A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
Given the products of adjacent cells, can you complete this Sudoku?
Can you explain the strategy for winning this game with any target?
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you complete this jigsaw of the multiplication square?
A game that tests your understanding of remainders.
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.
If you have only four weights, where could you place them in order to balance this equaliser?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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...
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Given the products of diagonally opposite cells - can you complete this Sudoku?
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Follow the clues to find the mystery number.
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
An environment which simulates working with Cuisenaire rods.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
An investigation that gives you the opportunity to make and justify predictions.