Other tags that relate to Area and Perimeter
Trial and improvement. Working systematically. Combinations. Perimeter. Visualising. Factors and multiples. Area - squares and rectangles. Generalising. Investigations. Addition & subtraction.There are 141 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising
Area and Perimeter
Age 7 to 11 Challenge Level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Doplication
Age 7 to 11 Challenge Level:
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Build it up More
Age 7 to 11 Challenge Level:
This task follows on from Build it Up and takes the ideas into three dimensions!
Journeys in Numberland
Age 7 to 11 Challenge Level:
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Magic Circles
Age 7 to 11 Challenge Level:
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?
Lost Books
Age 7 to 11 Challenge Level:
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?
Sums and Differences 2
Age 7 to 11 Challenge Level:
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?
Magic Constants
Age 7 to 11 Challenge Level:
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Polygonals
Age 7 to 11 Challenge Level:
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Sums and Differences 1
Age 7 to 11 Challenge Level:
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Calendar Calculations
Age 7 to 11 Challenge Level:
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 happens?
Tiling
Age 7 to 11 Challenge Level:
An investigation that gives you the opportunity to make and justify predictions.
Digit Addition
Age 5 to 11 Challenge Level:
Try out this number trick. What happens with different starting numbers? What do you notice?
Broken Toaster
Age 7 to 11 Short Challenge Level:
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Button-up Some More
Age 7 to 11 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Division Rules
Age 7 to 11 Challenge Level:
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Sitting Round the Party Tables
Age 5 to 11 Challenge Level:
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Sticky Triangles
Age 7 to 11 Challenge Level:
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Round the Three Dice
Age 7 to 11 Challenge Level:
What happens when you round these three-digit numbers to the nearest 100?
Oddly
Age 7 to 11 Challenge Level:
Find the sum of all three-digit numbers each of whose digits is odd.
Dice Stairs
Age 7 to 11 Challenge Level:
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Build it Up
Age 7 to 11 Challenge Level:
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Centred Squares
Age 7 to 11 Challenge Level:
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Break it Up!
Age 5 to 11 Challenge Level:
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.
Bundles of Cubes
Age 7 to 11 Challenge Level:
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Domino Numbers
Age 7 to 11 Challenge Level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Simple Train Journeys
Age 5 to 11 Challenge Level:
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
The Great Tiling Count
Age 7 to 11 Challenge Level:
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Surprising Split
Age 7 to 11 Challenge Level:
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Fault-free Rectangles
Age 7 to 11 Challenge Level:
Find out what a "fault-free" rectangle is and try to make some of your own.
Spirals, Spirals
Age 7 to 11 Challenge Level:
Here are two kinds of spirals for you to explore. What do you notice?
Number Tracks
Age 7 to 11 Challenge Level:
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?
Number Differences
Age 7 to 11 Challenge Level:
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?
Rope Mat
Age 7 to 11 Challenge Level:
How many centimetres of rope will I need to make another mat just like the one I have here?
Cuisenaire Rods
Age 7 to 11 Challenge Level:
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Round the Dice Decimals 1
Age 7 to 11 Challenge Level:
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Move a Match
Age 7 to 11 Challenge Level:
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Round and Round the Circle
Age 7 to 11 Challenge Level:
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.
Truth or Lie
Age 7 to 11 Challenge Level:
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Cut it Out
Age 7 to 11 Challenge Level:
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?
Counting Counters
Age 7 to 11 Challenge Level:
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Round the Dice Decimals 2
Age 7 to 11 Challenge Level:
What happens when you round these numbers to the nearest whole number?
Have You Got It?
Age 11 to 14 Challenge Level:
Can you explain the strategy for winning this game with any target?
Always, Sometimes or Never?
Age 5 to 11 Challenge Level:
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Crossings
Age 7 to 11 Challenge Level:
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?
Play to 37
Age 7 to 11 Challenge Level:
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Triangle Pin-down
Age 7 to 11 Challenge Level:
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Always, Sometimes or Never? Shape
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Up and Down Staircases
Age 7 to 11 Challenge Level:
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?
Odd Squares
Age 7 to 11 Challenge Level:
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
NRICH is part of the family of activities in the Millennium Mathematics Project.