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1 Math CAMPPP 2011 Proportional Reasoning: Learning Goals & Consolidating Questions Breakout #2 K - Grade 4

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Minds On The odds of hitting your target go up dramatically when you aim at it. Mal Pancoast

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Action! Read the following sections of Recognising the Difference Between Additive and Multiplicative Thinking in Young Children by Lorraine Jacob & Sue Willis: Introduction Research Results (Sections of interest) Conclusion & Implications Appendix: Description of Tasks

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Hitting The Target? K - Gr. 2: The Butterfly House by Eve Bunting Grade 3-4: Centipedes 100 Shoes by Tony Ross

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Butterfly House: K-2 How many wings on 26 butterflies?

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The Butterfly House - K NS1.7 demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation; NS1.12 investigate addition and subtraction in everyday activities through the use of manipulatives (e.g., interlocking cubes), visual models (e.g., a number line, tally marks, a hundreds carpet), or oral exploration (e.g., dramatizing of songs). Use counting and/or addition as a solution strategy. Recognize the quantity of number increasing as numbers are added.

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The Butterfly House - Gr. 1 Solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of strategies Count forward by 1s, 2s, 5s and 10s to 100, using a variety of tools and strategies; solve a variety of problems involving the addition and subtraction of whole numbers to 20 See the additive nature of numbers. Use addition or skip-counting as a solution strategy. Recognize the quantity of number increasing as numbers are added.

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The Butterfly House - Gr. 2 Solve problems involving the addition and subtraction of one-and- two-digit whole numbers, using a variety of strategies, and investigate multiplication and division; Count forward by 1s, 2s, 5s,10s and 25s to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10; Represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups; Begin to see connections between repeated addition and multiplication. Explore multiplicand (2 wings) and multiplier (number of butterflies). Use addition, skip-counting, or experiment with multiplication as a solution strategy.

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Centipedes 100 Shoes: Gr. 3-4 Centipede decides to give away his 100 shoes. He gives shoes to: 5 spiders (8 legs each), 2 worms, 2 woodlice (14 legs each), 4 beetles (6 legs each) 1 grasshopper (6 legs each) Is the author's math right? Did centipede give away the right number of shoes?

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Centipedes 100 Shoes - Gr. 3 Solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 1000. Relate multiplication of one-digit numbers to real-life situations, using a variety of tools and strategies. Begin to see sets of numbers multiplicatively (recognize multiplicand OR multiplier) and experiment using multiplication as a solution strategy.

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Centipedes 100 Shoes - Gr. 4 Solve problems involving the multiplication of one-digit whole-numbers, using a variety of mental strategies; Describe relationships that involve simple whole- number multiplication. Identify the multiplicative nature of sets of numbers (recognize multiplicand AND multiplier) (animal legs and number of animals) and use multiplication as a solution strategy.

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Lesson Goals K - Use counting and/or addition as a solution strategy. Recognize the quantity of number increasing as numbers are added. Gr. 1 - See the additive nature of numbers. Use addition or skip-counting as a solution strategy. Recognize the quantity of number increasing as numbers are added. Gr. 2 - Begin to see connections between repeated addition and multiplication. Explore multiplicand (2 wings) and multiplier (number of butterflies). Use addition, skip-counting, or experiment with multiplication as a solution strategy. Gr. 3 - Begin to see sets of numbers multiplicatively (recognize multiplicand OR multiplier) and experiment using multiplication as a solution strategy. Gr. 4 - Identify the multiplicative nature of sets of numbers (recognize multiplicand AND multiplier) (animal legs and number of animals) and use multiplication as a solution strategy. Did the question Hit the target ?

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Ask yourself… Did this question provide students the opportunity to demonstrate the lesson goal? Did this question Hit the target ?

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Further Consolidation Journal Reflection: Reflect on a lesson that has really hit the target. Describe the elements that were present.

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