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Bridging Practices Among CT Mathematics Educators

Bridging Practices Among CT Mathematics Educators . June 24, 2014. Day 2 – Mathematics. By Fabiana Cardetti & Álvaro Lozano-Robledo. Goals for today. Define ratios and proportions. Analyze and evaluate students’ procedures for solving problems.

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Bridging Practices Among CT Mathematics Educators

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  1. Bridging Practices Among CT Mathematics Educators June 24, 2014 Day 2 – Mathematics By Fabiana Cardetti & Álvaro Lozano-Robledo

  2. Goals for today • Define ratios and proportions. • Analyze and evaluate students’ procedures for solving problems. • Apply a variety of strategies to solve problems; and recognize when to use them. • Use strip diagrams to solve problems that require proportional reasoning. • Continue to recognize the depth and complexities of proportional reasoning.

  3. Definition: A ratio is a pair of non-negative numbers, A and B, which are not both zero. Symbolically: A:B, A to B, B:A, B to A The value of A:B is the fraction, if B in non-zero Example: Tree A The ratio of height of tree before to height of tree after is 8:14. The value of this ratio is 4/7 and it represents…

  4. Ratios and Fractions are two different concepts! Example 2: Egg carton Suppose the ratio of white to brown eggs is 1:2, Does this mean you will have ½ of each? using a visual… What fraction of the eggs is brown? And white?

  5. Equivalent ratios A:B and C:D are equivalent if and only if they have the same value. What are the consequences of this?

  6. Example: Orangey Juice How can “oraginess” be quantified? • Keep ratio same • Use a proportion! If we wanted to prepare juice with the same oranginess as Pitcher A but using 5 cans of orange concentrate, how much water should we use? Pitcher A  orange to water 1:3 or 1/3 We need same value! How do we find that? Use a proportion! Try it…

  7. Ratio: Two Perspectives A Composed unit/Batch Fixed numbers of parts Two quantities are in a ratio of A to B if for every A units present of the first quantity there are B units present of the second quantity. Example: For every 7 female project participants in this room there is 1 male project participant. Two quantities are in a ratio of A to B if we divide the first quantity into A equal parts, then the second quantity consist of B equal parts of the same size. Example: Alvaro’s favorite trail mix requires 1 parts of raisins, 4 parts granola, and 5 parts of M&M peanuts a bag/bowl.

  8. Ratio: Two Perspectives A Composed unit/Batch Fixed numbers of parts Example: For every 7 female project participants in this room there is 1 male project participant. Example: Alvaro’s favorite trail mix requires 2 parts of raisins, 4 parts granola, and 5 parts of M&M peanuts in each bowl.

  9. Solving Proportions Problems • What are some ways to do it? • Ratio tables • …? • …?

  10. Food for thought… Precise terminology CCSS.MATH.PRACTICE.MP6: Attend to precision Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. … Do you have clear definitions of • Ratio, fraction, proportion? • How about rate, percentage, rational number, quotient, decimal? • Are some of these different words for the same concepts? • HMW: Write careful definitions for each one.

  11. Time to Take Stock • What did we learn today? • More specific • Take away about ratios, fractions, and proportions. • Important definitions/ideas/results. • Take away from different ways to represent the solutions. • Questions you still have

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