There are **35** NRICH Mathematical resources connected to **Making and testing hypotheses**, you may find related items under Thinking Mathematically.

Challenge Level

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

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?

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?

Challenge Level

This activity focuses on similarities and differences between shapes.

Challenge Level

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

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?

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?

Challenge Level

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

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.

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?

Challenge Level

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

Challenge Level

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

Challenge Level

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Challenge Level

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

Challenge Level

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

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?

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. . . .

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.

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

Challenge Level

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

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?

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?

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?

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?

This article explores the process of making and testing hypotheses.

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?

Challenge Level

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

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?

Challenge Level

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

Challenge Level

Can you make a hypothesis to explain these ancient numbers?

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?

Challenge Level

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

Challenge Level

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

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?