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Why has the way we teach math changed?
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Difference in the standards
(2003 COS Third Grade) Solve addition and subtraction problems, including word problems, involving two- and three-digit numbers with and without regrouping. (2010 ACCRS Third Grade) Fluently add and subtract within using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
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Why ACCRS? Deeper Concept Level Application not just memorization
Transfer of knowledge to other situations Ex: variables, decimals, fractions, irrational numbers Addresses the drop in scores from 7th to 8th
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Disconnect Resources chosen to teach the standards
Curriculum vs. Standards Grading Concerns
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First day of 5th grade
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Jose’s class has a goal of collecting 169 cans for their recycling project. They have collected 94 so far. How many more do they need to reach their goal?
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Decomposing Numbers to Add
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The problem was 48 + 78= If a child understands this then they will understand 3x + 5 = 14
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Justification
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Some students choose not to solve the problem they are given.
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Solve in two ways
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Doubling/ Halving Strategy
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Decomposing Numbers to Solve Multiplication
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Standard Algorithm
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Area Model
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If a child understands that there are 4 multiplication problems in 78 x 34.
Then they will understand (70 +8)(30+4) (5 + n)(3a- 2) (4+3𝑥) 2
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Using visual models
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What does this child know about fractions? Multiplication?
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