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 1: Whole number THOAN problems. You can earn a trophy if you get at least 7 questions correct.

 $$\times 2$$$$+3$$$$43$$Matthew says:'I think of a number. I double my number and add 3 the answer is 43'What number was Matthew first thinking of? Working: Ethan says:'I am also thinking of a number. If I multiply my number by 2 and add 6 the answer is 42'What number was Ethan first thinking of? Working: Andrew says:'I think of a number. I multiply my number by 3 and add 5 the answer is 11'What number was Andrew first thinking of? Working: Daniel says:'Can you guess what number I am thinking of if when I multiply it by 5 and add 3 the answer is 58?'What number was Daniel first thinking of? Working: Christopher says:'If I divide my number by 5 and add 6 the answer is 17'What number was Christopher first thinking of? Working: Joseph says:'If I multiply my number by 5 then add 6 then add 2 then add 6 the answer is 84'What number was Joseph first thinking of? Working: William says:'I am thinking of my favourite number. If I add 12 to my number then divide the result by 2, the answer is 17'What number was William first thinking of? Working: David says:'My plan was to add 5 to my number then multiply the result by 5. Then I multiplied the result by 6 and finally subtracted 2. The answer is 448'What number was David first thinking of? Working: Nicholas says:'I decided to add 3 to my number then multiply the result by 3, After that I subtracted 3 then doubled the result. The answer is 78'What number was Nicholas first thinking of? Working: James says:'If I multiply my number by 4 and subtract 4 then multiply the result by 4, the answer is 5 less than 261'What number was James first thinking of? Working:
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This is Think of a Number level 1. You can also try:
Level 2 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.

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Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

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"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

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Answer multiple choice questions about basic mathematical ideas. If you get a number of questions correct you will be invited to post a question of your own. The bank of questions grows larger every day.

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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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