Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Rearranged Rectangle

Age 7 to 11
Challenge Level

How many different rectangles can you make using this set of rods?

Plates of Biscuits

Age 7 to 11
Challenge Level

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

Build it Up

Age 7 to 11
Challenge Level

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Broken Toaster

Age 7 to 11 Short
Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Button-up Some More

Age 7 to 11
Challenge Level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Bean Bags for Bernard's Bag

Age 7 to 11
Challenge Level

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Counting on Letters

Age 11 to 14
Challenge Level

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Sweets in a Box

Age 7 to 11
Challenge Level

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Making Cuboids

Age 7 to 11
Challenge Level

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Mystery Matrix

Age 7 to 11
Challenge Level

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

A Bit of a Dicey Problem

Age 7 to 11
Challenge Level

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Whose Face?

Age 5 to 11
Challenge Level

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?

Calcunos

Age 7 to 11
Challenge Level

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Ice Cream

Age 7 to 11
Challenge Level

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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.

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?

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.

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?

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?

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.

Multiples Grid

Age 7 to 11
Challenge Level

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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?

Room Doubling

Age 7 to 11
Challenge Level

Investigate the different ways you could split up these rooms so that you have double the number.

It Figures

Age 7 to 11
Challenge Level

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Sealed Solution

Age 7 to 11
Challenge Level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

The Moons of Vuvv

Age 7 to 11
Challenge Level

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

A Square of Numbers

Age 7 to 11
Challenge Level

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Route Product

Age 7 to 11
Challenge Level

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Reach 100

Age 7 to 11
Challenge Level

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.

Multiplication Squares

Age 7 to 11
Challenge Level

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Seven Square Numbers

Age 7 to 11
Challenge Level

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Ribbon Squares

Age 7 to 11
Challenge Level

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Code Breaker

Age 7 to 11
Challenge Level

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Stairs

Age 5 to 11
Challenge Level

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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?

Extra Challenges from Madras

Age 11 to 14
Challenge Level

A few extra challenges set by some young NRICH members.

Octa Space

Age 7 to 11
Challenge Level

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Pouring the Punch Drink

Age 7 to 11
Challenge Level

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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?

Sums and Differences 1

Age 7 to 11
Challenge Level

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Multiply Multiples 3

Age 7 to 11
Challenge Level

Have a go at balancing this equation. Can you find different ways of doing it?

Eight Queens

Age 7 to 11
Challenge Level

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

1 to 8

Age 7 to 11
Challenge Level

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Two on Five

Age 5 to 11
Challenge Level

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

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?

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.

Finding All Possibilities Upper Primary

Age 7 to 11
Challenge Level

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.