What's my number?
Purpose:
The purpose of this activity is to engage students in using their knowledge of number operations to
find an unknown.
Achievement Objectives:
NA2-6: Communicate and interpret simple additive strategies, using words, diagrams (pictures), and
symbols.
NA2-7: Generalise that whole numbers can be partitioned in many ways.
Description of mathematics:
In readiness for this problem, the students should have familiarity with each of the following
components of mathematics. The problem may be solved with different combinations of these
components.
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basic addition and subtraction facts
skip counting
multiplying
solving inverse problems such as 6 + ? = 21
This activity may be carried out with guidance, or by allowing the student to follow their own
method of solution. The approach should be chosen in sympathy with students’ skills and depth of
understanding.
Activity:
I’m thinking of a number.
I get the same answer if I add 8 to my number, or if I don’t add 8 but
instead I triple my number.
What number am I thinking of?
The arithmetic approach
The student is able to form equations from the information given to solve for an unknown.
Prompts from the teacher could be:
1. Try your own number. Triple it and what do you get? Add 8 to your number and what do you
get?
2. How close was your own number? Would it have been better to try a bigger or a smaller
value?
3. Try another number that is likely to give the same answer when it is tripled as when 8 is
added.
4. Did that work? If not, try again with a number that is likely to be closer.
The conceptual approach
The student is able to use the information given to solve for an unknown.
Prompts from the teacher could be:
1. What does tripling a number do to it? Think about a number, triple it, then think about what
happened to that original number?
2. When you triple a number, it is the same as adding in up ...how many times?
3. What does adding 8 do to a number? How much bigger will it get?
4. If adding 8 gives the same answer as tripling it, what can you say about that number?