Number Talks with Multiplication
Drop the Zero! NOT!
April 14, 2016

For Number Talks (NT) this week,  the Pre-Service Teachers (PST) were engage with multiplication using landmark numbers. PST were to mentally solve 6 x 50 and 6 x 300. This type of problem is not a real challenge. However, I wanted to see PST's approach to solving the problems. I wanted to hear thinking as relate to multiplying numbers with the multiples of 10. What approach would they choose? The following conversation took place:

Teacher: How did you solve it?
PST1: I multiplied 6 x5 first. That is 30. Then I dropped the zero. So the answer is 300.
Teacher: What do you mean by dropping the zero at the end?
PST1: I mean since the you are multiplying by 50 so I multiply 6x5 and drop the zero at the end.
Teacher: So in reality what are you multiplying? Where did you get the 5?
PST 1: I got the 5 from 50. 5 x 10 is 50. So I separated the 50 into 5 x 10. Then I multiplied 6 x 5 which is 30 then multiplied 30 x 10. This makes 300.
PST 2: You decomposed 50 into 5 x10.

The goal I am interested in is making sure PST understand the mathematics behind multiplying by 10s and 100s.  You are not simply dropping zeros at the end of the number which is a misconception when multiplying multiples of 10s and 100s etc.. 
By allowing for mathematics discourse, PST are made to attend to precision. Mathematically proficient students try to use clear definitions in discussion with others and in their own reasoning. They calculate accurately and efficiently, express numerical answers  with a degree of precision appropriate for problem context. Content wise, third grade students are expected to multiply one digit whole numbers by multiples of 10 using place value and properties of operations.

The same kind of discussion happened with the problem 6 x 300. The following is this dialogue
Teacher: How did you get 1800?
PST 3: I multiplied 6 x 3. And dropped two zeros behind the 18.
Teacher: You know the question I will ask? Where did you get the 3?
PST 3: Well, I did it in my head.
Teacher: Keep going?
PST 3: Ok. I broke down 300 into 3 x 100. Then I rearranged the problem into 6 x 3 x100.
I multiplied 6 x 3 which is 18. Then I multiplied 18 x100. This gave 1800.
PST: You want your students to use the correct mathematical terminology to understand and solve problems.........

Again PST used misconception about adding the zeros at then end because there are zeros in one of the factors. Allowing this discourse to discuss and explain importance of attending to precision will allow them to become better mathematics teachers.






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