An investigation that gives you the opportunity to make and justify
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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?
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
Can you place the numbers from 1 to 10 in the grid?
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.
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
If there is a ring of six chairs and thirty children must either
sit on a chair or stand behind one, how many children will be
behind each chair?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
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?
Find the squares that Froggie skips onto to get to the pumpkin
patch. She starts on 3 and finishes on 30, but she lands only on a
square that has a number 3 more than the square she skips from.
This package will help introduce children to, and encourage a deep
exploration of, multiples.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Can you find any perfect numbers? Read this article to find out more...
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Can you find the chosen number from the grid using the clues?
You can make a calculator count for you by any number you choose.
You can count by ones to reach 24. You can count by twos to reach
24. What else can you count by to reach 24?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Follow the clues to find the mystery number.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
56 406 is the product of two consecutive numbers. What are these
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
This activity focuses on doubling multiples of five.
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Help share out the biscuits the children have made.