# Resources tagged with: Generalising

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### There are 128 results

Broad Topics > Thinking Mathematically > Generalising ### Semi-square

##### Age 14 to 16Challenge Level

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle? ### Pareq Calc

##### Age 14 to 16Challenge Level

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . . ### 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? ### Loopy

##### Age 14 to 16Challenge Level

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture? ### Areas of Parallelograms

##### Age 14 to 16Challenge Level

Can you find the area of a parallelogram defined by two vectors? ### In a Spin

##### Age 14 to 16Challenge Level

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse? ### Dotty Triangles

##### Age 11 to 14Challenge 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? ### 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. ### Converging Means

##### Age 14 to 16Challenge Level

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. . . . ### Lower Bound

##### Age 14 to 16Challenge Level

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 = ### A Tilted Square

##### Age 14 to 16Challenge Level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices? ### 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? ### Go Forth and Generalise

##### Age 11 to 14

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important. ### Tourism

##### Age 11 to 14Challenge Level

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable. ### 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? ### All Tangled Up

##### Age 14 to 18Challenge Level

Can you tangle yourself up and reach any fraction? ### 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? ### Generating Triples

##### Age 14 to 16Challenge Level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more? ### Equilateral Areas

##### Age 14 to 16Challenge Level

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF. ### AMGM

##### Age 14 to 16Challenge Level

Can you use the diagram to prove the AM-GM inequality? ##### Age 11 to 14Challenge Level

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. . . . ### Magic Squares

##### Age 14 to 18

An account of some magic squares and their properties and and how to construct them for yourself. ### Pinned Squares

##### Age 14 to 16Challenge Level

What is the total number of squares that can be made on a 5 by 5 geoboard? ### Square Pizza

##### Age 14 to 16Challenge Level

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square? ### 2001 Spatial Oddity

##### Age 11 to 14Challenge 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. ### Dicing with Numbers

##### Age 11 to 14Challenge Level

In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal? ### 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? ### For Richer for Poorer

##### Age 14 to 16Challenge Level

Charlie has moved between countries and the average income of both has increased. How can this be so? ### 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 ### Problem Solving, Using and Applying and Functional Mathematics

##### Age 5 to 18Challenge Level

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information. ### 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? ### More Number Pyramids

##### Age 11 to 14Challenge Level

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

##### Age 11 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges? ### 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?” ### 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? ### Take Three from Five

##### Age 11 to 16Challenge Level

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him? ### Harmonic Triangle

##### Age 14 to 16Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows? ### Nim-like Games

##### Age 7 to 16Challenge Level

A collection of games on the NIM theme ### Nim

##### Age 14 to 16Challenge Level

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 loser is the player who takes the last counter. ### 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. ### Jam

##### Age 14 to 16Challenge Level

A game for 2 players ### The Bridges of Konigsberg

##### Age 11 to 18Challenge Level

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg. ### 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? ### Winning Lines

##### Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games. ### 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? ### Consecutive Negative Numbers

##### Age 11 to 14Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers? ### 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? ### 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? ### Multiplication Arithmagons

##### Age 14 to 16Challenge Level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?