There is a special number in each of these envelopes.

When you get your envelope, open it and find out what your number is.

This number is the solution to a maths problem that YOU make up.

What is your problem?

Students are challenged to create their own number problems. This can require a deeper understanding than solving a given problem.

Some students may simply suggest an equation such as 23 + 24 = ? Some may be able to confidently embed an equation in a story context, and other students might readily suggest contextual problems that involve more than one step, or an operation other than addition.

This open problem has students use their imaginations to create word problems of their own and to apply the mathematics that they are learning.

A series of similar problems span Level 1 to Level 5. These problems are Make Up Your Own, Level 2, Invent-A-Problem, Level 3, Create a Question, Level 4, Cart Before The Horse, Level 5 and Working Backwards, Level 5.

You may find that this serves as a useful assessment task.

### The Problem

There is a special number in each of these envelopes.

When you get your envelope, open it and find out what your number is.

This number is the solution to a maths problem that YOU make up.

What is your problem?

## Teaching sequence

There are many ways to have your students create their own problems for others to solve.

This is just one possible way to consider.

Use numbers on the copymaster or write ones that better suit your students.

- Ask students to tell you what they have most enjoyed learning in the current class inquiry.
- Explain that their challenge is to write some interesting maths problems related to their learning and that classmates will be challenged to solve these.
- Write a 2-digit number for which a related problem can be written. (eg. 24)

Have students suggest what the problem might be for which the 2-digit number is the solution. (eg. 47 children from two classes were were in the hall. 23 were from our class. How many children were in the other class? 23 + ? = 47) - Record this and ask for other problems for which the given number is the problem solution. Suggest (and model as appropriate) that students might make up the equation first, then put words to it. Encourage them to consider operations other than addition.
- Record several student problems, suggest improvements, and highlight key words that students may need as they write their own problems.
- Read the given
**Problem**together. Ensure the students understand the task. - As they work singly or in groups, support with wording as appropriate.
- Those students who finish quickly might like to try to write another problem using a different operation, or solve someone else’s problem.
- Have buddies check that problems make sense before students put the finished problem in an envelope for someone else to solve (having first removed the number solution).

### Solution

The solutions here will depend on your class.