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?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Follow the clues to find the mystery number.
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?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
56 406 is the product of two consecutive numbers. What are these
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?
Can you work out what a ziffle is on the planet Zargon?
Have a go at balancing this equation. Can you find different ways of doing it?
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 find just the right bubbles to hold your number?
Can you work out some different ways to balance this equation?
Are these domino games fair? Can you explain why or why not?
Can you place the numbers from 1 to 10 in the grid?
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?
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?
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
Got It game for an adult and child. How can you play so that you know you will always win?
This activity focuses on doubling multiples of five.
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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 cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?