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### There are 41 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Making and testing hypotheses

### Different Sizes

##### Age 5 to 11 Challenge Level:

A simple visual exploration into halving and doubling.

### National Flags

##### Age 7 to 11 Challenge Level:

This problem explores the shapes and symmetries in some national flags.

### 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?

### 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?

### Sorting Logic Blocks

##### Age 5 to 11 Challenge Level:

This interactivity allows you to sort logic blocks by dragging their images.

### Light the Lights

##### Age 5 to 7 Challenge Level:

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

### Light the Lights Again

##### Age 7 to 11 Challenge Level:

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

### Black Box

##### Age 16 to 18 Challenge Level:

This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?

### Our Numbers

##### Age 5 to 7 Challenge Level:

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

### I Like ...

##### Age 5 to 7 Challenge Level:

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

### Table Patterns Go Wild!

##### Age 7 to 11 Challenge Level:

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

### How Much Can We Spend?

##### Age 11 to 14 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

### Cuboid Challenge

##### Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper?

### Can They Be Equal?

##### Age 11 to 14 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

### Searching for Mean(ing)

##### Age 11 to 14 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

### Reaction Timer

##### Age 11 to 14 Challenge Level:

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

### Arithmagons

##### Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges?

### Where Can We Visit?

##### Age 11 to 14 Challenge Level:

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

### 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. . . .

### Observing the Sun and the Moon

##### Age 7 to 14 Challenge Level:

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

### On the Importance of Pedantry

##### Age 16 to 18

A introduction to how patterns can be deceiving, and what is and is not a proof.

### Spot Thirteen

##### Age 7 to 11 Challenge Level:

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

### Sorting Letters

##### Age 5 to 11 Challenge Level:

This interactivity allows you to sort letters of the alphabet into two groups according to different properties.

### Charlie's Delightful Machine

##### Age 11 to 16 Challenge Level:

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### 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?

### Four Coloured Lights

##### Age 11 to 14 Challenge Level:

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

### White Box

##### Age 7 to 18 Challenge Level:

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

### Which Numbers? (2)

##### Age 7 to 11 Challenge Level:

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

### Which Numbers? (1)

##### Age 7 to 11 Challenge Level:

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

### Understanding Hypotheses

##### Age 14 to 18

This article explores the process of making and testing hypotheses.

### Pattern Recognition

##### Age 16 to 18 Challenge Level:

When does a pattern start to exhibit structure? Can you crack the code used by the computer?

### Logic Block Collections

##### Age 5 to 7 Challenge Level:

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

### Shapes in the Alphabet

##### Age 5 to 7 Challenge Level:

In this problem, we're going to find sets of letter shapes that go together.

### In the Bag

##### Age 11 to 14 Challenge Level:

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

### Ishango Bone

##### Age 7 to 18 Challenge Level:

Can you decode the mysterious markings on this ancient bone tool?

### Babylon Numbers

##### Age 11 to 18 Challenge Level:

Can you make a hypothesis to explain these ancient numbers?

### Gr8 Coach

##### Age 11 to 14 Challenge Level:

Can you coach your rowing eight to win?

### Marvellous Matrix

##### Age 7 to 11 Challenge 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?

### Seven Pots of Plants

##### Age 7 to 11 Challenge Level:

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

### Folding, Cutting and Punching

##### Age 7 to 11 Challenge Level:

Exploring and predicting folding, cutting and punching holes and making spirals.

### The Mathemagician's Seven Spells

##### Age 7 to 11 Challenge Level:

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?