# Resources tagged with: Investigations

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### There are 147 results

Broad Topics > Thinking Mathematically > Investigations

### Sets of Four Numbers

##### Age 7 to 11Challenge Level

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

### Caterpillars

##### Age 5 to 7Challenge Level

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

### Worms

##### Age 7 to 11Challenge Level

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

### Polo Square

##### Age 7 to 11Challenge Level

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

### It Was 2010!

##### Age 5 to 11Challenge Level

If the answer's 2010, what could the question be?

### Sometimes We Lose Things

##### Age 7 to 11Challenge Level

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

### Bean Bags for Bernard's Bag

##### Age 7 to 11Challenge Level

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

### Street Sequences

##### Age 5 to 11Challenge Level

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

### Abundant Numbers

##### Age 7 to 11Challenge 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?

### The Pied Piper of Hamelin

##### Age 7 to 11Challenge Level

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### Month Mania

##### Age 5 to 11Challenge Level

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

### Calendar Patterns

##### Age 7 to 11Challenge 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?

### Sorting the Numbers

##### Age 5 to 11Challenge 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?

### Marvellous Matrix

##### Age 7 to 11Challenge Level

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

### Five Coins

##### Age 5 to 11Challenge Level

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

### Number Squares

##### Age 5 to 11Challenge 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?

##### Age 7 to 11Challenge 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.

### Exploring Wild & Wonderful Number Patterns

##### Age 7 to 11Challenge Level

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

### Sending Cards

##### Age 7 to 11Challenge 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?

### It Figures

##### Age 7 to 11Challenge 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?

### Homes

##### Age 5 to 7Challenge Level

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

### Sets of Numbers

##### Age 7 to 11Challenge Level

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

### Doplication

##### Age 7 to 11Challenge 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?

### Magic Constants

##### Age 7 to 11Challenge Level

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

### Stairs

##### Age 5 to 11Challenge 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.

### Calcunos

##### Age 7 to 11Challenge Level

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

##### Age 7 to 11Challenge Level

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

### Room Doubling

##### Age 7 to 11Challenge Level

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

### Alien Counting

##### Age 7 to 11Challenge Level

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

### Pebbles

##### Age 7 to 11Challenge 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?

### Two on Five

##### Age 5 to 11Challenge 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?

### Consecutive Numbers

##### Age 7 to 14Challenge Level

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

##### Age 7 to 11Challenge 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?

### Sweets in a Box

##### Age 7 to 11Challenge 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?

### Let's Investigate Triangles

##### Age 5 to 7Challenge Level

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

### Tiling

##### Age 7 to 11Challenge Level

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

### Cubes Here and There

##### Age 7 to 11Challenge 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?

### So It's 28

##### Age 5 to 7Challenge Level

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

### Sticks and Triangles

##### Age 7 to 11Challenge 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?

### Gran, How Old Are You?

##### Age 7 to 11Challenge Level

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

### Polygonals

##### Age 7 to 11Challenge Level

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

### Crossing the Town Square

##### Age 7 to 11Challenge Level

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

### Building with Rods

##### Age 7 to 11Challenge Level

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

### Birthday Cake Candles

##### Age 7 to 11Challenge Level

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

### Making Cuboids

##### Age 7 to 11Challenge 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?

### Magazines

##### Age 7 to 11Challenge 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.

### Street Party

##### Age 7 to 11Challenge Level

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

##### Age 7 to 11Challenge 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?

### Lost Books

##### Age 7 to 11Challenge 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?

### 3 Rings

##### Age 7 to 11Challenge Level

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?