Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
What is the smallest number with exactly 14 divisors?
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?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
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. . . .
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
The sums of the squares of three related numbers is also a perfect
square - can you explain why?
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.
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
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?
Show that is it impossible to have a tetrahedron whose six edges
have lengths 10, 20, 30, 40, 50 and 60 units...
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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.
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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?
Take any prime number greater than 3 , square it and subtract one.
Working on the building blocks will help you to explain what is
special about your results.
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
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?
Manufacturers need to minimise the amount of material used to make
their product. What is the best cross-section for a gutter?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Can you find the area of a parallelogram defined by two vectors?
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.
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .
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?
Which set of numbers that add to 10 have the largest product?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you describe this route to infinity? Where will the arrows take you next?
A circle of radius r touches two sides of a right angled triangle,
sides x and y, and has its centre on the hypotenuse. Can you prove
the formula linking x, y and r?
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?
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?
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.
Explore the effect of combining enlargements.
Use the differences to find the solution to this Sudoku.