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Resources tagged with Working systematically similar to How Many Pieces?:

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

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Putting Two and Two Together

Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Cuboid-in-a-box

Age 7 to 11 Challenge Level:

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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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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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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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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Paw Prints

Age 7 to 11 Challenge Level:

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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Shunting Puzzle

Age 7 to 11 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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Single Track

Age 7 to 11 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

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Tetrafit

Age 7 to 11 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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Display Boards

Age 7 to 11 Challenge Level:

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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Jigsaw Pieces

Age 7 to 11 Challenge Level:

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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Open Boxes

Age 7 to 11 Challenge Level:

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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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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Nine-pin Triangles

Age 7 to 11 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

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Tangram Tangle

Age 5 to 7 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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Counters

Age 7 to 11 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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Counting Cards

Age 7 to 11 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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Tri.'s

Age 7 to 11 Challenge Level:

How many triangles can you make on the 3 by 3 pegboard?

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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'.

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More Transformations on a Pegboard

Age 7 to 11 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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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?

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Egyptian Rope

Age 7 to 11 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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Coloured Squares

Age 5 to 7 Challenge Level:

Use the clues to colour each square.

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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?

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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.

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Knight's Swap

Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Waiting for Blast Off

Age 7 to 11 Challenge Level:

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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A City of Towers

Age 5 to 7 Challenge Level:

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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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. . . .

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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?

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Map Folding

Age 7 to 11 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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Inside Triangles

Age 5 to 7 Challenge Level:

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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Triangles All Around

Age 7 to 11 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

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Square Corners

Age 7 to 11 Challenge Level:

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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Quadrilaterals

Age 7 to 11 Challenge Level:

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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Triangle Animals

Age 5 to 7 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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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?

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Hexpentas

Age 5 to 11 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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Teddy Bear Line-up

Age 5 to 7 Challenge Level:

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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Let's Investigate Triangles

Age 5 to 7 Challenge Level:

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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Four Triangles Puzzle

Age 5 to 11 Challenge Level:

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

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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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Inky Cube

Age 7 to 14 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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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?

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Matching Time

Age 5 to 7 Challenge Level:

Try this matching game which will help you recognise different ways of saying the same time interval.

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Finding All Possibilities Lower Primary

Age 5 to 7 Challenge Level:

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

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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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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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Making Maths: Double-sided Magic Square

Age 7 to 14 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?