For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
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.
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. . . .
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?"
Given the products of adjacent cells, can you complete this Sudoku?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Is there an efficient way to work out how many factors a large number has?
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.
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
Are these statements always true, sometimes true or never true?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
An investigation that gives you the opportunity to make and justify
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?
Can you complete this jigsaw of the multiplication square?
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?
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?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
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!
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Got It game for an adult and child. How can you play so that you know you will always win?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
If you have only four weights, where could you place them in order
to balance this equaliser?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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.
Can you find any perfect numbers? Read this article to find out more...
Number problems at primary level that may require determination.