96 seconds = ? seconds 99.96 meters 100 meters

  9. So what have I modeled? • Engage our students • Embed the math in realistic contexts • Give our students a reason for learning new content and approaches • Focus on problem solving, reasoning and communication

  10. Is the claim valid? Everyday 12% of Americans eat at McDonalds!!! REALLY? There are: • About 1.3 x 104 McDonalds restaurants in the U.S. • There are about 3 x 108 Americans

  11. Happy New Year Handshake • If a “Happy New Year Handshake Across America” starts in New York City and is planned to end in downtown Los Angeles at the stroke of midnight on December 31, 2012, how many people will have to line up and when should the shake start in New York City? • Quick estimates? • What additional data do we need? • BTW: There are 307 million Americans and it is 2462 miles from NY to LA

  12. A Tale of Two States South Dakota and North Dakota rank 45 and 47 in population of all the states. South Dakota has 721,000 people in 75,896 sq. miles. North Dakota has 638,000 people in 68,994 sq. miles. Which state has the greater pop. Density? How many people in one state would have to move to the other to make the pop density of the two states equal?

  13. What’s the story here?

  14. What’s the question? • How many people? • How long a parade? • Beer? • Male/female balance? • How many toilets are needed? • Why should we care? • Other?

  15. The caption: Before the parade passes by. Bob Becker of Gotogo in Killingworth, sets up portable toilets next to Soldiers and Sailors Memorial Arch in Bushnell Park in Hartford on Friday. Becker said that more than 100 portable toilets would be set up for 200,000 people expected.

  16. Why ARE roads crowded?

  17. Today’s big ideas so far • 10% more is + 10% or times 1.1 • 10% less is – 10% or times .9 • Compounding x .05, x .05, x .05 = x .053 • Proportions are equivalent ratios and proportions are multiplicative relationships • Percents help us compare ratios with different totals

  18. Looking at volume (measurement, problem solving, number)

  19. Melons Here’s what we know: • Volume of a sphere: V = 4/3 π r3 • Melon rind = ½ inch • Pits and pulp = 2” in diameter sphere Here’s the question: • Which has more edible melon – one 8” in diameter melon or two 6” in diameter melons?

  20. Are these dimensions suitable? • How much aluminum is used for each can? • What dimensions would create a can that holds 200 cm3 and use the least amount of metal?

  21. Your turn:

  22. So? • Order from smallest to largest and justify. • What is the height of Glass 3?. • What is the volume of each? • If Glass 1 has volume V, express volume of Glasses 2 and 3 in terms of V. • When Glass 1 is ½ full, the height of the liquid is 3 cm. What are the heights of the liquid in Glasses 2 and 3 when they are ½ full?

  23. An assortment of thinking and reasoning algebraically and spatially

  24. Thank you! I hope this was helpful SLeinwand@air.org

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