Hands on With the Distributive Property and Multiples of 10

Are you worried if your students can handle using the Distributive Property of Multiplication with larger numbers?  I was!  My students have moved onto multiplying with multiples of 10 (CCSS 3.NBT.A.3).  I continue to use the hands on approach to ground my students in the concrete before moving onto the symbolic and abstract.  I started with the following question for them to solve.  Normally they tackle the problem on their own.  But because we needed a lot of room to work for a large piece of chart paper and I had a limited supply of the foam tiles, I had the students work in pairs.

Presenting the Problem
We first gathered on the rug, read the problem together and then I asked them:

What do question(s) do you need to answer? As you can see in the picture, we underlined it.

What information are you given? We circled the information given.

What materials will you be using?  Large graph paper, foam tiles, pencil.

Once they received the materials, off they went in pairs to problem solve.  A few of the pairs I saw trying to build separate arrays and I hinted that they were to work together.  A few pairs were trying to fill FIVE rows, again I hinted that maybe the problem didn't say that.  Once I found a pair that had formed 3 rows of 20, I asked everyone to stop and come and look at their array. I tried not to just say what they had done right, instead I asked:

What do you think this pair of students is showing with their array?


Students using the Distributive Property to Solve with Multiples of 10.
Then I had the pair also explain what they had done and why.  Then I sent everyone back to continue working and the pair who had finished building the array, proceeded to shade in the graph paper to record it.  Once everyone was or had shaded in their array, I reminded them that they still had to solve the problem and answer the question using some kind of equation or other method.  Amazingly, they had remembered how to use the distributive property and pretty much 80% were able to write an accurate equation using the distributive property.  Relief!

From there, I brought up some example charts to put on the white board and we discussed how the distributive property helps to break down larger problems into smaller ones to make it easier to solve.  We discussed where arrays should be broken apart (strategic points are 4, 5 and 10).  About a week later the class took their multiplication chapter test and there was one particular problem that resembled the one they had worked on with the tiles.  Interestingly, almost all used the Distributive Property correctly.  On the test, the student had to shade in an array to represent the problem and label the diagram, write an equation using the distributive property and of course, solve the problem.  The only error that I did see in their work was not labeling the diagram correctly with the 2 arrays -- yet they were still able to write an equation using the distributive property.  I believe that my students have really understood the concept of multiplication and the use of the Properties of Multiplication to solve problems.  Next, on to division!
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