Headline Story
Algebra Machines and Puzzles, #3
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Introduction
Read the Headline Story to the students. Encourage students to list what they know for sure, to perform experiments to figure out new information, to notice patterns in their results, and to pose new problems.
Headline Story
- I’m thinking of a 3-digit number greater than 900.
- It’s divisible by 2, and the sum of its digits is divisible by 6.
Possible student responses
The hundreds digit must be 9. The units digit must be 0, 2, 4, 6, or 8. If the units digit is 0, the number could be 930 or 990 because 9 + 3 + 0 is divisible by 6, as is 9 + 9 + 0. If the units digit is 2, the number could be 912 or 972, because the sum of the digits must be either 12, 18, or 24. There are only 5 other possibilities: 954, 936, 996, 918, and 978. The tens digit must be odd. If another clue was added, such as “The number I’m thinking of is the smallest number possible that can be made this way,” then a single number can be selected.
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