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?

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?

Count the Trapeziums

Age 7 to 11
Challenge Level

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

The Games' Medals

Age 5 to 7
Challenge Level

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

Two by One

Age 7 to 11
Challenge Level

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

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.

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?

Cover the Tray

Age 7 to 11
Challenge Level

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

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?

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?

Chain of Changes

Age 5 to 7
Challenge Level

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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?

Order the Changes

Age 7 to 11
Challenge Level

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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?

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?

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.

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.

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?

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?

Dienes' Logiblocs

Age 5 to 7
Challenge Level

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

What Shape and Colour?

Age 5 to 7
Challenge Level

Can you fill in the empty boxes in the grid with the right shape and colour?

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?

Triangle Edges

Age 5 to 7
Challenge Level

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

Nine-pin Triangles

Age 7 to 11
Challenge Level

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

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?

Tri.'s

Age 7 to 11
Challenge Level

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

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?

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.

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?

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?

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?

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?

Fencing Lambs

Age 7 to 11
Challenge Level

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Making Squares

Age 7 to 11

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Quadrilaterals

Age 7 to 11
Challenge Level

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

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?

Stairs

Age 5 to 11
Challenge Level

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18
Challenge Level

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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.

Briefcase Lock

Age 5 to 7
Challenge Level

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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?

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?

Triangles All Around

Age 7 to 11
Challenge Level

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

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

Fifteen Cards

Age 7 to 11
Challenge Level

Can you use the information to find out which cards I have used?

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?

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.

Half Time

Age 5 to 11
Challenge Level

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