Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Alphabetti Sudoku

Age 11 to 16
Challenge Level

This Sudoku requires you to do some working backwards before working forwards.

Multiply the Addition Square

Age 11 to 14
Challenge Level

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Cayley

Age 11 to 14
Challenge Level

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Ones Only

Age 11 to 14
Challenge Level

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Take Three Numbers

Age 7 to 11
Challenge Level

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Integrated Product Sudoku

Age 11 to 16
Challenge Level

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Football Sum

Age 11 to 14
Challenge Level

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Add to 200

Age 11 to 14
Challenge Level

By selecting digits for an addition grid, what targets can you make?

Gabriel's Problem

Age 11 to 14
Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Read This Page

Age 11 to 14
Challenge Level

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

An Introduction to Magic Squares

Age 7 to 16

Find out about Magic Squares in this article written for students. Why are they magic?!

Two and Two

Age 11 to 16
Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Curious Number

Age 7 to 11
Challenge Level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Peaches Today, Peaches Tomorrow...

Age 11 to 14
Challenge Level

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

All the Digits

Age 7 to 11
Challenge Level

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Adding Plus

Age 7 to 11
Challenge Level

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

A First Product Sudoku

Age 11 to 14
Challenge Level

Given the products of adjacent cells, can you complete this Sudoku?

Multiples Sudoku

Age 11 to 14
Challenge Level

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

How Old Are the Children?

Age 11 to 14
Challenge Level

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Journeys in Numberland

Age 7 to 11
Challenge Level

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Prison Cells

Age 7 to 11
Challenge Level

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

ABC

Age 7 to 11
Challenge Level

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Making Maths: Double-sided Magic Square

Age 7 to 14
Challenge Level

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Number Daisy

Age 11 to 14
Challenge Level

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Cinema Problem

Age 11 to 14
Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

The Moons of Vuvv

Age 7 to 11
Challenge Level

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Zargon Glasses

Age 7 to 11
Challenge Level

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Making a Difference

Age 11 to 14
Challenge Level

How many different differences can you make?

Open Squares

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Dart Target

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Consecutive Negative Numbers

Age 11 to 14
Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Pole Star Sudoku 2

Age 11 to 16
Challenge Level

This Sudoku, based on differences. Using the one clue number can you find the solution?

Tiling

Age 7 to 11
Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

Trebling

Age 7 to 11
Challenge Level

Can you replace the letters with numbers? Is there only one solution in each case?

Two Egg Timers

Age 7 to 11
Challenge Level

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Star Product Sudoku

Age 11 to 16
Challenge Level

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

American Billions

Age 11 to 14
Challenge Level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Magic Vs

Age 7 to 11
Challenge Level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Reach 100

Age 7 to 14
Challenge Level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Multiplication Squares

Age 7 to 11
Challenge Level

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

One to Fifteen

Age 7 to 11
Challenge Level

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Pair Sums

Age 11 to 14
Challenge Level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Neighbourly Addition

Age 7 to 14
Challenge Level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

A Mixed-up Clock

Age 7 to 11
Challenge Level

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Sums and Differences 1

Age 7 to 11
Challenge Level

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Multiply Multiples 3

Age 7 to 11
Challenge Level

Have a go at balancing this equation. Can you find different ways of doing it?

Product Sudoku

Age 11 to 16
Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares.

Greater Than or Less Than?

Age 7 to 11
Challenge Level

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Multiply Multiples 2

Age 7 to 11
Challenge Level

Can you work out some different ways to balance this equation?

Multiply Multiples 1

Age 7 to 11
Challenge Level

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?