This activity involves rounding four-digit numbers to the nearest thousand.
Find the sum of all three-digit numbers each of whose digits is
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
Think of a number, add one, double it, take away 3, add the number
you first thought of, add 7, divide by 3 and take away the number
you first thought of. You should now be left with 2. How do I. . . .
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you explain how this card trick works?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Are these statements always true, sometimes true or never true?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Here are two kinds of spirals for you to explore. What do you notice?
An investigation that gives you the opportunity to make and justify
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many centimetres of rope will I need to make another mat just
like the one I have here?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
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?
A collection of games on the NIM theme
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Got It game for an adult and child. How can you play so that you know you will always win?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?