Problem Solving

There are 366 different Starters of The Day, many to choose from. You will find below some starters on the topic of Problem Solving. A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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Problem Solving Starters:

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 expression for 100 which uses all the digits 1 to 9?

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?

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

Broken Calculator

Use only the 1, 5 and 0 keys on a calculator to make given totals.

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.

ClockEquate

Can you use the digits on the left of this clock along with any mathematical operations to equal the digits on the right?

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?

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?

Hole in One

If six girls can plant 90 trees in a day. How many trees can ten girls plant in a day? The unitary method.

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

Work out what the missing digits in the calculations are.

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?

One Torch Tunnel

Work out the least amount of time for four people to walk through a tunnel?

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

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

Record 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 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 word sum?

Advanced Problem Solving Starters

 

Exercises

Area and Perimeter of a Rectangle

Area and Perimeter of a Rectangle

Questions on the areas and perimeters of rectangles which will test your problem solving abilities.

Area Maze

Area Maze

Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams.

Area Wall Puzzles

Area Wall Puzzles

Divide the grid into rectangular pieces so that the area of each piece is the same as the number it contains.

Arithmagons

Arithmagons

An extensive collection of Arithmagons arranged in levels according to their features. Find the missing numbers in these online, self-checking exercises and discover the wonders of Arithmagons.

Aunt Sophie's Post Office

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.

Bidmaze

Bidmaze

Find your way through the maze encountering mathematical operations in the correct order to achieve the given total.

Braille

Braille

Investigate the possibility of redesigning the Braille alphabet to make it easier to learn.

Brainbox

Brainbox

A puzzle requiring the arrangement of numbers on the function machines to link the given input numbers to the correct output.

Broken Calculator

Broken Calculator

Some of the buttons are missing from this calculator. Can you make the totals from 1 to 20?

Car Park Puzzle

Car Park Puzzle

Can you get your car out of the very crowded car park by moving other cars forwards or backwards?

Centexpression

Centexpression

Arrange the numbers from 1 to 9 to make an expression with a value of 100.

Clue Sudoku

Clue Sudoku

A different way to complete a Sudoku puzzle with clues available at every stage.

Code Cracker

Code Cracker

Crack the code by replacing the encrypted letters in the given text. There are lots of hints provided about code breaking techniques.

Consecutive Numbers

Consecutive Numbers

Find the consective numbers that are added or multiplied to give the given totals

Countdown

Countdown

How close can you get to the target by making a calculation out of the five numbers given?

Cracked Clock Quiz

Cracked Clock Quiz

A self marking set of ten mathematical questions about a clock which cracked!

Crossing the River

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.

Digivide

Digivide

Arrange the numbers from 1 to 6 in the spaces to make the division calculation correct.

Divisive

Divisive

Arrange the digits one to nine on the spaces provided to make two division calculations containing multiples of three.

Dominoes Puzzle

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

Double Treble

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.

Fleur-De-Lis

Fleur-De-Lis

Click on six fleur-de-lis to leave an even number in each row and column.

Four Sum

Four Sum

Arrange the given number tiles to make two 2 digit numbers that add up to the given total.

Go Figure

Go Figure

Arrange the digits one to nine to make the four calculations correct.

Green Fingers

Green Fingers

Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible.

How Many of Each?

How Many of Each?

Work out how many items were bought from the information given.

How Many Rectangles?

How Many Rectangles?

Investigate the number of rectangles on a grid of squares. What strategies will be useful in coming up with the answer?

How Many Triangles?

How Many Triangles?

A self marking step by step approach to calculating the number of triangles in a design.

Ice-cream Combinations

Ice-cream Combinations

How many two-scoop ice creams can you make from the given flavours?

Jugs

Jugs

Can you make 4 litres if you only have 7 and 5 litre jugs?

Largest Product

Largest Product

A drag and drop activity challenging you to arrange the digits to produce the largest possible product.

Ludicross

Ludicross

Arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same.

Magic Square

Magic Square

Each row, column and diagonal should produce the same sum.

Mine Find

Mine Find

Find where the mines are hidden without stepping on one.

Mixpressions

Mixpressions

Arrange the cards to create a valid mathematical statement.

Multi-step Problems

Multi-step Problems

Solve multi-step problems in contexts, deciding which operations and methods to use and why.

Multitude

Multitude

Arrange the given digits to make three numbers such that the third is the product of the first and the second.

Nine Digits

Nine Digits

Arrange the given digits to make three numbers such that two of them add up to the third.

Nine Nine Nine

Nine Nine Nine

Use the digits 1 to 9 to make three 3 digit numbers which add up to 999.

Not Too Close

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.

Number Jigsaws

Number Jigsaws

Online, interactive jigsaw puzzles of grids of numbers.

Numskull

Numskull

Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.

One Digit Only

One Digit Only

Find expressions using only one digit which equal the given targets.

One Torch Tunnel

One Torch Tunnel

Solve the problem of getting four people through a tunnel with one torch in the minimum amount of time.

Pancake Day

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.

Pentadd Quiz

Pentadd Quiz

Find the five numbers which when added or multiplied together in pairs to produce the given sums or products.

Pentominoes

Pentominoes

Arrange the twelve pentominoes in the outline of a rectangle.

Pick Up Sticks

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?

Plane Numbers

Plane Numbers

Arrange numbers on the plane shaped grid to produce the given totals

Plus

Plus

A number arranging puzzle with seven levels of challenge.

Polygon Pieces

Polygon Pieces

Arrange the nine pieces of the puzzle on the grid to make different polygons.

Prime Square

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.

Puzzle Cube Net

Puzzle Cube Net

A jumbled moving-block puzzle cube is shown as a net. Can you solve it?

Pyramid Puzzle

Pyramid Puzzle

Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target?

River Crossing

River Crossing

The traditional River Crossing challenge. Can you do it in the smallest number of moves?

Roman Numerals Jigsaw

Roman Numerals Jigsaw

An online interactive jigsaw puzzle of a grid of Roman numerals.

Satisfaction

Satisfaction

This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.

Satisfy

Satisfy

Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers.

Scheduling Puzzle

Scheduling Puzzle

Make a schedule for the 24-hour Darts Marathon which will take into account everyone's requests and keep everyone happy.

Scouts in Boats

Scouts in Boats

Arrange a rota for the Scouts to travel in boats so that they are with different people each day.

Sheep Herding

Sheep Herding

Arrange the sheep in the field according to the instructions. An introduction to loci.

Shunting Puzzles

Shunting Puzzles

Move the trams to their indicated parking places in the shunting yard as quickly as possible.

Six Discrimination

Six Discrimination

The six button has dropped off! How could these calculations be done using this calculator?

Spinsum

Spinsum

Arrange the numbers on the squares so that the totals along each line of three squares are equal.

Square and Even

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.

Squorder

Squorder

The Transum version of the traditional sliding tile puzzle.

Stable Scales

Stable Scales

Ten balance puzzles to prepare you for solving equations.

Stamp Sticking

Stamp Sticking

Drag stamps onto the envelopes to make the exact postage as shown at the top left of each envelope.

Suko Sujiko

Suko Sujiko

Interactive number-based logic puzzles similar to those featuring in daily newspapers.

Superfluous

Superfluous

Find a strategy to figure out the values of the letters used in these calculations.

T Puzzle

T Puzzle

Use the pieces of the T puzzle to fit into the outlines provided. A drag, rotate and drop interactive challenge.

Tangram Table

Tangram Table

Use the pieces of the tangram puzzle to make the basic shapes then complete the table showing which shapes are possible.

Tantrum

Tantrum

A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid.

The Miller's Puzzle

The Miller's Puzzle

This is an interactive version of the puzzle described by Henry Ernest Dudeney in The Canterbury Puzzles

Thrice

Thrice

Can you arrange all of the counters on the grid to form 10 lines of three counters?

Tools

Tools

In how many different ways can the numbers be arranged to give the same totals?

Tower of Hanoi

Tower of Hanoi

Move the pieces of the tower from one place to another in the minimum number of moves.

Trafalgar Square

Trafalgar Square

Solve the number puzzles drawn on the pavement of Trafalgar Square in London.

Tran Towers

Tran Towers

An adventure game requiring students to solve puzzles as they move through the old mansion.

Tran Tunnels

Tran Tunnels

An adventure game requiring you to answer questions and solve puzzles as you move through the tunnels.

Triside Totals

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.

Unitary Method

Unitary Method

Ten questions which can be solved using the unitary method.

Unmagic Square

Unmagic Square

Like the magic square but all of the totals should be different.

Vector Cops

Vector Cops

Help the cops catch the robbers by finding the vectors that will end the chase.

Where's Wallaby?

Where's Wallaby?

Find the hidden wallaby using the clues revealed at the chosen coordinates.

Window View

Window View

Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house.

Word Sums Guide

Word Sums Guide

A step by step guide showing how to solve a Word Sum where each letter stands for a different digit.

Xmas Presents

Xmas Presents

Work out the cost of the Christmas presents from the information given.

 

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