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#### Resources tagged with 2D shapes and their properties similar to Two by One:

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### There are 53 results

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

### Two by One

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

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

### 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?

### 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?

### Count the Trapeziums

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

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

### Shapely Tiling

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

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?

### Fault-free Rectangles

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

Find out what a "fault-free" rectangle is and try to make some of your own.

### 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?

### Triangular Hexagons

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

Investigate these hexagons drawn from different sized equilateral triangles.

### 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?

### Circle Panes

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

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

### 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?

### Overlapping Circles

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

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?

### Where Are They?

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

Use the isometric grid paper to find the different polygons.

### 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?

### 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.

### 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.

### 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?

### Sorting Logic Blocks

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

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

### Lafayette

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

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

### Bow Tie

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

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.

### 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?

### Playground Snapshot

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

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

### 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?

### 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.

### Arclets Explained

##### Age 11 to 16

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.

### 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?

### 2001 Spatial Oddity

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

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

### 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?

### LOGO Challenge - Circles as Animals

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

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

### LOGO Challenge 11 - More on Circles

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

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. . . .

### 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.

### Gym Bag

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

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

### 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?

### LOGO Challenge 6 - Triangles and Stars

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

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.

### From One Shape to Another

##### Age 7 to 14

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

### LOGO Challenge 12 - Concentric Circles

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

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.

### First Forward Into Logo 4: Circles

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

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

### Squaring the Circle

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

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. . . .

### Square Areas

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

Can you work out the area of the inner square and give an explanation of how you did it?

### Not So Little X

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

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?

### Floored

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

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?

### Lying and Cheating

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

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

### LOGO Challenge 2 - Diamonds Are Forever

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

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.

### LOGO Challenge 10 - Circles

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

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

### LOGO Challenge 8 - Rhombi

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

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

### 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?

### Square Pegs

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

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

### Circles, Circles Everywhere

##### Age 7 to 14

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

### 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.

### Opposite Vertices

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

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