List

Cambridge Primary Maths Mapping Stage 5

Alphabet Blocks
problem

Alphabet blocks

Age
5 to 11
Challenge level
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These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
Odd times Even
problem
Favourite

Odd times even

Age
5 to 7
Challenge level
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This problem looks at how one example of your choice can show something about the general structure of multiplication.
Abundant Numbers
problem
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Abundant numbers

Age
7 to 11
Challenge level
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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Trebling
problem
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Trebling

Age
7 to 11
Challenge level
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Can you replace the letters with numbers? Is there only one solution in each case?

The Deca Tree
problem
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The deca tree

Age
7 to 11
Challenge level
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Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Tables Without Tens
problem

Tables without tens

Age
7 to 11
Challenge level
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Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
Shape Times Shape
problem
Favourite

Shape times shape

Age
7 to 11
Challenge level
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These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Tug Harder!
problem
Favourite

Tug harder!

Age
7 to 11
Challenge level
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In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?
What Do you Need?
problem
Favourite

What do you need?

Age
7 to 11
Challenge level
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Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Nice or Nasty
problem
Favourite

Nice or nasty

Age
7 to 14
Challenge level
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There are nasty versions of this dice game but we'll start with the nice ones...
Which Would You Rather?
problem
Favourite

Which would you rather?

Age
7 to 11
Challenge level
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Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
Multiply Multiples 1
problem
Favourite

Multiply multiples 1

Age
7 to 11
Challenge level
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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Multiply Multiples 2
problem
Favourite

Multiply multiples 2

Age
7 to 11
Challenge level
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Can you work out some different ways to balance this equation?
Round the Dice Decimals 1
problem
Favourite

Round the dice decimals 1

Age
7 to 11
Challenge level
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Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Greater Than or Less Than?
problem
Favourite

Greater than or less than?

Age
7 to 11
Challenge level
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Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Forgot the Numbers
problem
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Forgot the numbers

Age
7 to 11
Challenge level
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On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Pumpkin Pie Problem
problem
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Pumpkin pie problem

Age
7 to 11
Challenge level
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Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Twenty Divided into Six
problem
Favourite

Twenty divided into six

Age
7 to 11
Challenge level
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Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Reach 100
problem
Favourite

Reach 100

Age
7 to 11
Challenge level
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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.

Factor Lines
problem
Favourite

Factor lines

Age
7 to 14
Challenge level
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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Cycling Squares
problem
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Cycling squares

Age
7 to 11
Challenge level
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Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Andy's Marbles
problem
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Andy's marbles

Age
7 to 11
Challenge level
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Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

Diagonal Sums
problem
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Diagonal sums

Age
7 to 14
Challenge level
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In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Four Go
problem
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Four go

Age
7 to 11
Challenge level
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This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Number the Sides
problem

Number the sides

Age
7 to 11
Challenge level
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The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
Doughnut percents
problem
Favourite

Doughnut percents

Age
7 to 14
Challenge level
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A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.
How Much?
problem

How much?

Age
7 to 11
Challenge level
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Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Matching Triangles
problem
Favourite

Matching triangles

Age
5 to 7
Challenge level
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Can you sort these triangles into three different families and explain how you did it?

A Cartesian Puzzle
problem
Favourite

A Cartesian puzzle

Age
7 to 11
Challenge level
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Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Nine-Pin Triangles
problem
Favourite

Nine-pin triangles

Age
7 to 11
Challenge level
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How many different triangles can you make on a circular pegboard that has nine pegs?

How Safe Are You?
problem
Favourite

How safe are you?

Age
7 to 11
Challenge level
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How much do you have to turn these dials by in order to unlock the safes?
National Flags
problem
Favourite

National flags

Age
7 to 11
Challenge level
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This problem explores the shapes and symmetries in some national flags.
Egyptian Rope
problem
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Egyptian rope

Age
7 to 11
Challenge level
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The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Cut Nets
problem
Favourite

Cut nets

Age
7 to 11
Challenge level
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Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Eight hidden squares
problem
Favourite

Eight hidden squares

Age
7 to 14
Challenge level
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On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Symmetry Challenge
problem
Favourite

Symmetry challenge

Age
7 to 11
Challenge level
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How many symmetric designs can you make on this grid? Can you find them all?
ReflectoR ! RotcelfeR
problem
Favourite

ReflectoR ! RotcelfeR

Age
7 to 11
Challenge level
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Can you place the blocks so that you see the reflection in the picture?

Olympic Turns
problem
Favourite

Olympic turns

Age
7 to 11
Challenge level
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This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

Shaping It
problem
Favourite

Shaping it

Age
5 to 11
Challenge level
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These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
Order, Order!
problem
Favourite

Order, order!

Age
5 to 11
Challenge level
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Can you place these quantities in order from smallest to largest?

How Tall?
problem
Favourite

How tall?

Age
5 to 11
Challenge level
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A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Cubes
problem
Favourite

Cubes

Age
7 to 11
Challenge level
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How many faces can you see when you arrange these three cubes in different ways?
Times
problem

Times

Age
7 to 11
Challenge level
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Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!
The Big Cheese
problem

The big cheese

Age
7 to 11
Challenge level
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Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
problem
Favourite

How many times?

Age
7 to 11
Challenge level
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On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

At the pumps
problem

At the pumps

Age
7 to 11
Challenge level
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How will you find out how much a tank of petrol costs?
Weighing fruit
problem

Weighing fruit

Age
7 to 11
Challenge level
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Can you use this information to estimate how much the different fruit selections weigh in kilos and pounds?
Tiles in the Garden
problem

Tiles in the garden

Age
7 to 11
Challenge level
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How many tiles do we need to tile these patios?
Watermelons
problem

Watermelons

Age
7 to 11
Challenge level
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These watermelons have been entered into a competition. Use the information to work out the number of points each one was awarded.
Shape Draw
problem
Favourite

Shape draw

Age
7 to 11
Challenge level
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Use the information on these cards to draw the shape that is being described.

Wrapping Presents
problem

Wrapping presents

Age
7 to 11
Challenge level
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Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
Numerically Equal
problem
Favourite

Numerically equal

Age
7 to 11
Challenge level
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Can you draw a square in which the perimeter is numerically equal to the area?

Slow Coach
problem

Slow coach

Age
7 to 11
Challenge level
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How many of this company's coaches travelling in the opposite direction does the 10 am coach from Alphaton pass before reaching Betaville?
problem
Favourite

Oh! Harry!

Age
7 to 11
Challenge level
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A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

The time is ...
problem
Favourite

The time is ...

Age
7 to 11
Challenge level
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Can you put these mixed-up times in order? You could arrange them in a circle.
Through the Window
problem
Favourite

Through the window

Age
7 to 11
Challenge level
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My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Probable Words
problem

Probable words

Age
5 to 7
Challenge level
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If you asked your mum/dad/friend to take you to the park today, what sort of response might you get?
Cashing Up
problem

Cashing up

Age
5 to 11
Challenge level
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What is the most common coin in this shopkeeper's till?
In the Playground
problem
Favourite

In the playground

Age
5 to 11
Challenge level
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What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Graphing Number Patterns
problem

Graphing number patterns

Age
7 to 11
Challenge level
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Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?
Odds or Sixes?
problem
Favourite

Odds or sixes?

Age
7 to 11
Challenge level
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Play this dice game yourself. How could you make it fair?
Three Spinners
problem

Three spinners

Age
7 to 11
Challenge level
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These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
The car that passes
problem
Favourite

The car that passes

Age
7 to 11
Challenge level
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What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

problem
Favourite

The twelve pointed star game

Age
7 to 11
Challenge level
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Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?