Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

Count the Trapeziums

Age 7 to 11
Challenge Level

How many trapeziums, of various sizes, are hidden in this picture?

Folded Number Line

Age 7 to 11
Challenge Level

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

More and More Buckets

Age 7 to 11
Challenge Level

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Counters in the Middle

Age 7 to 11
Challenge Level

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Wag Worms

Age 7 to 11
Challenge Level

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Newspapers

Age 7 to 11
Challenge Level

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Crack the Code

Age 7 to 11
Challenge Level

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

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?

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?

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?

Shaping Up

Age 7 to 11
Challenge Level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Cereal Packets

Age 7 to 11
Challenge Level

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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?

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?

Half Time

Age 5 to 11
Challenge Level

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

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.

Make Pairs

Age 7 to 11
Challenge Level

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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?

Crossing the Town Square

Age 7 to 11
Challenge Level

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Building with Rods

Age 7 to 11
Challenge Level

In how many ways can you stack these rods, following the rules?

Cubes Here and There

Age 7 to 11
Challenge Level

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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.

A Child Is Full of ...

Age 7 to 11 Short
Challenge Level

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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.

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?

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.

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?

Painting Possibilities

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Tiling

Age 7 to 11
Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

Dodecamagic

Age 7 to 11
Challenge Level

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

Open Squares

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Chocs, Mints, Jellies

Age 7 to 11
Challenge Level

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Two Dice

Age 5 to 7
Challenge Level

Find all the numbers that can be made by adding the dots on two dice.

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.

Four Colours

Age 5 to 11
Challenge Level

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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?

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?

Two Dots

Age 7 to 11
Challenge Level

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Creating Cubes

Age 7 to 11
Challenge Level

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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.

Tri-five

Age 7 to 11
Challenge Level

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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?

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?

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?

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 if you have an ordered approach.

How Many Times?

Age 7 to 11
Challenge Level

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.?

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.

Polo Square

Age 7 to 11
Challenge Level

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Home City

Age 7 to 11
Challenge Level

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