Other tags that relate to Geoboards
Area - squares and rectangles. Generalising. Pinboard/geoboard. Interactivities. Addition & subtraction. Investigations. Combinations. Squares. Working systematically. Visualising.There are 60 results
Broad Topics > Measuring and calculating with units > Area - squares and rectangles
Geoboards
Age 7 to 11 Challenge Level:
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
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?
Dicey Perimeter, Dicey Area
Age 7 to 11 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?
Cover the Tray
Age 7 to 11 Challenge Level:
These practical challenges are all about making a 'tray' and covering it with paper.
My New Patio
Age 7 to 11 Challenge Level:
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
Ribbon Squares
Age 7 to 11 Challenge Level:
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Tiles on a Patio
Age 7 to 11 Challenge Level:
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Rope Mat
Age 7 to 11 Challenge Level:
How many centimetres of rope will I need to make another mat just like the one I have here?
Area and Perimeter
Age 7 to 11 Challenge Level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Fit These Shapes
Age 5 to 11 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?
Tiling
Age 7 to 11 Challenge Level:
An investigation that gives you the opportunity to make and justify predictions.
A Square in a Circle
Age 7 to 11 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?
Fitted
Age 7 to 11 Challenge Level:
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Inside Seven Squares
Age 7 to 11 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?
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.
Lawn Border
Age 5 to 11 Challenge Level:
If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
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?
Two Squared
Age 7 to 11 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?
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.
Triangle Relations
Age 7 to 11 Challenge Level:
What do these two triangles have in common? How are they related?
Wrapping Presents
Age 7 to 11 Challenge Level:
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
Paper Halving
Age 5 to 11 Challenge Level:
In how many ways can you halve a piece of A4 paper? How do you know they are halves?
Framed
Age 11 to 14 Challenge Level:
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
How Random!
Age 7 to 11 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?
Exploration Versus Calculation
Age 5 to 11
This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.
Tiling Into Slanted Rectangles
Age 7 to 11 Challenge Level:
A follow-up activity to Tiles in the Garden.
Pebbles
Age 7 to 11 Challenge Level:
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Through the Window
Age 7 to 11 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?
Overlapping Squares
Age 7 to 11 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.
Approaches to Area
Age 5 to 11
This article for teachers gives some food for thought when teaching ideas about area.
Fencing
Age 7 to 11 Challenge Level:
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Great Squares
Age 7 to 11 Challenge Level:
Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
Numerically Equal
Age 7 to 11 Challenge Level:
Can you draw a square in which the perimeter is numerically equal to the area?
Transformations on a Pegboard
Age 7 to 11 Challenge Level:
How would you move the bands on the pegboard to alter these shapes?
Making Boxes
Age 7 to 11 Challenge Level:
Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?
Fence It
Age 11 to 14 Challenge Level:
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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.
A Day with Grandpa
Age 7 to 11 Challenge Level:
Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?
Shape Draw
Age 7 to 11 Challenge Level:
Use the information on these cards to draw the shape that is being described.
Perimeter Possibilities
Age 11 to 14 Challenge Level:
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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?
Being Curious - Primary Measures
Age 5 to 11 Challenge Level:
Measure problems for inquiring primary learners.
Changing Areas, Changing Perimeters
Age 11 to 14 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?
Always, Sometimes or Never? Shape
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Cutting it Out
Age 5 to 11 Challenge Level:
I cut this square into two different shapes. What can you say about the relationship between them?
Being Collaborative - Primary Measures
Age 5 to 11 Challenge Level:
Measure problems for primary learners to work on with others.
Being Resourceful - Primary Measures
Age 5 to 11 Challenge Level:
Measure problems at primary level that require careful consideration.
NRICH is part of the family of activities in the Millennium Mathematics Project.