I Think of a Number

Introduction

In this lesson, we start with the answer. Your job is to work backwards.

Let start with an example:

Think of a number from 1 to 9;
Multiply it by 9;
Add up the "units" and "tens" digits of the answer;
Change the number to a letter (see the right):
Think of a country starting with that letter;
Choose the third letter of the country’s name;
Think of an animal starting with that letter.

I know what your country and animal are... Click here to find out if I am right!

How did I work it out?

Here is another psychic who will work out which number you are thinking of. How does it work? Play it a number of times, look for patterns, investigate until you too can be a Psychic yourself.

Thinking Backwards

I think of a number. I double it, then add 3. The answer is 11. What was my number?

How did you find my answer? Here is a video to show you how to think backwards.

Practise these questions with support on mathsframe.co.uk (there are 4 levels).

Practise these questions without support on transum (there are 3 levels).

Use this function builder to consolidate the concept of functions.

Below are more increasingly difficult questions:

Further Practice

Some of the essential skills introduced in this lesson are substitution, forming expressions and function machines. Practise these relevant skills on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.

Transum

Clouds - can you work out which numbers are hidden behind the clouds in these calculations?

Extension

At year 7, you are not required to be able to form and solve equations yet. This will come in Year 8. But will you want to find out more about this super important skill, watch this video for an introduction. The idea is all about balancing things on a scale.

Here is an interesting task on nRich called Super Shapes. Here are more similar ones on solvemoji.com. Be very careful!

Lemon Law is another one on transum where you change the numbers on the apples so that the number on the lemon is the given total.

Then there are more fun puzzles on https://solveme.edc.org/.