Your child will be learning about multiplication, division, and area over the course of several units.  During this unit, your child will develop an understanding of the multiple meanings of multiplication and division of whole numbers through activities and problems involving equal –sized groups, arrays, and area sized models. An understanding of the commutative property will also be developed as arrays are built to solve problems. 

Your child will also solve problems to develop an understanding of the connection between multiplication and the measurement of area.  He/she will recognize area as an attribute of two dimensional regions, and will measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps (a square with sides of unit length being the standard unit for measuring area).  Finally, your child will understand that rectangular arrays can be decomposed into identical rows or into identical columns.  By decomposing rectangles into rectangular arrays of squares, students will connect area to multiplication.

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Key Vocabulary:  Array, Area, Commutative Property of Multiplication, Dividend, Divisor, Factor, Multiple, Partition, Product, Square Unit, Quotient

Students need to:

  • Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.  Describe a context in which a total number of objects can be expressed as 5 x 7.

Multiplication Arrays

Equal Groups

Number Lines
  • Identify arithmetic patterns (including patterns in the addition and multiplication table) and explain them using properties of operations.

Patterns

Describing Patterns
  • Apply properties of operations as strategies to multiply and divide. If 6 x 4 is known, then 4 x 6 = 24 is also known. (commutative property of multiplication)

Repeated Addition

Commutative Property

Number Lines
  • Interpret whole-number quotients of whole numbers.  For example, 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 equally into equal shares of 8 objects each.  Describe a context in which a number of shares or a number of groups can be expressed as 56/8

Multiplication and Division
Relationships
  • Use multiplication and division within 100 to solve word problems in situations involving equal groups, and arrays.  Use drawings and equations with a symbol for the unknown number to represent the problem.

Solving with Arrays

Solving with Bar Models

Area

Students need to:

  • Recognize area as an attribute of plane figures and understand concepts of area and measurement.
    • A square with length 1 unit, called ‘a unit square”, is said to have “one square unit” of area, and can be used to measure area.

      Square Units

      Using Squares
    • A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

      Squares as Units

      Counting Square Units
  • Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units).
  • Relate area to the operations of multiplication and addition.
    • Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths

      Rows and Columns

      Multiplying Rows and Columns