See also: Matching topics (16) Matching titles (120)
1125 problems, 81 games, 310 articles, 183 general resources, 7 interactive environments, 233 from Stage 1, 543 from Stage 2, 569 from Stage 3, 503 from Stage 4, 373 from Stage 5
2009 Challenge
Stage: 3, 4 and 5 Challenge Level: 
We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.
Stats Statements
Stage: 5 Challenge Level:
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which Spinners?
Stage: 3 Challenge Level:
Which spinners were used to generate these frequency charts?
Data Collection Tool
Stage: 3 and 4 Challenge Level:
An interactivity that enables you collect data from an experiment with true/false outcomes.
All in a Jumble
Stage: 3 Challenge Level:
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
Cannon Balls
Stage: 5 Short Challenge Level:
How high will a ball taking a million seconds to fall travel?
Weights
Stage: 3 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Adding and Subtracting Positive and Negative Numbers
Stage: 3 and 4
How can we help students make sense of addition and subtraction of negative numbers?
Scale Invariance
Stage: 5 Challenge Level:
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Sea Level
Stage: 2 Challenge Level:
The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?
Tug of War
Stage: 1 Challenge Level:
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Consecutive Negative Numbers
Stage: 3 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
First Connect Three
Stage: 2 and 3 Challenge Level:
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Overarch 1
Stage: 5 Short Challenge Level:
This short question asks if you can work out the most precarious way to balance four tiles.
Napier's Location Arithmetic
Stage: 4 Challenge Level:
Have you seen this way of doing multiplication ?
Interactive Number Patterns
Stage: 4 Challenge Level:
How good are you at finding the formula for a number pattern ?
Spotting the Loophole
Stage: 4 Challenge Level:
A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
Difference Sudoku
Stage: 3 and 4 Challenge Level:
Use the differences to find the solution to this Sudoku.
Caterpillars
Stage: 1 Challenge 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?
Walking Around a Cube
Stage: 3 and 4 Challenge Level:
Find the length along the shortest path passing through certain points on the cube.
Matchless
Stage: 3 and 4 Challenge Level:
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
Sine and Cosine
Stage: 4 Challenge Level:
The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?
Six Places to Visit
Stage: 2 Challenge Level:
Can you describe the journey to each of the six places on these maps? How would you turn at each junction?
How Safe Are You?
Stage: 2 Challenge Level:
How much do you have to turn these dials by in order to unlock the safes?
Equation Attack
Stage: 5 Challenge Level:
The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
Dating Made Easier
Stage: 4 Challenge Level:
If a sum invested gains 10% each year how long before it has doubled its value?
Nicely Similar
Stage: 4 Challenge Level:
If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?
Route Product
Stage: 2 Challenge Level:
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Parallel Lines
Stage: 3 Challenge Level:
How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?
Integrated Product Sudoku
Stage: 3 and 4 Challenge Level:
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Growing Garlic
Stage: 1 Challenge Level:
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Factor-multiple Chains
Stage: 2 Challenge Level:
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Integrated Sums Sudoku
Stage: 3 and 4 Challenge Level:
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
Tens
Stage: 5 Challenge Level:
When is 7^n + 3^n a multiple of 10? Can you prove the result by two different methods?
Spaces for Exploration
Stage: 3 and 4
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
It's a Tie
Stage: 2 Challenge Level:
Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?
All about Ratios
Stage: 5 Challenge Level:
A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.
Equal Temperament
Stage: 4 Challenge Level:
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
Music to My Ears
Stage: 2 Challenge Level:
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Fractions Jigsaw
Stage: 3 Challenge Level:
A jigsaw where pieces only go together if the fractions are equivalent.
Cunning Card Trick
Stage: 3 Challenge Level:
Delight your friends with this cunning trick! Can you explain how it works?
...on the Wall
Stage: 3 Challenge Level:
Explore the effect of reflecting in two intersecting mirror lines.
Mirror, Mirror...
Stage: 3 Challenge Level:
Explore the effect of reflecting in two parallel mirror lines.
Transformation Game
Stage: 3 Challenge Level:
Why not challenge a friend to play this transformation game?
Factors and Multiples Puzzle
Stage: 3 Challenge Level:
A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?
Intersections
Stage: 4 and 5 Challenge Level:
Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
Multiples Grid
Stage: 2 Challenge Level:
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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