There are 128 results
Broad Topics > Mathematical thinking skills > Generalising
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
Elevenses
Age 11 to 14
Challenge Level
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Searching for Mean(ing)
Age 11 to 16
Challenge Level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Consecutive Negative Numbers
Age 11 to 14
Challenge Level
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
More Twisting and Turning
Age 11 to 16
Challenge Level
It would be nice to have a strategy for disentangling any tangled ropes...
Sums of Pairs
Age 11 to 16
Challenge Level
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Spaces for Exploration
Age 11 to 14
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
Triangle Numbers
Age 11 to 14
Challenge Level
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
Route to Infinity
Age 11 to 14
Challenge Level
Can you describe this route to infinity? Where will the arrows take you next?
Cunning Card Trick
Age 11 to 14
Challenge Level
Delight your friends with this cunning trick! Can you explain how it works?
Who is the fairest of them all ?
Age 11 to 14
Challenge Level
Explore the effect of combining enlargements.
...on the Wall
Age 11 to 14
Challenge Level
Explore the effect of reflecting in two intersecting mirror lines.
Mirror, Mirror...
Age 11 to 14
Challenge Level
Explore the effect of reflecting in two parallel mirror lines.
More Magic Potting Sheds
Age 11 to 16
Challenge Level
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?
Areas of Parallelograms
Age 14 to 16
Challenge Level
Can you find the area of a parallelogram defined by two vectors?
Litov's Mean Value Theorem
Age 11 to 14
Challenge Level
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Squares in Rectangles
Age 11 to 14
Challenge Level
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Harmonic Triangle
Age 14 to 16
Challenge Level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Cubes Within Cubes Revisited
Age 11 to 14
Challenge Level
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
Partitioning Revisited
Age 11 to 14
Challenge Level
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
Multiplication Square
Age 14 to 16
Challenge Level
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Arithmagons
Age 11 to 16
Challenge Level
Can you find the values at the vertices when you know the values on the edges?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Tilted Squares
Age 11 to 14
Challenge Level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Coordinate Patterns
Age 11 to 14
Challenge Level
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Seven Squares - Group-worthy Task
Age 11 to 14
Challenge Level
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Shear Magic
Age 11 to 14
Challenge Level
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
More Number Pyramids
Age 11 to 14
Challenge Level
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Number Pyramids
Age 11 to 14
Challenge Level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Pair Products
Age 14 to 16
Challenge Level
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Picturing Square Numbers
Age 11 to 14
Challenge Level
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Picturing Triangular Numbers
Age 11 to 14
Challenge Level
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Mind Reading
Age 11 to 14
Challenge Level
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 know?
Pick's Theorem
Age 14 to 16
Challenge Level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Take Three from Five
Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Got It
Age 7 to 14
Challenge Level
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.
Frogs
Age 11 to 14
Challenge Level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Egyptian Fractions
Age 11 to 14
Challenge Level
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
Attractive Tablecloths
Age 14 to 16
Challenge Level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Enclosing Squares
Age 11 to 14
Challenge Level
Can you find sets of sloping lines that enclose a square?
Where Can We Visit?
Age 11 to 14
Challenge Level
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
What's Possible?
Age 14 to 16
Challenge Level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Beelines
Age 14 to 16
Challenge Level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Of All the Areas
Age 14 to 16
Challenge Level
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Plus Minus
Age 14 to 16
Challenge Level
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Odd Differences
Age 14 to 16
Challenge Level
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
Summing Consecutive Numbers
Age 11 to 14
Challenge Level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Is There a Theorem?
Age 11 to 14
Challenge Level
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Counting Factors
Age 11 to 14
Challenge Level
Is there an efficient way to work out how many factors a large number has?
Have You Got It?
Age 11 to 14
Challenge Level
Can you explain the strategy for winning this game with any target?
NRICH is part of the family of activities in the Millennium Mathematics Project.