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.


Calculate the total cost of four cars from the information given.


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.


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.


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.


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.


The height of this giraffe is three and a half metres plus half of its height. How tall is the giraffe?


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.


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.


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.


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.


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?


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.


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


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