Resources tagged with: Working systematically

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

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Getting the Balance

Age 5 to 7 Challenge Level:

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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Coloured Squares

Age 5 to 7 Challenge Level:

Use the clues to colour each square.

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Difference

Age 7 to 11 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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Find the Difference

Age 5 to 7 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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Junior Frogs

Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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Finding All Possibilities Lower Primary

Age 5 to 7 Challenge Level:

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

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Dart Target

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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2,4,6,8

Age 5 to 7 Challenge Level:

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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Arrangements

Age 7 to 11 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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Cuisenaire Counting

Age 5 to 7 Challenge Level:

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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Same Length Trains

Age 5 to 7 Challenge Level:

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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Three Ball Line Up

Age 5 to 7 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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Red Even

Age 7 to 11 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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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?

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Are You Well Balanced?

Age 5 to 7 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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How Long Does it Take?

Age 7 to 11 Challenge Level:

In this matching game, you have to decide how long different events take.

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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?

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Triangle Edges

Age 5 to 7 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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Name the Children

Age 5 to 7 Challenge Level:

Can you find out in which order the children are standing in this line?

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A Right Charlie

Age 7 to 11 Challenge Level:

Can you use this information to work out Charlie's house number?

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Tessellate the Triominoes

Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

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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.

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One to Fifteen

Age 7 to 11 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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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?

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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?

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Ordered Ways of Working Lower Primary

Age 5 to 7 Challenge Level:

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

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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?

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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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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?

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Whose Sandwich?

Age 5 to 7 Challenge Level:

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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Growing Garlic

Age 5 to 7 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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Teddy Town

Age 5 to 14 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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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?

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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?

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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?

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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!

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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.

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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.

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Winning the Lottery

Age 7 to 11 Challenge Level:

Try out the lottery that is played in a far-away land. What is the chance of winning?

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Ordered Ways of Working Lower Primary

Age 5 to 7 Challenge Level:

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

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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.

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Different Deductions

Age 7 to 11 Challenge Level:

There are lots of different methods to find out what the shapes are worth - how many can you find?

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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 ...?

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Leap Frog

Age 5 to 7 Challenge Level:

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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Ladybird Box

Age 5 to 11 Challenge Level:

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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Tea Cups

Age 7 to 14 Challenge Level:

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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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.

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Shape Times Shape

Age 7 to 11 Challenge Level:

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

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Late Again

Age 5 to 7 Challenge Level:

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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On Target

Age 7 to 11 Challenge Level:

You have 5 darts and your target score is 44. How many different ways could you score 44?