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Resources tagged with Area similar to Arranging Counters:

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Broad Topics > Measures and Mensuration > Area

Making Rectangles

Stage: 2 and 3 Challenge Level:

A task which depends on members of the group noticing the needs of others and responding.

How Random!

Stage: 2 Challenge Level:

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Disappearing Square

Stage: 3 Challenge Level:

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

Appearing Square

Stage: 3 Challenge Level:

Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .

Fencing

Stage: 2 Challenge Level:

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Triangle Relations

Stage: 2 Challenge Level:

What do these two triangles have in common? How are they related?

Overlapping Squares

Stage: 2 Challenge Level:

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

Cylinder Cutting

Stage: 2 and 3 Challenge Level:

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

A Square in a Circle

Stage: 2 Challenge Level:

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Poly-puzzle

Stage: 3 Challenge Level:

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Fit These Shapes

Stage: 1 and 2 Challenge Level:

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Growing Rectangles

Stage: 3 Challenge Level:

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Inside Seven Squares

Stage: 2 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Different Sizes

Stage: 1 and 2 Challenge Level:

A simple visual exploration into halving and doubling.

Two Squared

Stage: 2 Challenge Level:

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Wrapping Presents

Stage: 2 Challenge Level:

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

Cover the Tray

Stage: 2 Challenge Level:

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

Isosceles

Stage: 3 Challenge Level:

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

From One Shape to Another

Stage: 2

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.

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

Rope Mat

Stage: 2 Challenge Level:

How many centimetres of rope will I need to make another mat just like the one I have here?

Pick's Theorem

Stage: 3 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Rati-o

Stage: 3 Challenge Level:

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Lying and Cheating

Stage: 3 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!

Inscribed in a Circle

Stage: 3 Challenge Level:

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Extending Great Squares

Stage: 2 and 3 Challenge Level:

Explore one of these five pictures.

Changing Areas, Changing Perimeters

Stage: 3 Challenge Level:

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level:

A follow-up activity to Tiles in the Garden.

Dicey Perimeter, Dicey Area

Stage: 2 Challenge Level:

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Ribbon Squares

Stage: 2 Challenge Level:

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Through the Window

Stage: 2 Challenge Level:

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Area and Perimeter

Stage: 2 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Tiling

Stage: 2 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

Fence It

Stage: 3 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Tilted Squares

Stage: 3 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Exploration Versus Calculation

Stage: 1, 2 and 3

This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.

More Transformations on a Pegboard

Stage: 2 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.

Circle Panes

Stage: 2 Challenge Level:

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

A Day with Grandpa

Stage: 2 Challenge Level:

Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?

Uncanny Triangles

Stage: 2 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Transformations on a Pegboard

Stage: 2 Challenge Level:

How would you move the bands on the pegboard to alter these shapes?

Pie Cuts

Stage: 3 Challenge Level:

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).

The Pillar of Chios

Stage: 3 Challenge Level:

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

Towers

Stage: 3 Challenge Level:

A tower of squares is built inside a right angled isosceles triangle. The largest square stands on the hypotenuse. What fraction of the area of the triangle is covered by the series of squares?

Shear Magic

Stage: 3 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

F'arc'tion

Stage: 3 Challenge Level:

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

Bull's Eye

Stage: 3 Challenge Level:

What fractions of the largest circle are the two shaded regions?

Geoboards

Stage: 2 Challenge Level:

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.