3.OA.5 Distributive Property of Multiplication with Cooperative Groups

Objective

Common Core: Apply properties of operations (distributive) as strategies to multiply.

Specific/Student Friendly: Students will multiply by combining two smaller arrays to make a larger array.

Materials Needed

Distributive Property sheets, Sheet 1 for ¼ of the class, and Sheet 2for ¼, Sheet 3 for ¼, and Sheet 4 for ¼.

Color tiles or grid paper

Teacher Input

1.Ask: How can we break up 7 x 6 into two easier to solve multiplication problems? [(One Possible Answer: Break it up into (2 + 5) x 6 and then (2 x 6)+(5 x 6)]

Guided Practice

2.Demonstrate, using student input, making an array of two arrays put together for the problem referenced in step 1.

3.Demonstrate, using student input, creating an equation and simplifying it for the problem referenced in step 1 [(2 x 6) + (5 x 6); 12 + 30 = 42]

Independent Practice

4.Student groups of four work together to solve problems on the Distributive Property sheets. All students in each group should have a different version of the sheet. Student 1 is given the equation for the total array. Students 2 and 3 are given equations of the smaller arrays. Students 1, 2, and 3 share their information with student 4 then solve their own equations. Student 4 creates the total array, made up of the two smaller arrays.

5.Students their shares solutions with one another. They check to see that the sum of the solutions of students 2 and 3 equals student 1’s solution. They also check that Student 4’s array matches the equations.

6.All four students write the distributive equation and its solution.

7.Students then switch roles for the next problem, and continue to switch each subsequent problem. The sheet offers more clarity on this.

Check for Understanding

8.Check that students are creating accurate arrays, multiplying accurately, and correctly completing the equations. Debrief whole class at the end of the activity to share struggles and confusions students may have had and how they resolved them.

Distributive Property Sheet 1

My Name_____ Group Names ______

1.Tell student 4 that the sides of the total array are 4 units and 7 units, then find the area:

4 x 7 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( 4 x 7 )

______+ ______= ______

2.Tell student 3 that the sides of the red array are 8 units and 2 units. Then find the area:

8 x 2 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( 8 x 2 ) = ( ____ x ____)

______+ ______= ______

3.Tell student 2 that the sides of the blue array are 4 units and 3 units. Then find the area:

4 x 3 = _____

With the help of the others in your group, complete the equations below:

( 4 x 3 ) + ( ____ x ____ ) = ( ____ x ____ )

______+ ______= ______

4.After getting instructions from the other members of your group, create the correct red and blue arrays that combine to make a larger array.

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( ____ + ____ )

______+ ______= ______

Distributive Property Sheet 2

My Name_____ Group Names ______

1.Tell student 4 that the sides of the red array are 4 units and 2 units. Then find the area:

4 x 2 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( 4 x 2 ) = ( ____ x ____)

______+ ______= ______

2.Tell student 3 that the sides of the blue array are 8 units and 5 units. Then find the area:

8 x 5 = _____

With the help of the others in your group, complete the equations below:

( 8 x 5 ) + ( ____ x ____ ) = ( ____ x ____ )

______+ ______= ______

3.After getting instructions from the other members of your group, create the correct red and blue arrays that combine to make a larger array.

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( ____ + ____ )

______+ ______= ______

4.Tell student 1 that the sides of the total array are 9 units and 3 units, then find the area:

9 x 3 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( 9 x 3 )

______+ ______= ______

Distributive Property Sheet 3

My Name_____ Group Names ______

1.Tell student 4 that the sides of the blue array are 4 units and 5 units. Then find the area:

4 x 5 = _____

With the help of the others in your group, complete the equations below:

( 4 x 5 ) + ( ____ x ____ ) = ( ____ x ____ )

______+ ______= ______

2.After getting instructions from the other members of your group, create the correct red and blue arrays that combine to make a larger array.

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( ____ + ____ )

______+ ______= _____

3.Tell student 2 that the sides of the total array are 4 units and 8 units, then find the area:

4 x 8 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( 4 x 8 )

______+ ______= ______

4.Tell student 1 that the sides of the red array are 4 units and 3 units. Then find the area:

4 x 3 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( 4 x 3 ) = ( ____ x ____)

______+ ______= ______

Distributive Property Sheet 4

My Name_____ Group Names ______

1.After getting instructions from the other members of your group, create the correct red and blue arrays that combine to make a larger array.

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( ____ + ____ )

______+ ______= ______

2.Tell student 3 that the sides of the total array are 8 units and 7 units, then find the area:

8 x 7 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( ____ x ____ ) = ( 8 x 7 )

______+ ______= ______

3.Tell student 2 that the sides of the red array are 4 units and 5 units. Then find the area:

4 x 5 = _____

With the help of the others in your group, complete the equations below:

( ____ x ____) + ( 4 x 5 ) = ( ____ x ____)

______+ ______= ______

4.Tell student 1 that the sides of the blue array are 5 units and 3 units. Then find the area:

5 x 3 = _____

With the help of the others in your group, complete the equations below:

( 5 x 3 ) + ( ____ x ____ ) = ( ____ x ____ )

______+ ______= ______

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