Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

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?

Count the Trapeziums

Age 7 to 11
Challenge Level

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

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?

Two by One

Age 7 to 11
Challenge Level

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

Torn Shapes

Age 7 to 11
Challenge Level

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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?

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?

Numerically Equal

Age 7 to 11
Challenge Level

Can you draw a square in which the perimeter is numerically equal to the area?

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?

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?

Quadrilaterals

Age 7 to 11
Challenge Level

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

Nine-pin Triangles

Age 7 to 11
Challenge Level

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

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?

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?

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?

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.

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?

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

Cover the Tray

Age 7 to 11
Challenge Level

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

LOGO Challenge - Following On

Age 11 to 18
Challenge Level

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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?

Peg and Pin Boards

Age 5 to 11

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

Tri.'s

Age 7 to 11
Challenge Level

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

Brush Loads

Age 7 to 11
Challenge Level

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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'?

Multilink Cubes

Age 7 to 11
Challenge Level

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

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?

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.

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?

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?

Triangles All Around

Age 7 to 11
Challenge Level

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

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.

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?

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.

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?

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. . . .

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.

Shapes on the Playground

Age 7 to 11
Challenge Level

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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?

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?

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.

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?

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?

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.?

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.

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.

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?

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.

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?