![]() ![]() The squares are the same size and don’t directly represent the quantities. Linda and Rachel’s method is more abstract.Their version is more concrete, since the squares are in proportion to the quantities represented. Mark and Andrew’s method shows the order it was constructed: red, then black, then blue, then pink.We discussed the various methods in this order (A, B, C, D, F and G). On chart paper: Demonstrate each of your methods with the multiplication problem 26 x 35.Įach group shared their chart paper demonstrations.Can it be used for other kinds of multiplication (decimals, fractions, binomials)?.What are its advantages? Disadvantages?.Practice the method with a few other multiplication problems. Small groups responded to the following instructions: TaskĮach handout showed a sample calculation, but didn’t name the method or explain how it worked. We quickly looked at standard algorithm for multiplying when using paper and pencil, then broke up into pairs to look at 8 alternative algorithms for multiplication. We used the second definition to think about multiplication. An accepted process or set of rules to be followed in calculations.A recipe, series of steps that work with different ingredients.We talked about some possible definitions: ![]() I asked the group what they thought of when they heard the word algorithm 2. (Find more information on these properties in Chapter 2 of Math Matters, by Chapin & Johnson) Examining Multiplication Algorithms If we’re teaching these properties, a number talk would be a way to show students that they already use the strategies without realizing it. My guess is that Mark and Davida didn’t consciously decide to use the associative and distributive properties, but instead chose what was easiest or most efficient when multiplying mentally. Davida made use of the distributive property of multiplication, which allowed her to separate 16 into two addends (10 and 6) and distribute the multiplication into 25 x 10 and 25 x 6. For example, Mark’s strategy made use of the associative property of multiplication, which allowed him to separate 16 into the factors 4 and 4, then group and multiply all the factors in a different order than is in the original multiplication problem. After the number talk, I talked about how I tried to take notes on the strategies in a way that would show the mathematical properties that people used to make the calculations easier. Mark realized that there are four 4’s in 16, so he could multiply 4 by 25 to get 100, then multiply 100 by 4 to get 400.ĭavida knew that 16 is the same as 10 + 6, so she multiplied 25 by 10 and 25 by 6 and added the two products together.ĭuring the number talk, there was some discussion of the distributive and associative properties of multiplication, but we didn’t connect them explicitly to each strategy. In talking with Mark, Rachel realized that she had gotten the wrong answer (230) and was willing to explain her strategy in order to find out why it didn’t work.Īfter Davida demonstrated the area model method at the bottom, Rachel realized that she had forgotten to multiply some of the numbers (5 x 10 & 20 x 6). Write their name above the calculations on the board. Ask a volunteer to explain how they got the answer.So, what’s the answer? 400 and 230 were possible answers.Turn to a partner and explain how you got your answer.You might find even more while we’re talking about it. If you have two ways of getting the answer, put out another finger. ![]() Putting your thumb right by your chest lets me know that you’re ready, but doesn’t disturb people who are still thinking.
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