Split a Factor
o (I can use the distributive property to help find the product of an unknown
multiplication fact)
Discussion:
This strategy encourages students to split one of the factors into two or three friendly
equations of known facts.
Materials
Several sheets of 1 cm grid paper
Split a factor recording sheet
Supply students with several sheets of centimeter grid paper. Assign each pair of students a
product such as 6 x 8. The task is to find all of the different ways to make a single slice
through the rectangle. For each slice students write an equation. For a slice of one row of
eight, students would write 6 x 8 = (5 x 8) + (1 x 8). The individual products can be written in
the arrays as was done in the figure below:
1x8 = 8
5x8 = 40
After students have had multiple experiences with this introduce the following steps:
1) choose a factor and split it into two numbers whose sum equals that number
For example: 6 x 7
6 x (2 +5)
2) Distribute the other factor to both numbers to create two multiplication expressions.
(6 x 2) + (6 x 5)
3) Find the sum of both multiplication expressions.
(12) + (30)
4) Add the two products together to find the product of the original multiplication fact.
(42)
Split a Factor cont...
Fitting Rectangular Arrays
Materials:
Fitting Rectangular Arrays and crayons for each child
Two number cubes: 0-5 and 5-10
Directions:
Fitting Rectangular Arrays is a game in which children seek to fill a 10 by 10 grid with smaller
rectangular arrays. The smaller arrays are determined by tossing one or both of the 0-5 and
5 -10 number cubes.
Divide the group into two teams, pairing each child with a member of the opposing team.
Teams alternate turns, each time choosing to toss both number cubes once or one cube
twice. The numbers that turn up determine the dimensions of an array to be shaded by
each team member on a 10 by 10 grid. However, for this version, students can split a factor
to create two small arrays to place on the board. If they choose to split a factor, they must
record their original array on the “Split a Factor” recording sheet and show the two arrays
they created when they split the factor.
For example:
If team “a” rolls a 5 and a 6, their number expression would be 5 x 6. Then, they have to
choose a factor to split. If they choose 5, they could construct a 2 x 6 array and a 3 x 6 array
by shading in both areas in on their grid. On their recording sheet, they would record their
original number expression in the first column and circle the factor they split. In the second
column, students would write the two smaller number expressions for the two arrays they
created from the original. Students should then circle the number sentence of the array(s)
they used to cover their board. If they used both arrays, both should be circled.
The object of the game is to completely shade in the 10 by 10 grid without covering any
square twice. On any turn, children unable to fit both arrays in their grid they may choose to
only shade in one of the arrays they have created. If they cannot identify an array that they
can use to shade an area on their board, they loose their turn. If the arrays are shaded in
different colors as they occur, a crazy – quilt effect is produced.
A team wins whenever one of its members is the first to completely fill their grid.
Split a Factor
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