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Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations

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Division Rules

Age 7 to 11 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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Exploring Number Patterns You Make

Age 7 to 11 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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The Domesday Project

Age 7 to 11 Challenge Level:

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

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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?

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9 Hole Light Golf

Age 5 to 18 Challenge Level:

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

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Count the Digits

Age 5 to 11 Challenge Level:

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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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.

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The Car That Passes

Age 7 to 11 Challenge Level:

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

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In the Playground

Age 5 to 11 Challenge Level:

What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?

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Ip Dip

Age 5 to 11 Challenge Level:

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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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.

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Follow the Numbers

Age 7 to 11 Challenge Level:

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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Become Maths Detectives

Age 7 to 11 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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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.

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Balance of Halves

Age 7 to 11 Challenge Level:

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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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.

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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.

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Abundant Numbers

Age 7 to 11 Challenge Level:

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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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?

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Buying a Balloon

Age 7 to 11 Challenge Level:

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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Five Coins

Age 7 to 11 Challenge Level:

Ben has five coins in his pocket. How much money might he have?

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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?

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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?

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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"?

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Round and Round the Circle

Age 7 to 11 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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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?

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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?

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Doplication

Age 7 to 11 Challenge Level:

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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Roll These Dice

Age 7 to 11 Challenge Level:

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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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?

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Cubes

Age 7 to 11 Challenge Level:

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

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Plants

Age 5 to 11 Challenge Level:

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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Chocolate

Age 7 to 14 Challenge Level:

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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Consecutive Numbers

Age 7 to 14 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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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.

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Number Families

Age 11 to 14 Challenge Level:

How many different sets of numbers with at least four members can you find in the numbers in this box?

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Sending and Receiving Cards

Age 7 to 11 Challenge Level:

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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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?

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Designing Table Mats

Age 11 to 16 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

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Troublesome Triangles

Age 7 to 14 Challenge Level:

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns!

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It's Times Again

Age 7 to 14 Challenge Level:

Which way of flipping over and/or turning this grid will give you the highest total? You'll need to imagine where the numbers will go in this tricky task!

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Building with Longer Rods

Age 7 to 14 Challenge Level:

A challenging activity focusing on finding all possible ways of stacking rods.

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Crossing the Town Square

Age 7 to 11 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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Tiling Into Slanted Rectangles

Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

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More Plant Spaces

Age 7 to 14 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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Building with Rods

Age 7 to 11 Challenge Level:

In how many ways can you stack these rods, following the rules?

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Tiles in the Garden

Age 7 to 11 Challenge Level:

How many tiles do we need to tile these patios?

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More Children and Plants

Age 7 to 14 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

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So It's Times!

Age 7 to 14 Challenge Level:

How will you decide which way of flipping over and/or turning the grid will give you the highest total?