A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
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.
Can you work out what step size to take to ensure you visit all the dots on the circle?
Can you explain the strategy for winning this game with any target?
A game in which players take it in turns to choose a number. Can you block your opponent?
A collection of resources to support work on Factors and Multiples at Secondary level.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you complete this jigsaw of the multiplication square?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
You'll need to know your number properties to win a game of Statement Snap...
How did the the rotation robot make these patterns?
Got It game for an adult and child. How can you play so that you know you will always win?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Is there an efficient way to work out how many factors a large number has?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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.
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.
Can you find any perfect numbers? Read this article to find out more...
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Can you work out how many lengths I swim each day?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
How many different number families can you find?
Are these statements always true, sometimes true or never true?
How many different rectangles can you make using this set of rods?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.