1089

Introduction

In this task, you will need to be able to do basic addition and subtraction.

Step 1 : Pick a three digit number. The three digits used must be different. e.g. 123

Step 2: Reverse that number. e.g. 123 becomes 321

Step 3: Take the smallest three digit number from the largest. e.g. 321 − 123 = 198

Step 4: Take the answer and reverse that number. e.g. 198 becomes 891

Step 5: Add that number to the answer of the subtraction. e.g. 891 + 198

What number did you get?

Repeat the steps above with different numbers, what numbers did you get?

Can you ever get different numbers?

Further Questions and Challenges

Can you explain why you (mostly) get 1089? Click here for an explanation.

Are you able to get 198? When does this happen? Why does this happen?

Can you do something to fix the calculation so that you end up with 1089? Look at the footnotes here for an answer.

What happens if the three digits are NOT different?

Further Practice

If you are struggling with adding and subtracting 3-digit numbers, you may wish to take a look at these videos: adding and subtracting. You may also wish to practise adding and subtracting with negative numbers. Do the relevant skills practice on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.


Transum

  • Formal Written Methods - examples of formal written methods for addition, subtraction, multiplication and division.

  • Number Skills Inventory - a checklist of basic numeracy techniques that every pupil should know. Look especially at the adding and subtracting activities.

  • Mix and Math - determine the nature of adding, subtracting and multiplying numbers with specific properties - not everything here is relevant.

  • What Are They? - an online exercise about sums, products, differences, ratios, square and prime numbers - not everything here is relevant.


Negative numbers

  • Boxed In Numbers - the classic dots and boxes game with the addition of some positive and negative numbers which determine your score.

  • Negative Magic - four partially completed magic squares containing negative numbers. Fill in the missing numbers.

  • Negative Numbers - use negative numbers in basic arithmetic and algebraic calculations and word problems.

  • Reading Scales - a self marking exercise on the reading of scales of different types.

  • Temperatures - test your understanding of negative numbers with this self marking quiz about temperatures.

Extension

More about 1089...

  1. Now calculate the following:

  • 1089 x 1

  • 1089 x 2

  • 1089 x 3

  • 1089 x 4

  • 1089 x 5

  • 1089 x 6

  • 1089 x 7

  • 1089 x 8

  • 1089 x 9

  1. Can you see any pattern? Hint: Look down the columns of digits!


  1. What about 1/1089? What does this equal to in decimal? If you need to, use a calculator.

    • Have you noticed any interesting pattern? Hint: think of the nine times table!


4. What about 1/9801? What does this equal to in decimal? If you need to, use a calculator.

  • Have you noticed any interesting pattern?


5. Now calculate the following:

  • 332

  • 3332

  • 33332

  • Can you see any pattern? Can you predict what the answer for 333332 is?


(Ideas taken from here)