Math Models
Parent Academy
Presented by:
Allison Curran
http://websites.nylearns.org/acurran1
Math Domains
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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
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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 multidigit numbers
• Reason about dividing whole numbers with twodigit 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 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