Represent and solve problems involving multiplication and division.
M.3.1
Fully covered
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each (e.g., describe context in which a total number of objects can be expressed as 5 × 7).
- Equal groups
- Equal groups
- Introduction to multiplication
- More ways to multiply
- Multiplication as equal groups
- Multiplication in contexts
- Multiplication in real world contexts
- Multiplication with arrays
- Multiply using groups of objects
- Multiply with arrays
- Understand equal groups as multiplication
- Understand multiplication using groups of objects
- Understand multiplication with arrays
M.3.2
Fully covered
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (e.g., describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8).
- Divide with visuals
- Division as equal groups
- Division in context
- Division in contexts
- Division with arrays
- Division with groups of objects
- Visualizing division with arrays
M.3.3
Fully covered
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).
- Division word problem: blueberries
- Division word problem: school building
- Multiplication and division word problems (within 100)
- Multiplication word problem: parking lot
- Multiplication word problem: soda party
- Relate division to multiplication word problems
M.3.4
Fully covered
Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 =?).
- Basic multiplication
- Find missing divisors and dividends (1-digit division)
- Find missing factors (1-digit multiplication)
- Unknowns with multiplication and division
Understand properties of multiplication and the relationship between multiplication and division.
M.3.5
Fully covered
Apply properties of operations as strategies to multiply and divide (e.g., If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known: Commutative Property of Multiplication. 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30: Associative Property of Multiplication. Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56: Distributive Property.
- Associative property of multiplication
- Associative property of multiplication
- Commutative property of multiplication
- Commutative property of multiplication
- Distributive property
- Distributive property when multiplying
- Properties and patterns for multiplication
- Properties of multiplication
- Represent the commutative property of multiplication
- Understand associative property of multiplication
- Understand the commutative property of multiplication
- Use associative property to multiply 2-digit numbers by 1-digit
- Using associative property to simplify multiplication
- Visualize distributive property
M.3.6
Fully covered
Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8).
- Division word problem: blueberries
- Division word problem: school building
- Fact families
- Relate division to multiplication
- Relate division to multiplication word problems
- Relate multiplication and division equations
- Relating division to multiplication
Multiply and divide within 100.
M.3.7
Mostly covered
Learn multiplication tables (facts) with speed and memory in order to fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or properties of operations by the end of Grade 3.
- Basic division
- Basic multiplication
- Divide by 1
- Divide by 10
- Divide by 2
- Divide by 3
- Divide by 4
- Divide by 5
- Divide by 6
- Divide by 7
- Divide by 8
- Divide by 9
- Find missing divisors and dividends (1-digit division)
- Find missing factors (1-digit multiplication)
- Multiply by 0 or 1
- Multiply by 10
- Multiply by 2
- Multiply by 2 and 4
- Multiply by 3
- Multiply by 3 and 6
- Multiply by 4
- Multiply by 5
- Multiply by 5 and 10
- Multiply by 6
- Multiply by 7
- Multiply by 8
- Multiply by 9
- Multiply with arrays
- Relate division to multiplication
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
M.3.8
Not covered
Solve two-step word problems using the four operations, represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
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M.3.9
Fully covered
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations (e.g., observe that 4 times a number is always even and explain why 4 times a number can be decomposed into two equal addends).
- Finding patterns in numbers
- Intro to even and odd numbers
- Math patterns
- Patterns in hundreds chart
- Patterns in hundreds chart
- Patterns in multiplication tables
- Patterns in multiplication tables
- Patterns with even and odd
- Patterns with multiplying even and odd numbers
- Recognizing number patterns
