Transcript Math Models - Lynbrook School
Math Models
Parent Academy Presented by: Allison Curran http://websites.nylearns.org/acurran1
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)
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
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 …
Number Bonds Bundles Rekenrek 5 and Ten Frames
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
Bundles Number Bonds Rekenrek
Ten Frames Number Bonds
Number Bonds
Number Lines
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
Number Bonds Bundles Number Lines
Place Value Discs
Grade 3
• • Major focus is multiplication Adding and subtracting fluently within 1,000
Number Bonds Arrays Distributive Property
Tape Diagrams Number Bonds
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
Tape Diagram Vertical Number Line Number Bonds
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
Tape Diagram “Box Method” Standard Algorithm
Multiple Representations
Standards for Mathematical Practice 1.
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Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for & express regularity in repeated reasoning