Oh no, gremlins have been in and covered up some numbers on the chart.

Can you put the equations back together?

This problem reinforces the use of addition and subtraction equations. Students 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 students 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.

Copymaster of the problem (English)

Copymaster of the problem (Māori)

Picture of gremlin "marks" to introduce the problem

### The Problem

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

### Teaching Sequence

- Create the scenario of gremlins visiting the class and drawing faces in place of numbers.
- Read the problem to the class.
- Ask the students to think about ways that they could solve the problem.
- Let the students 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? - Share solutions.
*What strategy did you use to find the missing number?*

Did anyone use a different strategy?

#### Extension to the 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

### Solution

9, 1, 6, 6, 4

Solution to the Extension:

Level One will not be using negative numbers so there is a limited number of possibilities for ? + ? = 13. Check that the students have remembered the (0, 13) pairing.

There are an infinite number of possibilites for 6 + ? = ? As the students work on this problem they will often use a sequence of numbers and notice the patterns in it, for example

6 + 1 = 7

6 + 2 = 8

6 + 3 = 9 etc