# Resources tagged with: Generalising

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Broad Topics > Mathematical Thinking > Generalising ### 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? ### Cuisenaire Squares

##### 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? ### 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? ### 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. ### Circles, Circles

##### Age 5 to 11 Challenge Level:

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? ### 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? ### Taking Steps

##### Age 7 to 11 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue. ### 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. ### 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"? ### Route to Infinity

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

Can you describe this route to infinity? Where will the arrows take you next? ### Steps to the Podium

##### Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns! ### Centred Squares

##### Age 7 to 11 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'. ### Sliding Puzzle

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

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves. ### 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. ### Hidden Rectangles

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard? ### Cunning Card Trick

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

Delight your friends with this cunning trick! Can you explain how it works? ### 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? ### 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? ### Christmas Chocolates

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

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes? ### 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? ### Tower of Hanoi

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

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice. ### Finding 3D Stacks

##### Age 7 to 11 Challenge Level:

Can you find a way of counting the spheres in these arrangements? ### 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? ### 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 ...? ### 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? ### Dotty Triangles

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

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw? ### 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? ### Tumbling Down

##### Age 7 to 11 Challenge Level:

Watch this animation. What do you see? Can you explain why this happens? ### 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. ### 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! ### 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? ### 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? ### 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? ### Cuboid Challenge

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

What's the largest volume of box you can make from a square of paper? ### 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? ### 2001 Spatial Oddity

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

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done. ### 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? ### 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? ### 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. ### More Number Pyramids

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

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

##### Age 7 to 11 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions. ### 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? ### 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? ### 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 ### Arithmagons

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

Can you find the values at the vertices when you know the values on the edges? ### 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? ### 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? ### Spirals, Spirals

##### Age 7 to 11 Challenge Level:

Here are two kinds of spirals for you to explore. What do you notice? ### 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. ### Keep it Simple

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

Can all unit fractions be written as the sum of two unit fractions?