# Resources tagged with: 2D shapes and their properties

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There are 116 NRICH Mathematical resources connected to 2D shapes and their properties, you may find related items under Angles, Polygons, and Geometrical Proof.

Broad Topics > Angles, Polygons, and Geometrical Proof > 2D shapes and their properties

### Always, Sometimes or Never? KS1

##### Age 5 to 7 Challenge Level:

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

### What's Happening?

##### Age 5 to 7 Challenge Level:

Shapes are added to other shapes. Can you see what is happening? What is the rule?

### Olympic Rings

##### Age 5 to 7 Challenge Level:

This problem is intended to get children to look really hard at something they will see many times in the next few months.

### Poly Plug Rectangles

##### Age 5 to 14 Challenge Level:

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

### Track Design

##### Age 14 to 16 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

### Shaping It

##### Age 5 to 11 Challenge Level:

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

### Sorting Logic Blocks

##### Age 5 to 11 Challenge Level:

This activity focuses on similarities and differences between shapes.

### Shapely Lines

##### Age 5 to 7 Challenge Level:

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

### What Shape?

##### Age 7 to 14 Challenge Level:

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

### Jig Shapes

##### Age 5 to 11 Challenge Level:

Can you each work out what shape you have part of on your card? What will the rest of it look like?

### Curvy Areas

##### Age 14 to 16 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

### Overlapping Again

##### Age 7 to 11 Challenge Level:

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

### 2 Rings

##### Age 5 to 7 Challenge Level:

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

### 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?

### Trapezium Four

##### Age 14 to 16 Challenge Level:

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

### Spokes

##### Age 16 to 18 Challenge Level:

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

### Board Block Challenge

##### Age 7 to 11 Challenge Level:

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

### Efficient Cutting

##### Age 11 to 14 Challenge Level:

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

### Salinon

##### Age 14 to 16 Challenge Level:

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

### Rolling Around

##### Age 11 to 14 Challenge Level:

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

### Semi-detached

##### Age 14 to 16 Challenge Level:

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

### Where Are They?

##### Age 7 to 11 Challenge Level:

Use the isometric grid paper to find the different polygons.

### Approximating Pi

##### Age 14 to 18 Challenge Level:

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

### Blue and White

##### Age 11 to 14 Challenge Level:

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

### Hex

##### Age 11 to 14 Challenge Level:

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

##### Age 14 to 16 Challenge Level:

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .

### Orthogonal Circle

##### Age 16 to 18 Challenge Level:

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

### Logosquares

##### Age 16 to 18 Challenge Level:

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

### Baby Circle

##### Age 16 to 18 Challenge Level:

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

### 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?

### Possible Pairs

##### Age 7 to 11 Challenge Level:

In this game, you turn over two cards and try to draw a triangle which has both properties.

### Name That Triangle!

##### Age 7 to 11 Challenge Level:

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

### Triangle or No Triangle?

##### Age 5 to 7 Challenge Level:

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

### Regular Rings 2

##### Age 7 to 11 Challenge Level:

What shape is made when you fold using this crease pattern? Can you make a ring design?

### Towering Trapeziums

##### Age 14 to 16 Challenge Level:

Can you find the areas of the trapezia in this sequence?

### What Shape for Two

##### Age 7 to 14 Challenge Level:

'What Shape?' activity for adult and child. Can you ask good questions so you can work out which shape your partner has chosen?

### Gym Bag

##### Age 11 to 16 Challenge Level:

Can Jo make a gym bag for her trainers from the piece of fabric she has?

### Witch's Hat

##### Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

### Curve Spotting

##### Age 5 to 7 Challenge Level:

Can you spot circles, spirals and other types of curves in these photos?

### Opening Patterns

##### Age 5 to 7 Challenge Level:

Look at some of the patterns in the Olympic Opening ceremonies and see what shapes you can spot.

### A Rational Search

##### Age 16 to 18 Challenge Level:

Investigate constructible images which contain rational areas.

### Sports Equipment

##### Age 7 to 11 Challenge Level:

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

### Opposite Vertices

##### Age 11 to 14 Challenge Level:

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

##### Age 14 to 16 Challenge Level:

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

### Efficient Packing

##### Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

### Logic Block Collections

##### Age 5 to 7 Challenge Level:

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

### 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?

### What's Inside/outside/under the Box?

##### Age 7 to 14

This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.

### Like a Circle in a Spiral

##### Age 7 to 16 Challenge Level:

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

### Spirostars

##### Age 16 to 18 Challenge Level:

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?