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.

2.

3.

4.

5.

6.

7.

8.

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