Have a go at balancing this equation. Can you find different ways of doing it?
This package contains a collection of problems from the NRICH
website that could be suitable for students who have a good
understanding of Factors and Multiples and who feel ready to take
on some. . . .
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Number problems at primary level that require careful consideration.
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Can you replace the letters with numbers? Is there only one
solution in each case?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
This Sudoku, based on differences. Using the one clue number can you find the solution?
Given the products of adjacent cells, can you complete this Sudoku?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Given the products of diagonally opposite cells - can you complete this Sudoku?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Follow the clues to find the mystery number.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
What happens when you round these three-digit numbers to the nearest 100?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
A Sudoku that uses transformations as supporting clues.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this matching game, you have to decide how long different events take.
The pages of my calendar have got mixed up. Can you sort them out?