The clues for this Sudoku are the product of the numbers in adjacent squares.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Use the differences to find the solution to this Sudoku.
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
What is the smallest number with exactly 14 divisors?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .
How many different symmetrical shapes can you make by shading triangles or squares?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
A game for 2 or more people, based on the traditional card game
Rummy. Players aim to make two `tricks', where each trick has to
consist of a picture of a shape, a name that describes that shape,
and. . . .
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There are lots of different methods to find out what the shapes are worth - how many can you find?
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
Here's a chance to work with large numbers...
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
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?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
Can you arrange these numbers into 7 subsets, each of three
numbers, so that when the numbers in each are added together, they
make seven consecutive numbers?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
Each of the following shapes is made from arcs of a circle of
radius r. What is the perimeter of a shape with 3, 4, 5 and n
Can you describe this route to infinity? Where will the arrows take you next?
The area of a square inscribed in a circle with a unit radius is,
satisfyingly, 2. What is the area of a regular hexagon inscribed in
a circle with a unit radius?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Chris and Jo put two red and four blue ribbons in a box. They each
pick a ribbon from the box without looking. Jo wins if the two
ribbons are the same colour. Is the game fair?
Can you maximise the area available to a grazing goat?
Explore the effect of reflecting in two parallel mirror lines.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Explore the effect of combining enlargements.
If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?