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##### Other tags that relate to Peeling the Apple or the Cone That Lost Its Head
Biology. Physics. Engineering. Maths Supporting SET. Investigations. Non Euclidean Geometry. Spreadsheets. Surface and surface area. Chemistry. Spheres, cylinders & cones.

### Peeling the Apple or the Cone That Lost Its Head

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

How much peel does an apple have?

### There's Always One Isn't There

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

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

### Take Ten Sticks

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

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

### Funnel

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

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

### The Legacy

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

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

### Cola Can

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

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

### Excel Technique: Logic Tests

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

Learn how to use logic tests to create interactive resources using Excel.

### Excel Investigation: Fraction Combinations

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

Choose four numbers and make two fractions. Use an Excel spreadsheet to investigate their properties. Can you generalise?

### Excel Investigation: Target Decimal

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

Use an Excel spreadsheet to approximate a decimal using trial and improvement.

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

Use Excel to investigate remainders and divisors. Was your result predictable?

### Excel Technique: LCM & HCF (or GCD)

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

Learn how to use the Excel functions LCM and GCD.

### Excel Investigation: Multiples of Three

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

Use Excel to investigate digit sums of multiples of three. Can you explain your findings?

### Excel Technique: LOOKUP Functions

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

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

### Excel Investigation: Pascal Multiples

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

This spreadsheet highlights multiples of numbers up to 20 in Pascal's triangle. What patterns can you see?

### Excel Investigation: Number Pyramids

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

Use Excel to create some number pyramids. How are the numbers in the base line related to each other? Investigate using the spreadsheet.

### Excel Technique: Triangular Arrays by Turning Off Zeros

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

Learn how to use Excel to create triangular arrays.

### Excel Investigation: Happy Numbers

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

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

### Excel Technique: Composite Bar Charts

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

Learn how to use composite bar charts in Excel.

### Excel Investigation: Ring on a String

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

This investigation uses Excel to optimise a characteristic of interest.

### Excel Technique: Conditional Formatting

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

Learn how to use conditional formatting to create attractive interactive spreadsheets in Excel.

### Excel Investigation: Pythagorean Triples

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

Use Excel to find sets of three numbers so that the sum of the squares of the first two is equal to the square of the third.

### Pythagoras’ Comma

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

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

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

A heap of beads was shared out by a professional bead sharer. Use the information given to find out how many beads there were at the start.

### Time of Birth

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

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

### Excel Technique: Making a Table for a Function of Two Independent

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

Learn how to make a simple table using Excel.

### Training Schedule

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

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

### Excel Interactive Resource: Make a Copy

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

Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.

### Excel Technique: Inserting an Increment Button

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

Learn how to use increment buttons and scroll bars to create interactive Excel resources.

### Excel Investigation: Power Crazy

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

When is 7^n + 3^n a multiple of 10? Use Excel to investigate, and try to explain what you find out.

### Getting to Know Excel

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

A number of useful techniques that can extend your use of Excel.

### Excel Investigation: Planks

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

I have an unlimited supply of planks, of lengths 7 and 9 units. Putting planks end to end, what total lengths can be achieved? Use Excel to investigate.

### Excel Investigation: Difference Tuples

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

Use an Excel spreadsheet to investigate differences between four numbers. Which set of start numbers give the longest run before becoming 0 0 0 0?

### Excel Investigation: the Difference of Two (same) Powers

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

If you take two integers and look at the difference between the square of each value, there is a nice relationship between the original numbers and that difference. Can you find the pattern using. . . .

### Euler's Squares

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

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

### What's the Weather Like?

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

With access to weather station data, what interesting questions can you investigate?

### The Fire-fighter's Car Keys

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

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

### Sending a Parcel

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

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

### Zeller's Birthday

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

What day of the week were you born on? Do you know? Here's a way to find out.

### Peaches in General

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

It's like 'Peaches Today, Peaches Tomorrow' but interestingly generalized.

### Unusual Long Division - Square Roots Before Calculators

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

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?

### 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.

### Minus One Two Three

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

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

### Excel Interactive Resource: Multiples Chain

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

Use an interactive Excel spreadsheet to investigate factors and multiples.

### Negative Power

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

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

### Excel Interactive Resource: Haitch

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

An Excel spreadsheet with an investigation.

### Small Change

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

In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?

### 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...

### Excel Interactive Resource: Fraction Multiplication

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

Use Excel to explore multiplication of fractions.