# Working backwards

The Ministry is migrating nzmaths content to Tāhurangi.
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available.

Purpose

This problem solving activity has a number focus.

Achievement Objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
NA5-6: Know and apply standard form, significant figures, rounding, and decimal place value.
NA5-7: Form and solve linear and simple quadratic equations.
Student Activity

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.

Specific Learning Outcomes
• Use their mathematical knowledge to invent problems.
• Devise and use problem solving strategies to explore situations mathematically.
Description of Mathematics

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. Some may be able to confidently embed an equation in a story context, and other students might readily suggest contextual problems that involve several steps, or a range of operations.

This open problem has students use their imaginations to create word problems of their own and to apply the mathematics that they are learning. You can adjust the difficulty of the problem by changing the numbers you place inside the envelopes.

A series of similar Number problems span Levels 1 to 5. These problems are You Be The Teacher, Level 1; Make Up Your Own, Level 2; Invent-A-Problem, Level 3; and Create a Question, Level 4.

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

Required Resource Materials
Activity

### 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.

### 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.
You can adjust the difficulty of the problem by changing the numbers you place inside the envelopes.

1. Tell the students that their challenge is to create some mathematics problems.
2. Ask the students to give you a number. Have them to make up a problem using that number as the answer.
4. Have them work singly or in groups to create problems of their own. If they produce a sum, product, difference or quotient rather than a problem, have them to find other ways to make up that number or help them to craft a word problem.
5. As students write their problems have them put them into an envelope for later use.
6. Those students who finish quickly might like to try to write another problem or solve someone else’s problem.
7. Pose some of the students’ problems from the sealed envelopes for the whole class to solve.
8. You might like to keep some of these problems to use with the class over the next few weeks. You might have students identify the best problem, the funniest problem, and so on.

### Extension

The problem is same. Use different numbers.

### Solution

The solutions will depend on your class.

Attachments