Distributive Property (Factors of 3 and 4)

In today's lesson, the students learn to use the distributive property to break apart factors into smaller numbers.   

I call the students to the carpet to have a whole class discussion about the distributive property.  I like for my students to be near me so that we can have a close community.  

 4 x 8=

 “How can we break this problem into 2 smaller problems? Let’s find out.”

First factor:

4 x 8 = (2 x 8) + (2 x 8)

                16 + 16 = 32

Second factor:

4 x 8= (4 x 5) + (4 x 3)

                    20 + 12=32

I send the students back to their seats and ask them to take out a sheet of paper.  I tell them, "Let’s try another one.  You work this problem, then we will work it together."

3 x 9 = (3 x __) + (3 x 4)

3 x 9 = (3 x _5_) + (3 x 4)

               _15__  + 12 = _27__

I let the students know that we can check our answers with arrays.

xxxxx

xxxxx

xxxxx

3 x 5 = 15

xxxx

xxxx

xxxx

3 x 4 = 12

Solution:  15 + 12 = 27

I let the students know that they will now practice the skill in groups.

For this activity, I let the students work with a partner on the concept.  By working with a partner, the students have an opportunity to hear their classmates reasoning of their answers.  Also, it gives the students a chance to communicate by justifying their answers and questioning their classmates (MP3). The students should use the Distributive Property Activity and two-color counters to understand how the Distributive Property can simplify multiplication.  The two-color counters are used to show a visual model of the two simpler problems.

As they work, I walk around to monitor and assess their progression of understanding through questioning. 

1. What two smaller numbers add together to equal the larger number?

2.  What operation will you use to put the two smaller problems together?

3. Which factor did you break apart, the first or the second?

4.  Does your model validate your answer?

As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students.  Any misconceptions are addressed at the point, as well as whole class at the end of the activity.

Any students that finish the assignment early, can go to the computer to practice the skill until we are ready for the whole group sharing: :  http://www.ixl.com/math/grade-4/properties-of-multiplication

After the students have worked together to understand the Distributive Property, I bring the class back together for a whole class discussion about the activity sheet.  I allow one or two pairs to share their answers.  It is important to share samples of good student work ( Student Work - Distributive Property) because it allows those students who do not understand the opportunity to see and hear how to solve the problem correctly.  Questioning is an excellent tool to use to accomplish this goal.  Also, I clear up any misconceptions at this time.

Misconception(s):

As I monitored the students while they were working in pairs, I noticed that some of the pairs tried to break apart both numbers.  In order to help the students understand that they should only break apart 1 number, I worked with the students using the two-color counters to give a visual.  I used the example of 3 x 7.  The students made an array of 3 x 7.  I had the students break apart the first number into 2 and 1.  Their arrays showed 2 x 7 and 1 x 7 for a total of 21.  Next, I had the students break apart the second number into 3 x 4 and 3 x 3 for a total of 21.  

To show why they should not break apart both numbers, I had the students show me an array were they  broke the 3 apart into 2 and 1, and they broke the 7 part into 4 and 3.  Their array showed  2 x 4 and 1 x 3.  They saw that this did not equal 21.