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Math Models Parent Academy Presented by: Allison Curran http://websites.nylearns.org/acurran1

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Math Domains Counting and Cardinality (P-K) Operations and Algebraic Thinking (P-5) Measurement and Data (P-5) Geometry (P-5) Number and Operations in Base Ten (K-5) Number and Operations – Fractions (3-5)

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Math Models as Strategies Algorithms VS. Strategies: The Standards distinguish strategies from algorithms Students use strategies for addition & subtraction in K-3 Fluently add & subtract whole numbers using standard algorithms by the end of Grade 4 Use strategies for multiplication & division 3-4 but use standard algorithm by the end of Grade 5 Computation Algorithm: A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly Computation Strategy: Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another

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Example of Progressions Numbers in Base 10 Kindergarten Draw special attention to 10 Children learn to view the whole numbers 11 through 19 as ten ones and some more ones They decompose 10 into pairs such as 1/9, 2/8, 3/7 …

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Number Bonds Bundles Rekenrek 5 and Ten Frames

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Grade 1 View ten ones as a unit called a ten Compose and decompose this unit flexibly View the numbers 11-19 as composed of one ten and some ones See two digit numbers as representing some tens Students add and subtract using this understanding

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Bundles Number Bonds Rekenrek

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Ten Frames Number Bonds

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Number Bonds

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Number Lines

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Grade 2 Students extend their base-ten understanding to hundreds Add and subtract within 1,000 Use composing and decomposing Fluent with addition and subtraction within 100

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Number Bonds Bundles Number Lines

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Place Value Discs

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Grade 3 Major focus is multiplication Adding and subtracting fluently within 1,000

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Number Bonds Arrays Distributive Property

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Tape Diagrams Number Bonds

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Grade 4 Use standard algorithm to add and subtract Multiply and divide with multi-digit numbers Extend knowledge on base-ten system Work with decimals – tenths & hundredths

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Tape Diagram Vertical Number Line Number Bonds

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Grade 5 Decimals to the thousandths place Reason using all four operations with decimals to the hundredths place Standard multiplication algorithm with multi- digit numbers Reason about dividing whole numbers with two- digit divisors

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Tape Diagram “Box Method” Standard Algorithm

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Multiple Representations

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Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.Look for & express regularity in repeated reasoning

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Common Core State Standards for Mathematics. 1.How many vertices are on a cube? 2.Subtract ½ from half a baker’s dozen. 3.How many prime numbers are between.

Common Core State Standards for Mathematics. 1.How many vertices are on a cube? 2.Subtract ½ from half a baker’s dozen. 3.How many prime numbers are between.

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