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?
Can you explain the strategy for winning this game with any target?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
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?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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.
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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!
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 complete this jigsaw of the multiplication square?
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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...
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
An investigation that gives you the opportunity to make and justify predictions.
Got It game for an adult and child. How can you play so that you know you will always win?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
If you have only four weights, where could you place them in order to balance this equaliser?
An environment which simulates working with Cuisenaire rods.
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?
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?
Are these statements always true, sometimes true or never true?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
A game that tests your understanding of remainders.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?