Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Sitting Round the Party Tables

Age 5 to 11
Challenge Level

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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.

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.

Birthday Cake Candles

Age 7 to 11
Challenge Level

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

Page Numbers

Age 7 to 11 Short
Challenge Level

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

Neighbours

Age 7 to 11
Challenge Level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

The Add and Take-away Path

Age 5 to 7
Challenge Level

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Jumping Squares

Age 5 to 7
Challenge Level

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Mrs Beeswax

Age 5 to 7
Challenge Level

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Half Time

Age 5 to 11
Challenge Level

What could the half time scores have been in these Olympic hockey matches?

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 ...?

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?

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.

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?

Arranging the Tables

Age 7 to 11
Challenge Level

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

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.

Consecutive Numbers

Age 7 to 14
Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

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?

Briefcase Lock

Age 5 to 7
Challenge Level

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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.

Routes 1 and 5

Age 5 to 7
Challenge Level

Find your way through the grid starting at 2 and following these operations. What number do you end on?

Money Bags

Age 5 to 11
Challenge Level

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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?

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?

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?

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.

Adding Plus

Age 7 to 11
Challenge Level

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Plate Spotting

Age 7 to 11
Challenge Level

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Family Tree

Age 7 to 11
Challenge Level

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Rearranged Rectangle

Age 7 to 11
Challenge Level

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

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?

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.

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.

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.

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?

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?

Wonky Watches

Age 7 to 11
Challenge Level

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Fake Gold

Age 7 to 11
Challenge Level

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

A-magical Number Maze

Age 7 to 11
Challenge Level

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

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?

5 on the Clock

Age 7 to 11
Challenge Level

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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?

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.