# Think of a Number

## Ten students think of a number then perform various operations on that number. You have to find what the original numbers were.

##### Level 1Level 2Level 3DescriptionHelpAlgebra

This is level 2: Decimal THOAN problems. You can earn a trophy if you get at least 7 questions correct.

 $$\times 2$$$$+6.8$$$$18$$Caleb says:'I think of a number. I double my number and add 6.8 the answer is 18'What number was Caleb first thinking of? Working: Justin says:'I am also thinking of a number. If I multiply my number by 2 and add 7.4 the answer is 17.2'What number was Justin first thinking of? Working: Austin says:'I think of a number. I multiply my number by 3 and add 4.4 the answer is 11'What number was Austin first thinking of? Working: Evan says:'Can you guess what number I am thinking of if when I multiply it by 8.7 and add 5.9 the answer is 70.28?'What number was Evan first thinking of? Working: Thomas says:'If I divide my number by 5 and add 2 the answer is 3.2'What number was Thomas first thinking of? Working: Luke says:'If I multiply my number by 3.9 then add 9.1 then add 5.1 then add 1.8 the answer is 27.7'What number was Luke first thinking of? Working: Mason says:'I am thinking of my favourite number. If I add 13.4 to my number then divide the result by 2, the answer is 10.65'What number was Mason first thinking of? Working: Aidan says:'My plan was to add 2.6 to my number then multiply the result by 9.3. Then I multiplied the result by 7.1 and finally subtracted 1.6. The answer is 724.73'What number was Aidan first thinking of? Working: Jackson says:'I decided to add 3.4 to my number then multiply the result by 3, After that I subtracted 7.3 then doubled the result. The answer is 64'What number was Jackson first thinking of? Working: Isaiah says:'If I multiply my number by 4.7 and subtract 4.1 then multiply the result by 2.8, the answer is 8.8 less than 105.232'What number was Isaiah first thinking of? Working:
Check

This is Think of a Number level 2. You can also try:
Level 1 Level 3

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

#### 23 or Bust

A game involving mental arithmetic and strategy for two players or one player against the computer. It is possible to beat the computer but you need a well thought out strategy.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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## Description of Levels

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Level 1 - Whole number THOAN problems

Level 2 - Decimal THOAN problems

Level 3 - Negative decimal THOAN problems

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Example

Daniel says 'If I double my number and add 6 the answer is 30'

### Method 1 - Work backwards

Start at the end of the sentence with the answer 30 and undo all of the operations Daniel performed on his number in reverse order.

30 minus 6 then divide by two

The number Daniel was thinking about was 12

### Method 2 - Form and solve an equation

Let the number that Daniel is first thinking of be n.

2n + 6 = 30

Subtract 6 from both sides

2n = 24

Divide both sides by 2

n = 12

The number Daniel was thinking about was 12

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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