Curriculum placement
Grade 3. This describes the skill, not a learner estimate.
Properties of addition and multiplication
Use associative commutative and distributive structure
Problem types
- Use one part of an array
- Count groups inside groups
- Add the regions of a split array
- Choose the facts that add to a product
- Facts that follow from known facts
- Group a product of three factors both ways
- Split a dividend into friendly parts
- Which property is it?
Builds on
- Multiplication as equal groups
- Turnaround addition facts · Earlier idea
A turnaround fact says the order of two addends does not change the sum. Multiplication has the same order rule: 3 × 4 and 4 × 3 make the same product.
Leads to
- Multiplying with partial products
- Reading a numerical expression
- Equivalent expressions · Extend the idea
Splitting an array into two parts to multiply is the distributive property. With a letter in place of a number it shows two expressions are equivalent.
Related skills
- Adding three numbers · Related idea
Adding three numbers in a different grouping gives the same total, which is the associative idea behind regrouping any product or sum.
- Number bonds to 10 · Related idea
Splitting a number into two parts is the same move as splitting an array into two smaller arrays whose totals add.
- Division as sharing and grouping · Shared foundations
- A fraction times a whole number · Shared foundations
- One-digit multiplication facts · Shared foundations
Open the interactive map to explore lessons and skill connections.