We received another letter from Professor Arbegla this week! She informed us that she has a trick that makes multiplying numbers outside the times table easier. The best way to describe it was to use an example. Students chose one of the three following problems to try and solve mentally -- without paper and pencil:
4 x 26 6 x 59 9 x 87
Each student took a turn sharing how they arrived at an answer. I was so impressed by all the creative strategies they used to figure it out.
We then used base ten blocks to test Professor Arbegla’s new strategy. Using the blocks to warm up, students practiced making two digit numbers. Next, we discussed the meaning of 3 x 46. Students made three sets of 46 with a partner and exchanged blocks to make 138. The question was then asked, “How do you write 46 using tens and ones?” (40 + 6 was the answer.) So, we decided another way to say 3 x 46 was to say that we have three 40's and three 6's. The students were able to build that and find the same answer of 138. We learned that the strategy of splitting up the two digit number and sharing the factor equally was called the distributive property over addition. The students practiced regrouping the blocks as I wrote the following on the board --> --> --> --> --> -->
3 x 46 = 3 x (40+6)
46 + 46 + 46 = (3 x 40) + (3 x 6)
138 = 120 + 18
138 = 138
The partners were then challenged to solve 4 x 38 using the base ten blocks and be prepared to share their strategy. Each pair solved the problem and took turns standing at the board explaining which strategy they used. I loved hearing how their minds worked, and how the partners shared the process together.
Next week we will learn how to write the distributive property algebraically, which always seems to throw them for a loop at first. We’ll take it slow and have some fun!