Resources tagged with: Working systematically

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

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?

School Fair Necklaces

Age 5 to 11 Challenge Level:

How many possible necklaces can you find? And how do you know you've found them all?

Jumping Cricket

Age 5 to 7 Challenge Level:

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Rearranged Rectangle

Age 7 to 11 Challenge Level:

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

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?

Finding All Possibilities Upper Primary

Age 7 to 11 Challenge Level:

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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?

Half Time

Age 5 to 11 Challenge Level:

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

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.

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.

Build it up More

Age 7 to 11 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

Elf Suits

Age 7 to 11 Challenge Level:

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

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.

Lots of Lollies

Age 5 to 7 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Unit Differences

Age 5 to 7 Challenge Level:

This challenge is about finding the difference between numbers which have the same tens digit.

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.

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?

Home City

Age 7 to 11 Challenge Level:

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Hubble, Bubble

Age 7 to 11 Challenge Level:

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Possible Pieces

Age 5 to 11 Challenge Level:

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Crack the Code

Age 7 to 11 Challenge Level:

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Team Scream

Age 7 to 11 Challenge Level:

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Bunny Hop

Age 7 to 11 Challenge Level:

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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?

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?

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.

Seating Arrangements

Age 7 to 11 Challenge Level:

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

This Pied Piper of Hamelin

Age 7 to 11 Challenge Level:

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

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.

Professional Circles

Age 7 to 11 Challenge Level:

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

The School Trip

Age 5 to 7 Challenge Level:

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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?

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.

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.

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?

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?

Button-up

Age 5 to 7 Challenge Level:

My coat has three buttons. How many ways can you find to do up all the buttons?

Prison Cells

Age 7 to 11 Challenge Level:

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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.

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?

Journeys in Numberland

Age 7 to 11 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Two Egg Timers

Age 7 to 11 Challenge Level:

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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?

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.

Centred Squares

Age 7 to 11 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Ordered Ways of Working Upper Primary

Age 7 to 11 Challenge Level:

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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 ...?

Ladybirds in the Garden

Age 5 to 7 Challenge Level:

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?