This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Use the interactivity to sort these numbers into sets. Can you give
each set a name?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
An odd version of tic tac toe
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Use the interactivities to complete these Venn diagrams.
This problem looks at how one example of your choice can show something about the general structure of multiplication.
This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
You can trace over all of the diagonals of a pentagon without
lifting your pencil and without going over any more than once. Can
the same thing be done with a hexagon or with a heptagon?
Can you find the chosen number from the grid using the clues?
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 put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Daisy and Akram were making number patterns. Daisy was using beads
that looked like flowers and Akram was using cube bricks. First
they were counting in twos.
This problem challenges you to find out how many odd numbers there
are between pairs of numbers. Can you find a pair of numbers that
has four odds between them?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
How many legs do each of these creatures have? How many pairs is
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Can you place the numbers from 1 to 10 in the grid?
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.
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
Follow the clues to find the mystery number.
Try grouping the dominoes in the ways described. Are there any left
over each time? Can you explain why?
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?