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...on the Wall

Stage: 3 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

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.

A Problem Is a Problem for All That

Stage: 2, 3 and 4

In this article, Jennifer Piggott talks about just a few of the problems with problems that make them such a rich source of mathematics and approaches to learning mathematics.

A Problem Is a Problem for All That...

Stage:

The very problem with problems, namely that they should result in you being stuck, is at the heart of what problem-solving is about. In this article for teachers I talk about just a few of the. . . .

Adding All Nine

Stage: 3 Challenge Level:

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

All about Ratios

Stage: 5 Challenge Level:

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

All Change!

Stage: 3 Short Challenge Level:

In how many ways can you give change for a ten pence piece?

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.

All in the Mind

Stage: 3 Challenge Level:

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

All Is Number

Stage: 2 and 3

Read all about Pythagoras' mathematical discoveries in this article written for students.

All Seated

Stage: 2 Challenge Level:

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

All Square

Stage: 3 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

All Square

Stage: 3 Challenge Level:

Solve the system of equations xy = 1 yz = 4 zx = 9

All Tangled Up

Stage: 3 Challenge Level:

Can you tangle yourself up and reach any fraction?

All the Digits

Stage: 2 Challenge Level:

This multiplication sum uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

All Tied Up

Stage: 4 Challenge Level:

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

All Wrapped Up

Stage: 2 Challenge Level:

What is the largest cuboid you can wrap in an A3 sheet of paper?

All-variables Sudoku

Stage: 3, 4 and 5 Challenge Level:

The challenge is to find the values of the variables if you are to solve this Sudoku.

Areas of Parallelograms

Stage: 3 Challenge Level:

Can you find the area of a parallelogram defined by two vectors?

Ball Bearings

Stage: 5 Challenge Level:

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Ball Packing

Stage: 4 Challenge Level:

If a ball is rolled into the corner of a room how far is its centre from the corner?

Balls and Bags

Stage: 4 Challenge Level:

Two bags contain different numbers of red and blue balls. A ball is removed from one of the bags. The ball is blue. What is the probability that it was removed from bag A?

Basically

Stage: 3 Challenge Level:

The number 3723(in base 10) is written as 123 in another base. What is that base?

Big and Small Numbers in Biology

Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Bigger or Smaller?

Stage: 4 Challenge Level:

When you change the units, do the numbers get bigger or smaller?

Board Block Challenge

Stage: 2 Challenge Level:

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Buying a Balloon

Stage: 2 Challenge 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?

Cannon Balls

Stage: 5 Short Challenge Level:

How high will a ball taking a million seconds to fall travel?

Clickety Click and All the Sixes

Stage: 5 Challenge Level:

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

Coordinate Challenge

Stage: 2 Challenge Level:

Use the clues about the symmetrical properties of these letters to place them on the grid.

Cuboid Challenge

Stage: 3 Challenge Level:

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

Cushion Ball

Stage: 4 Challenge Level:

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Cushion Ball Interactivity

Stage: 4 Challenge Level:

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Engaging Mathematics for All Learners

Stage: Challenge Level:

A project, funded by the QCA and designed to develop case studies on implementing rich tasks that will be of use to teachers.

Exploring the Challenge of Online Mediation

Stage:

This reports on students’ responses to a mathematical problem from the NRICH website. In particular, we were interested in students’ responses to a question that provided an. . . .

Extra Challenges from Madras

Stage: 3 and 4

A few extra challenges set by some young NRICH members.

Factors and Multiple Challenges

Stage: 3 Challenge Level:

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

FMN Thinking Mathematically 26 June 2008

Stage: Challenge Level:

Football Champs

Stage: 3 Challenge Level:

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

Football Crazy Hockey Mad

Stage: 3 Challenge Level:

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

Football Sum

Stage: 3 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Football World Cup Simulation

Stage: 2, 3 and 4 Challenge Level:

A maths-based Football World Cup simulation for teachers and students to use.

Fractional Wall

Stage: 2 Challenge Level:

Using the picture of the fraction wall, can you find equivalent fractions?

From All Corners

Stage: 4 Challenge Level:

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

Galley Division

Stage: 4 Challenge Level:

Can you explain how Galley Division works?

Generally Geometric

Stage: 5 Challenge Level:

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

Halloween Investigation

Stage: 2 Challenge Level:

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Hallway Borders

Stage: 3 Challenge Level:

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

Harmonically

Stage: 5 Challenge Level:

Is it true that a large integer m can be taken such that: 1 + 1/2 + 1/3 + ... +1/m > 100 ?