During this unit, your child will develop a conceptual understanding of decomposing multiplication problems through the use of the distributive property and the concept of area. Your child will not be required to use the properties explicitly, but will be expected to discuss the concepts and use area diagrams to support their reasoning.  In addition, your child will use area as a context to further develop multiplicative thinking.  This includes solving problems involving rectangular areas by multiplying side lengths and solving for and unknown number in related multiplication and division equations.

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Key Vocabulary

Students need to:

  • Apply properties of operations as strategies to multiply and divide.
    • If 3 x 5 x 2 can be found b 3 x 5 = 15, then 15 x 2= 30 , or by 5 x 2 = 10, then 3 x 10 = 30.  (associative property of multiplication)
    • Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5+2) = (8 x 5 ) = ( 8 x 2 ) – 40 + 16 = 56.  (distributive property)
  • Identify arithmetic patterns (including patterns in the addition and multiplication table) and explain them using properties of operations.
  • Determine the unknown whole number in a multiplication or division equation relating three whole numbers .   For example, determine the unknown number that makes the equation true in each of the equations 8 x ? = 48, 5 = __ / 3, 6 x 6 = ?.
  • Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.  By the end of Grade 3, know from memory all products of two one-digit numbers.
  • Use place value understanding to round whole numbers to the nearest 10 or 100.
  • Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
  • 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.

 Area

  • Relate area to the operations of multiplication and addition.
    •  Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b +c is the sum of a x b and a x c.  Use area models to represent the distributive property in mathematical reasoning.
    • Recognize area as additive.  Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non –overlapping rectangles, applying this technique to solve real world problems
    • Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
  • Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.
  • 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.