Search by Topic

Resources tagged with Plane shapes and their properties similar to What Shape?:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 36 results

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

problem icon

Hex

Stage: 3 Challenge Level: Challenge Level:1

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.

problem icon

Circles, Circles Everywhere

Stage: 2 and 3

This article for pupils gives some examples of how circles have featured in people's lives for centuries.

problem icon

Not So Little X

Stage: 3 Challenge Level: Challenge Level:1

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

problem icon

Floored

Stage: 3 Challenge Level: Challenge Level:1

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

problem icon

Square Pegs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

problem icon

Arclets Explained

Stage: 3 and 4

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

problem icon

Pi, a Very Special Number

Stage: 2 and 3

Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible.

problem icon

Pie Cuts

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

problem icon

Like a Circle in a Spiral

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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?

problem icon

LOGO Challenge - Circles as Animals

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

See if you can anticipate successive 'generations' of the two animals shown here.

problem icon

Opposite Vertices

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Sorting Logic Blocks

Stage: 1 and 2 Challenge Level: Challenge Level:1

This interactivity allows you to sort logic blocks by dragging their images.

problem icon

LOGO Challenge 6 - Triangles and Stars

Stage: 3 and 4 Challenge Level: Challenge Level:1

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

problem icon

Circle Panes

Stage: 2 Challenge Level: Challenge Level:1

Look at the mathematics that is all around us - this circular window is a wonderful example.

problem icon

Rolling Around

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem icon

Bow Tie

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

problem icon

Tied Up

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

problem icon

LOGO Challenge 11 - More on Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

problem icon

LOGO Challenge 12 - Concentric Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.

problem icon

Regular Rings 2

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Overlapping Again

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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.

problem icon

Sports Equipment

Stage: 2 Challenge Level: Challenge Level:1

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?

problem icon

Squaring the Circle

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

problem icon

LOGO Challenge 8 - Rhombi

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

problem icon

Shapely Tiling

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

problem icon

LOGO Challenge 2 - Diamonds Are Forever

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

problem icon

Shaping Up

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

problem icon

LOGO Challenge 10 - Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

problem icon

First Forward Into Logo 4: Circles

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

problem icon

Overlapping Circles

Stage: 2 Challenge Level: Challenge Level:1

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

problem icon

Efficient Cutting

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

problem icon

Blue and White

Stage: 3 Challenge Level: Challenge Level:1

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

problem icon

Count the Trapeziums

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

problem icon

Gym Bag

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem icon

Triangular Hexagons

Stage: 2 Challenge Level: Challenge Level:1

Investigate these hexagons drawn from different sized equilateral triangles.

problem icon

Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

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