Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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.

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.

Diagonal Product Sudoku

Age 11 to 16
Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku?

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?

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?

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?"

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.

Neighbourly Addition

Age 7 to 14
Challenge Level

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

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?

An Introduction to Magic Squares

Age 7 to 16

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

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

Ben's Game

Age 11 to 16
Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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...

Alphabetti Sudoku

Age 11 to 16
Challenge Level

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

Sticky Dice

Age 7 to 11
Challenge Level

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Shopping Basket

Age 11 to 16
Challenge Level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Multiples Sudoku

Age 11 to 14
Challenge Level

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

Product Sudoku

Age 11 to 16
Challenge Level

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

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?

Tiling

Age 7 to 11
Challenge Level

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

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?

Charitable Pennies

Age 7 to 14
Challenge Level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Neighbours

Age 7 to 11
Challenge Level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

A First Product Sudoku

Age 7 to 14
Challenge Level

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

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?

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?

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.

Calendar Cubes

Age 7 to 11
Challenge Level

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Summing Consecutive Numbers

Age 11 to 14
Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Six Is the Sum

Age 7 to 11
Challenge Level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Snails' Trails

Age 7 to 11
Challenge Level

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Round the Dice Decimals 2

Age 7 to 11
Challenge Level

What happens when you round these numbers to the nearest whole number?

Sticks and Triangles

Age 7 to 11
Challenge Level

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Multiply Multiples 2

Age 7 to 11
Challenge Level

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

Seven Pots of Plants

Age 7 to 11
Challenge Level

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Weights

Age 11 to 14
Challenge Level

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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?

Factor Lines

Age 7 to 14
Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Palindromic Date

Age 7 to 11
Challenge Level

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Coins (2)

Age 7 to 11
Challenge Level

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Ancient Runes

Age 7 to 11
Challenge Level

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Symmetry Challenge

Age 7 to 11
Challenge Level

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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?

The Pet Graph

Age 7 to 11
Challenge Level

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

Buying a Balloon

Age 7 to 11
Challenge Level

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Seven Flipped

Age 7 to 11
Challenge Level

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Pasta Timing

Age 7 to 11
Challenge Level

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

The Dice Train

Age 7 to 11
Challenge Level

This dice train has been made using specific rules. How many different trains can you make?

Sums and Differences 2

Age 7 to 11
Challenge Level

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?