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    • ▾3rd grade
      • ▸Addition, subtraction, estimation
        • •Mentally add within 1000
        • •Round to the nearest 10 or 100
        • •Add and subtract within 1000, abstract
      • ▸Multiplication
        • •Multiplication using rectangular arrays and equal groups, concrete and visual
        • •Multiplication as repeated addition
        • •Multiply, abstract
      • ▸Division
        • •Divide using equal groups
        • •Division as repeated subtraction
        • •Divide, abstract
      • ▸Fractions
        • •Equal shares of shapes and unit fractions
        • •Plot fractions on the number line
        • •Relating fractions to 1
        • •Representing whole numbers as fractions
        • •Comparing fractions with like numerators, denominators, or both
      • ▾Relating multiplication and division
        • •Missing number problems, multiplication and division
        • •Relating multiplication to division
        • •Use properties to multiply and divide
        • •Multiply one-digit numbers by multiples of 10
      • ▸Arithmetic patterns and problem solving
        • •Two-step word problems
        • •Arithmetic and geometric sequences
        • •Patterns in addition and multiplication
        • •Intro to the triangular numbers
        • •Intro to the Fibonacci sequence
        • •Intro to Pascal's triangle
      • ▸Geometry
        • •Shape heirarchy
        • •Area of composite rectangles by counting unit squares
        • •Area and units of measure
        • •Area as multiplication
        • •Area, perimeter, and how they're related
      • ▸Time, measurement, and data
        • •Tell and write time, minute increments
        • •Measure and estimate volumes and masses
        • •Scaled bar and picture graphs
        • •Line plots with fractions
     › 3rd grade › Relating multiplication and division

    Use properties to multiply and divide

    Use multiplication facts to solve other multiplication problems. For example, use 6 * 3 = 18 to solve __ * 6 = 18 or 3 * 6 = __. Use the fact that multiplication is associative, to make a problem easier. For example, 7 * 2 * 5 can be evaluated by seeing 2 * 5 = 10, and 10 * 7 = 70, which is much easier.

    Watch these Khan Academy videos:

    • Properties and patterns for multiplication
    • Properties of multiplication

    Do these Khan Academy exercises:

    • Use associative property to multiply 2-digit numbers by 1-digit
    • Understand associative property of multiplication
    • Distributive property
    • Represent the commutative property of multiplication
    • Commutative property of multiplication
    • Understand the commutative property of multiplication
    • Associative property of multiplication
    • Visualize distributive property

    Next, give your students these challenges:

    • A City of Towers by NRICH
    • What Could It Be? by NRICH

    Conclude by leading this investigation:

    Find the Attribute
    by MathPickle

    3.OA.B.5: Apply properties of operations as strategies to multiply and divide. Examples: 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.)

    Lessons and practice problems