What's My Number?

Activity One

 A copy of a hundreds board helps students eliminate possibilities. For question 2, the array could be extended to include the numbers 101–119.
Students need to approach the clues systematically. For example, in question 1:
i. “I am less than 90.”
0, 1, 2, 3, 4, … 86, 87, 88, 89
ii. “If you add my digits, the total is less than 10.”
10, 11, 12, 13, 14, 15, 16, 17, 18
20, 21, 22, … , 27
30, 31, … 36
40, 41, … 45
50, 51, … 54
…
80, 81
iii. “I am greater than 20.”
21, 22, … 27
30, 31, …
iv. “My tens digit is greater than my ones digit.”
21
30, 31, 32
40, 41, 42, 43
50, 51, 52, 53, 54
etc.

Activity Two

With this activity, discuss how students might develop similar problems. Suggest that a set of clues that leave only one solution is ideal. Discuss possible clues, such as:
“greater than”, “less than”, “even number”, “odd number”, “multiple of five”, “digits add to”, “difference of digits is”
Tell students that crossing out the numbers on a hundreds board that are affected by each new clue is a useful strategy.

Answers to Activities

Activity One
1. Any number out of: 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81
2. 112
Activity Two
Answers will vary.