Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different 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.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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 notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
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?
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.
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?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Can you describe this route to infinity? Where will the arrows take you next?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
How many different symmetrical shapes can you make by shading triangles or squares?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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. . . .
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G =
F and A-H represent the numbers from 0 to 7 Find the values of A,
B, C, D, E, F and H.
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400. . . .
Use the differences to find the solution to this Sudoku.
Can you maximise the area available to a grazing goat?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
If you move the tiles around, can you make squares with different coloured edges?
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?
What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?
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?
There are lots of different methods to find out what the shapes are worth - how many can you find?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Is there an efficient way to work out how many factors a large number has?
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 ?
Can you work out the dimensions of the three cubes?
Start with two numbers and generate a sequence where the next number is the mean of the last two 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?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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?
Explore the effect of reflecting in two parallel mirror lines.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Explore the effect of combining enlargements.
A spider is sitting in the middle of one of the smallest walls in a
room and a fly is resting beside the window. What is the shortest
distance the spider would have to crawl to catch the fly?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can all unit fractions be written as the sum of two unit fractions?
Which set of numbers that add to 10 have the largest product?
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?