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Essential Question: How can one know the sum of 5 consecutive numbers so quickly?
Essential Question: How can one know the sum of 5 consecutive numbers so quickly?
Act 1 - What is happening?
Act 1 - What is happening?
1. Watch the video.
1. Watch the video.
2. What do you notice? What do you wonder?
2. What do you notice? What do you wonder?
3. Question: How can the performer know the sum so quickly for any number chosen? (hypothesize how the trick works) Does this work for all numbers?
3. Question: How can the performer know the sum so quickly for any number chosen? (hypothesize how the trick works) Does this work for all numbers?
Act 2 - Investigation
Act 2 - Investigation
4. Look at a visual model of the problem.
4. Look at a visual model of the problem.
5. Use your hypothesis to determine how the trick works.
5. Use your hypothesis to determine how the trick works.
Act 3 - The solution
Act 3 - The solution
6. Share strategies and solutions.
6. Share strategies and solutions.
7. Ask students to hypothesize again about whether any number would work – like fractions or decimals. Have them work to figure it out.
7. Ask students to hypothesize again about whether any number would work – like fractions or decimals. Have them work to figure it out.
8. Make connections between equivalent expressions (i.e. the rules
8. Make connections between equivalent expressions (i.e. the rules
5n + 10 and 5(n + 2) ).
5n + 10 and 5(n + 2) ).
9. Revisit any initial student questions that were not answered.
9. Revisit any initial student questions that were not answered.
Based on the three act task: Consecutive Number Sums by mwiernicki .
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