Math ModelsParent Academy

Presented by:Allison Curranhttp://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 StrategiesAlgorithms 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 applicableto a class of problems that gives the correct result in every casewhen the steps are carried out correctly

• Computation Strategy: Purposeful manipulations that may bechosen for specific problems, may not have a fixed order, andmay be aimed at converting one problem into another

Example of ProgressionsNumbers in Base 10Kindergarten•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 BondsBundlesRekenrek5 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

BundlesNumber BondsRekenrek

Ten FramesNumber 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 BondsBundlesNumber Lines

Place Value Discs

Grade 3

•Major focus is multiplication•Adding and subtracting fluently within

1,000

Number BondsArraysDistributive Property

Tape DiagramsNumber 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 DiagramVertical Number LineNumber 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. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for & express regularity in repeated

reasoning