Problem
Oh no, gremlins have been in and covered up some numbers on the chart. Can you put the equations back together?

6 + 3 = J
9 - J = 8
J - 2 = 4
1+ J = 7
J + 5 = 9

What is this problem about?
This problem reinforces the use of addition and subtraction equations. Children become so accustomed to seeing addition equations in the form 1 + 5 = ___ and 5 – 2 = ___, that they automatically think that the "answer" is always the sum or the difference. If the children are only exposed to the traditional format they miss the opportunity to form understandings about all parts of the equation and how each part relates to the other.

Achievement Objectives
Number (Level 1)
- model and explain addition calculations with a sum of up to 20
- using up to 20 objects, model and explain subtraction calculations

Mathematical Processes
- devise and use problem solving strategies (act, draw)

Resources
picture of gremlin "marks" to introduce the problem
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- model and explain addition facts to 20.
- model and explain subtraction facts to 20.

Teaching Sequence

1. Create the scenario of gremlins visiting the class and drawing faces in place of numbers.
2. Read the problem to the class.
3. Ask the children to think about ways that they could solve the problem.
4. Let the children solve the problems. As they work circulate asking:
   Which numbers were easiest to figure out? Why?
   Which numbers were hardest to find? Why was that?
   How can you tell that you have found the right missing number?
   Do you think that more than one number might work? Why or why not?
5. Share solutions.

What strategy did you use to find the missing number?
Did anyone use a different strategy?

Extension problem
The gremlins have covered more than one number. Find as many number combinations as you can that work
J + J = 13
6 + J = J

Other contexts for the problem
Ink spots on the page