Resources tagged with: Investigations

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There are 145 results

Broad Topics > Mathematical Thinking > Investigations

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Tables Without Tens

Age 7 to 11 Challenge Level:

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

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Taking a Die for a Walk

Age 5 to 11 Challenge Level:

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

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Magazines

Age 7 to 11 Challenge Level:

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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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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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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Birds in the Garden

Age 5 to 11 Challenge Level:

This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

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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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Sorting the Numbers

Age 5 to 11 Challenge Level:

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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It Must Be 2000

Age 7 to 11 Challenge Level:

Here are many ideas for you to investigate - all linked with the number 2000.

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Calendar Patterns

Age 7 to 11 Challenge Level:

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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More Pebbles

Age 7 to 11 Challenge Level:

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

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Lost Books

Age 7 to 11 Challenge Level:

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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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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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?

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Experiencing Problem Solving

Age 5 to 11

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

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Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.

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Stairs

Age 5 to 11 Challenge Level:

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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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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Polygonals

Age 7 to 11 Challenge Level:

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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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 Great Tiling Count

Age 7 to 11 Challenge Level:

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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Number Squares

Age 5 to 11 Challenge Level:

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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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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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?

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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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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?

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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?

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Room Doubling

Age 7 to 11 Challenge Level:

Investigate the different ways you could split up these rooms so that you have double the number.

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Mobile Numbers

Age 5 to 11 Challenge Level:

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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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?

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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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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?

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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?

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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?

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Street Sequences

Age 5 to 11 Challenge Level:

Investigate what happens when you add house numbers along a street in different ways.

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Tiling

Age 7 to 11 Challenge Level:

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

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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?

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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?

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Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

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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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Tiling Into Slanted Rectangles

Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

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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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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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Eye View

Age 7 to 11 Challenge Level:

Why does the tower look a different size in each of these pictures?

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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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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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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?

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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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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 ...?