This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.
Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
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?
Follow the clues to find the mystery number.
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. Can you find
all the numbers in each set from these clues?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
This problem is designed to help children to learn, and to use, the two and three times tables.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Can you use the information to find out which cards I have used?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?
You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.
Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?
This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
Written for teachers, this article discusses mathematical
representations and takes, in the second part of the article,
examples of reception children's own representations.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Can you draw the shape that is being described by these cards?
Design your own scoring system and play Trumps with these Olympic Sport cards.
The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?
This Sudoku, based on differences. Using the one clue number can you find the solution?
You may like to read the article on Morse code before attempting
this question. Morse's letter analysis was done over 150 years ago,
so might there be a better allocation of symbols today?
Did you know that ancient traditional mazes often tell a story? Remembering the story helps you to draw the maze.
In this article for teachers, Bernard uses some problems to suggest
that once a numerical pattern has been spotted from a practical
starting point, going back to the practical can help explain. . . .
Investigate polygons with all the vertices on the lattice points of
a grid. For each polygon, work out the area A, the number B of
points on the boundary and the number of points (I) inside. . . .
Baker, Cooper, Jones and Smith are four people whose occupations
are teacher, welder, mechanic and programmer, but not necessarily
in that order. What is each person’s occupation?
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Can you rank these quantities in order? You may need to find out
extra information or perform some experiments to justify your
A random ramble for teachers through some resources that might add a little life to a statistics class.
Can you place these quantities in order from smallest to largest?
Invent a scoring system for a 'guess the weight' competition.
Can you use your powers of logic and deduction to work out the missing information in these sporty situations?
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
In a league of 5 football teams which play in a round robin
tournament show that it is possible for all five teams to be league
After some matches were played, most of the information in the
table containing the results of the games was accidentally deleted.
What was the score in each match played?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
The graph represents a salesman’s area of activity with the
shops that the salesman must visit each day. What route around the
shops has the minimum total distance?
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Four small numbers give the clue to the contents of the four