Missing Key Dilemma
Task
Holy cow!! My calculator does not have a 3 key that works! How can I use this broken calculator to do this problem? Explain your reasoning carefully and clearly.
Alternate Versions of Task
| More Accessible Version:
Holy cow!! My calculator does not have a 3 key that works! How can I use this broken calculator to do this problem? Explain your reasoning carefully and clearly.
23 + 45
More Challenging Version:
Holy cow!! My calculator does not have a 3 key that works! How can I use this broken calculator to do this problem? Explain your reasoning carefully and clearly.
3320 ÷ 40 |
Context
We had been studying multiplication and doing some mental math and talking about different strategies. I wanted to know if my students knew the theory behind multiplication, not just how accurate they were with the algorithm.
What This Task Accomplishes
This task will tell me if students really know what multiplication does, how it works and how flexible their thinking is.
What the Student Will Do
Most students solved the problem using the algorithm first. Then they began to try different strategies. Some students had to test out their theories to be sure they worked. Other students were confident that their strategy would work.
Time Required for Task
15 - 20 minutes
Interdisciplinary Links
This task is purely mathematical; there are no interdisciplinary links.
Teaching Tips
You might want to include this task as part of a test on multiplication. It reinforces the fact that algorithms need to be understood, not just memorized.
Suggested Materials
None
Possible Solutions
There are so many ways to approach this problem. Some possible solutions are:
22 x 45 + 45
24 x 45 - 45
Added 23 times or 23 added 45 times
11.5 x 90
22.5 x 46
(Use two numbers whose sum is 23) x 45
| More Accessible Version Solution:
There are many possible approaches to solving this task so solutions will vary.
The sum is 68.
More Challenging Version Solution:
There are many possible approaches to solving this task so solutions will vary.
The quotient is 83.
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Task Specific Assessment Notes
Novice:
Inappropriate concepts are applied. The student thinks that the strategy for addition (move one number up on the number line and the other number down on the number line) will also work with multiplication. His/her mathematical reasoning is faulty.
Apprentice:
The solution is not complete. The student found an estimate, not the exact answer. The student's solution is partially useful, leading some way to the solution, but not a full solution.
Practitioner:
This student has a broad understanding of the problem. S/he uses a strategy that leads to a solution of the problem and uses effective reasoning in a clear explanation.
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Expert:
This student has multiple solutions, showing a deep understanding of the problem. S/he has the ability to identify the appropriate mathematical concepts.
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