RATIOS AND PROPORTIONS

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Presentation transcript:

RATIOS AND PROPORTIONS NATASA, ANNE, AND LESLIE

WHAT IS DIFFERENT FROM CURRENT PRACTICE? (Many) multiple representations (tape diagram, percentages, table, double number line, graph, slope triangle, additive vs multiplicative process) New connection: geometry (scale drawings) New connection: probability and statistics (drawing conclusions about a population based on a random sample)

New Focus: Multiple Representations

CONNECTIONS TO GEOMETRY

HOW DOES THE IDEA GROW? Linear Functions Similar Figures Measurement Trigonometry Science: Measurements formed by ratios Average Rate of Change-> Derivative Statistics, Data Analysis Business: Profit and Loss Measurement Skip Counting Multiplication and division facts Proportional Reasoning Using Ratios to Solve Problems Percentages Rate Units Scale

Tools for Proportional Thinking: Double Number Lines & Tape Diagrams

CONNECTIONS TO PROBABILITY AND STATISTICS

QUESTIONS The distinction between rate and ratio: should we stress or de-stress? [The progressions document seems inconsistent here. See p. 2 vs. p. 4 vs. p. 13 (appendix)]

Problems Involving Rate A motor bike can run for 10 minutes on $0.30 worth of fuel. How long could it run on $1.05 worth of fuel? It takes 75 seconds to pump 20 dollars’ worth of gas into a car. After 60 additional seconds, the amount pumped reaches 20 gallons. Find the price of a gallon of gas. Anne and Brian set off at constant speeds towards a city 240 km away. When Anne reached the city, Brian was still 90 km away. Brian reached the city hours later. (a) Find Brian’s speed. (b) Find Anne’s speed.

Problems Involving Ratio The ratio of the number of Cole's storybooks to the number of Dan's storybooks is 4 : 11. If the two boys have 660 storybooks altogether, how many more storybooks does Dan have than Cole? Evelyn and Fiona shared 96 marbles in the ratio 5 : 3. Evelyn then shared her marbles with Greg in the ratio 11 : 4. How many fewer marbles did Greg het than Fiona?

IMPLICATIONS FOR TEACHING Do not rush from proportional reasoning to solving equations! Be certain to use and encourage students to use multiple representations to demonstrate proportional reasoning. Help students recognize the “whole” in the scenario.

Thank you