Resources tagged with: Working systematically

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

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Roll These Dice

Age 7 to 11 Challenge Level:

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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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?

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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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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.

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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?

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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.

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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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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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Crack the Code

Age 7 to 11 Challenge Level:

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

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Count the Trapeziums

Age 7 to 11 Challenge Level:

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

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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?

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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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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.

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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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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.

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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?

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Two by One

Age 7 to 11 Challenge Level:

An activity making various patterns with 2 x 1 rectangular tiles.

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Uncanny Triangles

Age 7 to 11 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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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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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?

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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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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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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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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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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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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?

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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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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.

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Is a Square a Rectangle?

Age 7 to 11 Challenge Level:

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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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?

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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.

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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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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?

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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?

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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.

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Cover the Tray

Age 7 to 11 Challenge Level:

These practical challenges are all about making a 'tray' and covering it with paper.

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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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The Third Dimension

Age 5 to 11 Challenge Level:

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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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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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?

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Ribbon Squares

Age 7 to 11 Challenge Level:

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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Multilink Cubes

Age 7 to 11 Challenge Level:

If you had 36 cubes, what different cuboids could you make?

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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.

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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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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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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.

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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.

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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.

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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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Coordinate Challenge

Age 7 to 11 Challenge Level:

Use the clues about the symmetrical properties of these letters to place them on the grid.