Area and Perimeter of a Rectangle
Questions on the areas and perimeters of rectangles which will test your problem solving abilities.
Number Jigsaws
Online, interactive jigsaw puzzles of grids of numbers.
Ice-cream Combinations
How many two-scoop ice creams can you make from the given flavours?
Prime Numbers Jigsaw
Interactive jigsaw puzzles of different types of grids containing prime numbers.
Four Sum
Arrange the given number tiles to make two 2 digit numbers that add up to the given total.
Brainbox
A puzzle requiring the arrangement of numbers on the function machines to link the given input numbers to the correct output.
Beam Balance
Achieve a perfect balance while hanging the treasure sacks off the balance beam pegs.
Broken Calculator
Some of the buttons are missing from this calculator. Can you make the totals from 1 to 20?
Tangram Table
Use the pieces of the tangram puzzle to make the basic shapes then complete the table showing which shapes are possible.
Consecutive Numbers
Find the consective numbers that are added or multiplied to give the given totals
Multitude
Arrange the given digits to make three numbers such that the third is the product of the first and the second.
Nine Digits
Arrange the given digits to make three numbers such that two of them add up to the third.
Roman Numerals Jigsaw
An online interactive jigsaw puzzle of a grid of Roman numerals.
Camp Bosrow
Place the camping items into the plots on the camp site according to the clues given.
Green Fingers
Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible.
Festive Fivesome
Use the number clues to answer the seasonal questions about the five festive figures.
Equatero
Find the expression from a series of guesses and clues.
Arithmagons
Find the missing numbers in these triangular, self-checking puzzles and discover the wonders of these fascinating structures.
Stable Scales
Ten balance puzzles to prepare you for solving equations.
How Many of Each?
Work out how many items were bought from the information given.
Cracked Clock Quiz
A self marking set of ten mathematical questions about a clock which cracked!
Awe-Sum
Arrange the given digits to make six 3-digit numbers that combine in an awesome way.
Largest Product
A drag and drop activity challenging you to arrange the digits to produce the largest possible product.
Area Maze
Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams.
Ludicross
Arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same.
Magic Square
Each row, column and diagonal should produce the same sum.
Triside Totals
Arrange the digits 1 to 9 on the triangle so that the sum of the numbers along each side is equal to the given total.
Not Too Close
The students numbered 1 to 8 should sit on the chairs so that no two consecutively numbered students sit next to each other.
T Puzzle
Use the pieces of the T puzzle to fit into the outlines provided. A drag, rotate and drop interactive challenge.
Squorder
The Transum version of the traditional sliding tile puzzle.
Area Wall Puzzles
Divide the grid into rectangular pieces so that the area of each piece is the same as the number it contains.
Mixpressions
Arrange the cards to create a valid mathematical statement.
Multi-step Problems
Solve multi-step problems in contexts, deciding which operations and methods to use and why.
Factor Trees Challenge
Can you determine the unique digits that will complete these factor trees?
Squareas
Square areas - some are shown and others can be deduced to find the unknown
How Many Triangles?
A self marking step by step approach to calculating the number of triangles in a design.
Nine Nine Nine
Use the digits 1 to 9 to make three 3 digit numbers which add up to 999.
Thrice
A challenge to place all nine counters on the grid in such a way that they form exactly 10 straight lines, with each line containing three counters.
Centexpression
Arrange the numbers from 1 to 9 to make an expression with a value of 100.
Trial And Improvement
Learn efficient ways of using trial and improvement to solve real-life and algebraic problems.
Superfluous
Find a strategy to figure out the values of the letters used in these calculations.
Numskull
Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.
Vector Cops
Help the cops catch the robbers by finding the vectors that will end the chase.
Jugs
Can you make four litres if you only have seven and five litre jugs?
Car Park Puzzle
Can you get your car out of the very crowded car park by moving other cars forwards or backwards?
One Digit Only
Find expressions using only one digit which equal the given targets.
Shunting Puzzles
Move the trams to their indicated parking places in the shunting yard as quickly as possible.
Partial Pyramids
Calculate the missing numbers in these partly completed pyramid puzzles.
Mine Find
Find where the mines are hidden without stepping on one.
Pentadd Quiz
Find the five numbers which when added or multiplied together in pairs to produce the given totals.
Clue Sudoku
A different way to complete a Sudoku puzzle with clues available at every stage.
Pick Up Sticks
If you were to pick up the sticks from this pile so that you were always removing the top stick what calculation would you create?
Logic Puzzle
Solve this deduction logic puzzle to find who, where and what.
Plane Numbers
Arrange numbers on the plane shaped grid to produce the given totals
River Crossing
The traditional River Crossing challenge. Can you do it in the smallest number of moves?
Goal Products
Arrange the numbered footballs on the goal posts to make three, 3-number products that are all the same.
Plus
A number arranging puzzle with seven levels of challenge.
Where's Wallaby?
Find the hidden wallaby using the clues revealed at the chosen coordinates.
Pyramid Puzzle
Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target?
Pancake Day
Toss the pancakes until they are neatly stacked in order of size. Find how to do this using the smallest number of moves.
Pentominoes
Arrange the twelve pentominoes in the outline of a rectangle.
Polygon Pieces
Arrange the nine pieces of the puzzle on the grid to make different polygons.
Unitary Method
Ten questions which can be solved using the unitary method.
Six Discrimination
The six button has dropped off! How could these calculations be done using this calculator?
Egg Timers
The classic hourglass puzzle; Time the boiling of an egg using only the two egg timers provided.
Spinsum
Arrange the numbers on the squares so that the totals along each line of three squares are equal.
Thai Numbers Jigsaw
An online interactive jigsaw puzzle of a grid of Thai number symbols.
Go Figure
Arrange the digits one to nine to make the four calculations correct.
Suko Sujiko
Interactive number-based logic puzzles similar to those featuring in daily newspapers.
Bidmaze
Find your way through the maze encountering mathematical operations in the correct order to achieve the given total.
Divisive
Arrange the digits one to nine on the spaces provided to make two division calculations containing multiples of three.
Tantrum
A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid.
Sheep Herding
Arrange the sheep in the field according to the instructions. An introduction to loci.
Chinese Numbers Jigsaw
An online interactive jigsaw puzzle of a grid of Chinese number symbols.
Partition Clues
Partition numbers in different ways according to the clues given. The higher levels are quite hard!
Product Square
Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products.
The Miller's Puzzle
This is an interactive version of the puzzle described by Henry Ernest Dudeney in The Canterbury Puzzles
Circumfraction
Quite a challenging number placing puzzle involving fractions.
Tools
In how many different ways can the numbers be arranged to give the same totals?
Satisfy
Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.
Perfect Magic Square
Arrange the sixteen numbers on the four by four grid so that groups of four numbers in a pattern add up to the same total.
Puzzle Cube Net
A jumbled moving-block puzzle cube is shown as a net. Can you solve it?
Unmagic Square
Like the magic square but all of the totals should be different.
Tran Towers
An adventure game requiring students to solve puzzles as they move through the old mansion.
Which Operation?
Decide which mathematical operation is required then use it to find the answers.
Square and Even
Arrange the numbers on the cards so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even.
Triangled Hexagram
Arrange the twelve numbers in the triangles on the hexagram so that the numbers in each line of five triangles add up to the same total.
Code Cracker
Crack the code by replacing the encrypted letters in the given text. There are lots of hints provided about code breaking techniques.
Pandigital Squares
Arrange the digits 1 to 9 to form one or more square numbers.
Tower of Hanoi
Move the pieces of the tower from one place to another in the minimum number of moves.
Hexagram Star
Arrange the twelve numbers on the hexagram so that the numbers in each line add up to the same total.
Fleur-De-Lis
Click on six fleur-de-lis to leave an even number in each row and column.
Prime Square
Drag the numbers into the red cells so that the sum of the three numbers in each row and each column is a prime number.
Digivide
Arrange the numbers from 1 to 6 in the spaces to make the division calculation correct.
Satisfaction
This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.
Double Treble
Arrange the digits to make three 3 digit numbers such that the second is double the first and the third is three times the first.
Doughnut Dissection
A puzzle to find four different ways of making 900 by multiplying together three different numbers.
One Torch Tunnel
Solve the problem of getting four people through a tunnel with one torch in the minimum amount of time.
Octagram Star
Arrange the sixteen numbers on the octagram so that the numbers in each line add up to the same total.
Unbeknownst
Some picture grid puzzles which can be solved by using simultaneous equations.
Framed Numbers
Figure out which numbers will complete the sentences in the frame correctly. A drag and drop activity.
Scheduling Puzzle
Make a schedule for the 24-hour Darts Marathon which will take into account everyone's requests and keep everyone happy.
Tran Tunnels
A mini adventure game containing maths puzzles and problems. Find your way through the maze of tunnels to find Goldberg's magic harpsicord.
Power Shift
Arrange the given numbers as bases and indices in the three-term sum to make the target total.
Trafalgar Square
Solve the number puzzles drawn on the pavement of Trafalgar Square in London.
Window View
Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house.
Problems Leading To Quadratics
Situations from 1885 which can be described using algebra and explained by solving quadratic equations
Scouts in Boats
Arrange a rota for the Scouts to travel in boats so that they are with different people each day.
Dominoes Puzzle
Arrange the dominoes in seven squares. The number of dots along each side of the square must be equal to the number in the middle.
Some Sums and Products
Number puzzles involving adding, multiplying and problem solving
Green Fingers
Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible.
Crossing the River
Two men and two boys want to cross a river and they only have one canoe which will only hold one man or two boys.
Aunt Sophie's Post Office
Investigate the ways of making up various postage amounts using 3p and 8p stamps. An online stamp calculator is provided for you to check your working.
Jugs
Can you make four litres if you only have seven and five litre jugs?
How Many Rectangles?
Investigate the number of rectangles on a grid of squares. What strategies will be useful in coming up with the answer?
Egg Timers
The classic hourglass puzzle; Time the boiling of an egg using only the two egg timers provided.
Tantrum
A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid.
Tower of Hanoi
Move the pieces of the tower from one place to another in the minimum number of moves.
Braille
Investigate the possibility of redesigning the Braille alphabet to make it easier to learn.
Window View
Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house.
Search for Infinity
Manipulate the Lissajou curve to produce a perfectly symmetrical (vertically and horizontally) infinity symbol.
Puzzles In The Simpsons
The Simpson's 26th season finale. 'Mathlete's Feat' is full of mathematical problems that Presh solves.
The Train Fly Problem
This video from Mind Your Decisions teaches a trick so you can solve the puzzle quickly.
Problems with Zero
Dividing by zero, zero divided by zero and zero to the power of zero - all pose problems!
Ice-cream Combinations
How many two-scoop ice creams can you make from the given flavours?
Countdown
How close can you get to the target by making a calculation out of the five numbers given?
Word Sums Guide
A step by step guide showing how to solve a Word Sum where each letter stands for a different digit.
Satisfaction
This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.
Add 'em
Add up a sequence of consecutive numbers. Can you find a quick way to do it?
All for 100
Can you write an ex
Area Two
How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines?
Balloon Bursting Buttons
Use only the 1, 5 and 0 keys on a calculator to make given totals.
Bizarre Triangle
By how much would the area of this triangle increase if its base was enlarged to 8cm?
Boxing Day
Work out the contents and the cost of the Christmas boxes from the given clues.
Calculator Nim
A game in which players take turns to add a single-digit number to what is already in the calculator. The winner is the player who makes the display show 30.
Cars
Calculate the total cost of four cars from the information given.
Chin-Ups
Work out the number of chin ups the characters do on the last day of the week give information about averages.
Christmas Presents
Work out the total cost of five Christmas presents from the information given.
Coins On The Table
A puzzle about the number of coins on a table given information about fractions of them.
Consecutive
Three consecutive numbers multiplied together give a given product. Pupils are asked to figure out what the numbers are.
Consecy Brothers
Which three consecutive numbers multiplied together give the given answer.
Cracked Clock
How did the clock break if the numbers on each of the pieces added up to the same total?
Cube Calendar
What numbers should be on each face of the two cubes to make this perpetual calendar?
Dice Nets
Determine whether the given nets would fold to produce a dice.
Digivide
Arrange the digits 1 to 6 to make a three digit number divided by a two digit number giving a one digit answer.
Family Buses
Fit families onto eleven seater buses without splitting up the families.
Faulty Button
Find out which of the calculator keys is faulty from the given information. A mathematical puzzle requiring good problem solving strategies.
For Thought
Add up the answers to the four real life questions.
Four Gone
An activity involving a broken calculator which is missing the four button. Can you evaluate the given expressions without using the four?
Four to Seven
Which of the numbers from one to twenty can you make with the digits 4, 5, 6 and 7?
Four's Independence
A clock face containing only the number 4. Can you make a clock face containing any other single number?
Framed Numbers
Figure out which numbers will complete the sentences in the frame correctly.
Freemason's Cipher
Find symmetric words in this ancient cipher.
Giraffe
The height of this giraffe is three and a half metres plus half of its height. How tall is the giraffe?
Handshakes
If all the students in this room shook hands with each other, how many handshakes would there be altogether?
How Do You Do?
A little lateral thinking will help you solve this number puzzle.
How Many Triangles? 1
How many Triangles can you find in the diagram?
How Many Triangles? 2
How many triangles are hidden in the pattern? What strategy might you use to count them all to ensure you don't miss any out?
How Many Triangles? 3
Find a systematic way of counting the number of triangles in the given diagram.
Justundera Quid
Find a word whose letters would cost exactly ninety nine pence.
Know Weigh
Find the weight of one cuboid (by division) of each colour then add your answers together.
Letter Clue Calculations
Work out what the calculations might be from the letter clues.
Light Shopping
A lamp and a bulb together cost 32 pounds. The lamp costs 30 pounds more than the bulb. How much does the bulb cost?
Match Fish
A classic matchstick puzzle designed to challenge your spacial awareness.
Missing digits
Find which digits are missing from the randomly generated calculations.
Missing Pound
A puzzle about a restaurant bill. Exactly where did the missing pound go?
Nine Digit Sum
Arrange the digits one to nine to make a correct addition calculation.
Nine Nine Nine
Arrange the numbers 1-9 to make three 3 digit numbers that add up to 999.
Not Too Close
This activity requires eight students to sit non consecutively on a grid of chairs.
One Digit 100
How many ways can you write an expression for 100 which only uses the same digit repeated and any operations?
Palindromic Times
Can you use the digits on the left of this clock along with any mathematical operations to equal the digits on the right?
Peanuts and Buttons
Two questions involving estimating a quantity.
Pentadd
Five numbers are added together in pairs and the sums shown. What might the five numbers be?
Plane Numbers
Arrange numbers on the plane shaped grid to produce the given totals
Plant More Trees
If six girls can plant 90 trees in a day. How many trees can ten girls plant in a day? The unitary method.
Product Placement
Arrange the numbers to produce the largest product.
Pyramid Puzzle
Arrange numbers at the bottom of the pyramid which will give the largest total at the top.
Rabbits and Chickens
There are some rabbits and chickens in a field. Calculate how many of each given the number of heads and feet.
Rail Weigh
Use the weights of the trains to work out the weight of a locomotive and a coach. A real situation which produces simultaneous equations.
Render Digitful
Find a calculation for the current year which uses all of the digits 1 to 9.
Roundabout
Go around the roundabout performing each of the operations. Which starting point gives the largest answer?
Rows of Roses
Can you draw 4 straight lines, without taking your pencil off the paper, which pass through all 9 roses?
Santa's Sleigh
Work out the number of clowns and horses given the number of heads and feet.
Sea Shells
A question which can be best answered by using algebra.
Shadow Sums
Make sums from the three digit numbers given.
Shunting Problem
Allow two trains to pass by using the limited amount of siding space.
Siam Symbols
Can you work out what each of the strange symbols represents in these calculations?
Simple Nim
The classic game of Nim played with a group of pens and pencils. The game can be extended to the multi-pile version.
Simultaneous Occasions
A problem which can best be solved as a pair of simultaneous equations.
Six Discrimination
An activity involving a calculator which is missing the six button. Can you evaluate the given expressions without using the six?
Small Satisfaction
Arrange the digits one to nine in the grid so that they obey the row and column headings.
Snowman and Woman
How many different ways can you spell out the word snowman by moving from snowflake to snowflake.
Spinsum
Arrange the numbers on the grid of squares so that the totals along each line of three squares are equal.
Square and Even
Arrange the numbers on the cards so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even.
Square Pairs
Arrange the numbered trees so that adjacent sums are square numbers.
Squared Animals
Separate three rows of three animals using three squares.
Stair Perimeter
Use the information implied in the diagram to calculate the perimeter of this shape.
Stencils
Which of the coloured stencils will fit over the numbered card to produce correct calculations?
Step Perimeter
Is it possible to work out the perimeter of this shape if not all the side lengths are given?
Suko
Interactive number-based logic puzzle similar to those featuring in The Times and Telegraph newspapers.
Sum Equals Product
What are the numbers if their sum equals their product?
Sum of the Signs
Each traffic sign stands for a number. Some of the sums of rows and columns are shown. What numbers might the signs stand for?
Sum Square
Arrange the numbers one to eight into the calculations to make the totals correct..
Team Age
Work out who is in which team from the information given.
Tindice
How can you put the dice into the tins so that there is an odd number of dice in each tin?
Tran's Hats
In how many different ways might Tran decide to wear his hats in one week?
Two Twins and Tim
A tricky problem set on a coordinate grid.
Unmagic Square
Arrange the numbers 1 to 9 in a 3 by 3 grid so that none of the line totals are the same.
Word Sum
Each letter stands for a different digit. Can you make sense of this word sum?
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Teachers might find the complete Problem Solving Topic List useful.
What good is being a master of calculation if you cannot apply your skills to problem solving? This topic provides lots of examples, activities and situations in which pupils can practise their problem solving skills.
