Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
Nearly all of us have made table patterns on hundred squares, that
is 10 by 10 grids. This problem looks at the patterns on
differently sized square grids.
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?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
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?
56 406 is the product of two consecutive numbers. What are these
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Kimie and Sebastian were making sticks from interlocking cubes and
lining them up. Can they make their lines the same length? Can they
make any other lines?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Can you place the numbers from 1 to 10 in the grid?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Use the interactivity to sort these numbers into sets. Can you give
each set a name?
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.
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?
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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.
Can you find the chosen number from the grid using the clues?
This package will help introduce children to, and encourage a deep
exploration of, multiples.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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.
A game that tests your understanding of remainders.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
On a farm there were some hens and sheep. Altogether there were 8
heads and 22 feet. How many hens were there?
Can you work out what a ziffle is on the planet Zargon?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
This activity focuses on doubling multiples of five.
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?
If you count from 1 to 20 and clap more loudly on the numbers in
the two times table, as well as saying those numbers loudly, which
numbers will be loud?
Look at the squares in this problem. What does the next square look
like? I draw a square with 81 little squares inside it. How long
and how wide is my square?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?