Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
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....?
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 fill in these Carroll diagrams. How do you know where to place the numbers?
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?
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?
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 find the chosen number from the grid using the clues?
An odd version of tic tac toe
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
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
Try grouping the dominoes in the ways described. Are there any left
over each time? Can you explain why?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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.
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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.
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?
Are these domino games fair? Can you explain why or why not?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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 place the numbers from 1 to 10 in the grid?
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.
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Use the interactivity to sort these numbers into sets. Can you give
each set a name?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
Follow the clues to find the mystery number.
I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
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?
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.
How would you create the largest possible two-digit even number
from the digit I've given you and one of your choice?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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?
Use the interactivities to complete these Venn diagrams.
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.
How many legs do each of these creatures have? How many pairs is
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.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Each child in Class 3 took four numbers out of the bag. Who had
made the highest even number?