Resources tagged with: Investigations

Filter by: Content type:
Age range:
Challenge level:

There are 141 results

Broad Topics > Thinking Mathematically > Investigations

Bracelets

Age 7 to 11
Challenge Level

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Cuboid-in-a-box

Age 7 to 11
Challenge Level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Escher Tessellations

Age 7 to 11
Challenge Level

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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?

Triangular Hexagons

Age 7 to 11
Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.

Egyptian Rope

Age 7 to 11
Challenge Level

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

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.

Four Layers

Age 5 to 11
Challenge Level

Can you create more models that follow these rules?

It's a Fence!

Age 5 to 11
Challenge Level

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Two by One

Age 7 to 11
Challenge Level

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

Little Boxes

Age 7 to 11
Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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.

Triangle Relations

Age 7 to 11
Challenge Level

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

28 and It's Upward and Onward

Age 7 to 11
Challenge Level

Can you find ways of joining cubes together so that 28 faces are visible?

Redblue

Age 7 to 11
Challenge Level

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

Triangle Shapes

Age 5 to 11
Challenge Level

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Squareo'scope Determines the Kind of Triangle

Age 11 to 14

A description of some experiments in which you can make discoveries about triangles.

Cutting Corners

Age 7 to 11
Challenge Level

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Tri.'s

Age 7 to 11
Challenge Level

How many triangles can you make on the 3 by 3 pegboard?

All Wrapped Up

Age 7 to 11
Challenge Level

What is the largest cuboid you can wrap in an A3 sheet of paper?

Sweets in a Box

Age 7 to 11
Challenge Level

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Brush Loads

Age 7 to 11
Challenge Level

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

The Numbers Give the Design

Age 7 to 11
Challenge Level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Sticks and Triangles

Age 7 to 11
Challenge Level

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Tessellating Transformations

Age 7 to 11
Challenge Level

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

Double Your Popcorn, Double Your Pleasure

Age 7 to 11
Challenge Level

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Tessellating Triangles

Age 7 to 11
Challenge Level

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

How Tall?

Age 5 to 11
Challenge Level

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Cubes

Age 7 to 11
Challenge Level

How many faces can you see when you arrange these three cubes in different ways?

Presents

Age 7 to 11
Challenge Level

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

Making Cuboids

Age 7 to 11
Challenge Level

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

Triple Cubes

Age 5 to 11
Challenge Level

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

More Pebbles

Age 7 to 11
Challenge Level

Have a go at this 3D extension to the Pebbles problem.

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?

Watch Your Feet

Age 7 to 11
Challenge Level

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

It Figures

Age 7 to 11
Challenge Level

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

New House

Age 7 to 11
Challenge Level

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

Are You a Smart Shopper?

Age 7 to 11
Challenge Level

In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?

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?

Two on Five

Age 5 to 11
Challenge Level

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

Sticky Triangles

Age 7 to 11
Challenge Level

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Triangle Pin-down

Age 7 to 11
Challenge Level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Birthday Cake Candles

Age 7 to 11
Challenge Level

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

Cubes Here and There

Age 7 to 11
Challenge Level

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Hexpentas

Age 5 to 11
Challenge Level

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

Experiencing Problem Solving

Age 5 to 11

Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.