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. . . .
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?"
Can you complete this jigsaw of the multiplication square?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
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?
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!
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Are these statements always true, sometimes true or never true?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
An investigation that gives you the opportunity to make and justify
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Can you find any perfect numbers? Read this article to find out more...
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
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.
Given the products of adjacent 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?