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#### Resources tagged with Generalising similar to Mixing More Paints:

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### There are 125 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising

### All Tangled Up

##### Stage: 3 Challenge Level:

Can you tangle yourself up and reach any fraction?

### How Much Can We Spend?

##### Stage: 3 Challenge Level:

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

### Handshakes

##### Stage: 3 Challenge Level:

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

### Keep it Simple

##### Stage: 3 Challenge Level:

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

### More Twisting and Turning

##### Stage: 3 Challenge Level:

It would be nice to have a strategy for disentangling any tangled ropes...

### Harmonic Triangle

##### Stage: 3 Challenge Level:

Can you see how to build a harmonic triangle? Can you work out the next two rows?

### Arithmagons

##### Stage: 3 Challenge Level:

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

### Searching for Mean(ing)

##### Stage: 3 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

### Litov's Mean Value Theorem

##### Stage: 3 Challenge Level:

Start with two numbers. This is the start of a sequence. The next number is the average of the last two numbers. Continue the sequence. What will happen if you carry on for ever?

### Number Pyramids

##### Stage: 3 Challenge Level:

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

### Sum Equals Product

##### Stage: 3 Challenge Level:

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .

### Pick's Theorem

##### Stage: 3 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.

##### Stage: 3 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. . . .

### Shear Magic

##### Stage: 3 Challenge Level:

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

### Picturing Square Numbers

##### Stage: 3 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

### Multiplication Square

##### Stage: 3 Challenge Level:

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

### Mirror, Mirror...

##### Stage: 3 Challenge Level:

Explore the effect of reflecting in two parallel mirror lines.

### Triangle Numbers

##### Stage: 3 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?

### Enclosing Squares

##### Stage: 3 Challenge Level:

Can you find sets of sloping lines that enclose a square?

### Painted Cube

##### Stage: 3 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?

### Summing Consecutive Numbers

##### Stage: 3 Challenge Level:

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### Lower Bound

##### Stage: 3 Challenge 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 =

### Partitioning Revisited

##### Stage: 3 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

### Make 37

##### Stage: 2 and 3 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

### Frogs

##### Stage: 2 and 3 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### Tilted Squares

##### Stage: 3 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

### Go Forth and Generalise

##### Stage: 3

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.

### Consecutive Negative Numbers

##### Stage: 3 Challenge Level:

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

### Christmas Chocolates

##### Stage: 3 Challenge Level:

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

### Intersecting Circles

##### Stage: 3 Challenge Level:

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

##### Stage: 3 Challenge 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. . . .

### What Numbers Can We Make?

##### Stage: 3 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

### Squares in Rectangles

##### Stage: 3 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?

### ...on the Wall

##### Stage: 3 Challenge Level:

Explore the effect of reflecting in two intersecting mirror lines.

### Who Is the Fairest of Them All?

##### Stage: 3 Challenge Level:

Explore the effect of combining enlargements.

### Steps to the Podium

##### Stage: 2 and 3 Challenge Level:

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

### For Richer for Poorer

##### Stage: 3 Challenge Level:

Charlie has moved between countries and the average income of both has increased. How can this be so?

### Adding in Rows

##### Stage: 3 Challenge Level:

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

### Dicing with Numbers

##### Stage: 3 Challenge 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?

### Where Can We Visit?

##### Stage: 3 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?

### Masterclass Ideas: Generalising

##### Stage: 2 and 3 Challenge Level:

A package contains a set of resources designed to develop pupils’ mathematical thinking. This package places a particular emphasis on “generalising” and is designed to meet the. . . .

### 2001 Spatial Oddity

##### Stage: 3 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.

### Cuboid Challenge

##### Stage: 3 Challenge Level:

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

### One O Five

##### Stage: 3 Challenge Level:

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

### Egyptian Fractions

##### Stage: 3 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.

### Chocolate Maths

##### Stage: 3 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

### Converging Means

##### Stage: 3 Challenge 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. . . .

### Mini-max

##### Stage: 3 Challenge Level:

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

### Semi-square

##### Stage: 4 Challenge 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?

### Cubes Within Cubes Revisited

##### Stage: 3 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?