Task: Multiplicative Comparison

Task Planning

Multiplication (Equal Groups):

  • V has some pockets.  He puts a few pennies in each pocket.  How many pennies does V have?
  • Alternate numbers:    Easier: (2, 3); Hard: (9, 4); Harder: (15, 8); Hardest: (12, 28; 32, 44)
  • Questions to Ask: What is happening in the story? How many pockets do you have? What information you need to find an answer?

Comparison (Product Unknown):

  • L picked up some rocks. S picked up a few times as many rocks as L. How many rocks did L pick up?
  • Alternate numbers:    Easier: (2, 4) or (6, 2) or (3, 4); Hard: (9, 6); Harder: (13, 7 OR 14, 8); Hardest: (23, 24)
  • Questions to Ask: What is happening in the story? Do you collect rocks? What are things that you collect? What information you need to find an answer?

Comparison (Group Size Unknown – Partition Division):

  • N has some fish. N has a few times as many as A. How many fish does A have?
  • Alternate numbers:    Easier: (10, 2) or (6, 3); Hard: (25, 5) or (42, 7); Harder: (110, 11) or (132, 12); Hardest: (304, 16)
  • Questions to Ask: What is happening in the story? Do you have fish or other pets or stuffed animals? What information you need to find an answer?

Comparison (Number of Groups Unknown — Measurement Division):

  • P has a few pieces of chocolate. V has even fewer pieces of chocolate. How many times as many pieces of chocolate did P have compared to V?
  • Alternate numbers:    Easier: (10, 2) or (6, 3); Hard: (25, 5) or (42, 7); Harder: (110, 11) or (132, 12); Hardest: (304, 16)
  • Questions to Ask: What is happening in the story? Do you like chocolate or other candies? What are candies that you like? What information you need to find an answer?

Reflection on Task and Implementation

The implementation was good, but a little rushed! I’m still learning how to keep them on track. I’ll figure this out eventually. It seemed that communicating my expectations about how they used the resources still needs work.
I felt like it was going better by the last group – starting out with brief expectations and getting them focused. I worked with four groups of three students each. The second-to-last asked if they could have one minute of free play before we began and that did seem to help somewhat, but it was difficult to keep them on task, so I didn’t do that again with the last group.
Well – I thought I had left out numbers, but forgot that “few” is fairly well defined as “3 or 4” and students in each group pointed that out. So I will know better next time! But that means they are good at looking for the key words.
For the first question, I asked students to think about the story and to count their pockets to see what a good number would be for V’s pockets, and then I told them some number of pennies. Students in every group automatically multiplied, so I asked them how they knew it was multiplication and could they show me using the squares. One student literally put squares in each pocket and then counted them up, others grouped the squares flat on the desk or in stacks or other designs.
I learned that the students overall had a pretty good sense of multiplication and comparison. One student, and a few others, mentioned on the third question that it felt tricky – it felt like A should have more fish than N, even though they said they could see N had the most fish.
On the other hand, some students did struggle with using blocks to represent the story, hesitating to figure out why they could use squares in groups to find the answer. I tried in the third or fourth question to encourage them to write numbers on the squares instead of counting out every square that they needed, because their teacher had shown them they could do that in the intro to the lesson. It didn’t seem that any of the students felt comfortable with that – although one student drew squares on her desk with the number in the square to represent each group and so her group members also tried that.  I’m not entirely sure if the other students’ discomfort was about writing on the squares or whether they just liked to use the squares or if they really were struggling to see the representation. So, that was interesting!
I also learned that the students really responded when I left the questions open – for each question, I asked which numbers made sense to use and thought they might always choose simple numbers. I had them take turns, and some were simple – like 6 times 6 but others were a little harder like 11 times 4, 24 times 6, or 500 times 5.  One student suggested 11 times 4 – he and one of the other team members knew it was 44 right away, but the third member didn’t. But she did really well to find a strategy – she told me she could just make it 4 times 10 instead and then add 4 to get 44.
They also really liked having their names in the problems and they enjoyed suggesting other things they might pick up or own.
I feel that I probably did not get exactly what I should have from the activity – mainly because of the lack of time. Also, I think the students are not yet completely comfortable with me in the classroom.
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One response to “Task: Multiplicative Comparison

  1. Pingback: Week 5: Reflection | Sense-Making in a Complex Field

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