# Resources tagged with: Generalising

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Broad Topics > Mathematical thinking skills > Generalising ### Cuboid Challenge

##### Age 11 to 16Challenge Level

What's the largest volume of box you can make from a square of paper? ### Elevenses

##### Age 11 to 14Challenge 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 16Challenge 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 14Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers? ### More Twisting and Turning

##### Age 11 to 16Challenge Level

It would be nice to have a strategy for disentangling any tangled ropes... ### Sums of Pairs

##### Age 11 to 16Challenge 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 14Challenge 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 14Challenge Level

Can you describe this route to infinity? Where will the arrows take you next? ### Cunning Card Trick

##### Age 11 to 14Challenge Level

Delight your friends with this cunning trick! Can you explain how it works? ### Who is the fairest of them all ?

##### Age 11 to 14Challenge Level

Explore the effect of combining enlargements. ### ...on the Wall

##### Age 11 to 14Challenge Level

Explore the effect of reflecting in two intersecting mirror lines. ### Mirror, Mirror...

##### Age 11 to 14Challenge Level

Explore the effect of reflecting in two parallel mirror lines. ### More Magic Potting Sheds

##### Age 11 to 16Challenge 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 16Challenge Level

Can you find the area of a parallelogram defined by two vectors? ### Litov's Mean Value Theorem

##### Age 11 to 14Challenge 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 14Challenge 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 16Challenge 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 14Challenge 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 14Challenge 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 16Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice? ### Arithmagons

##### Age 11 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges? ### Painted Cube

##### Age 14 to 16Challenge 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 14Challenge 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 14Challenge 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 14Challenge 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 14Challenge 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 14Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge... ### Number Pyramids

##### Age 11 to 14Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change? ### Pair Products

##### Age 14 to 16Challenge 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 14Challenge 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 14Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers? ##### Age 11 to 14Challenge 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 16Challenge 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 16Challenge 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 14Challenge 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 14Challenge 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 14Challenge 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 16Challenge 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 14Challenge Level

Can you find sets of sloping lines that enclose a square? ### Where Can We Visit?

##### Age 11 to 14Challenge 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 16Challenge 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 16Challenge 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 16Challenge Level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid? ### Plus Minus

##### Age 14 to 16Challenge Level

Can you explain the surprising results Jo found when she calculated the difference between square numbers? ### Odd Differences

##### Age 14 to 16Challenge Level

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = nÂ² Use the diagram to show that any odd number is the difference of two squares. ### Summing Consecutive Numbers

##### Age 11 to 14Challenge 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 14Challenge 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 14Challenge Level

Is there an efficient way to work out how many factors a large number has? ### Have You Got It?

##### Age 11 to 14Challenge Level

Can you explain the strategy for winning this game with any target?