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

##### Stage: 4 Challenge Level:

How much peel does an apple have?

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

##### Stage: 4 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

##### Stage: 3 and 4 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?

### The Legacy

##### Stage: 4 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?

### Funnel

##### Stage: 4 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 ?

### Excel Technique: Logic Tests

##### Stage: 3 and 4 Challenge Level:

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

### Excel Technique: LOOKUP Functions

##### Stage: 3 and 4 Challenge Level:

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

### Excel Investigation: Happy Numbers

##### Stage: 3 and 4 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: Using Paste Special to Lift a Copy of Values

##### Stage: 3 and 4 Challenge Level:

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

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

##### Stage: 3 and 4 Challenge Level:

Learn how to use the Excel functions LCM and GCD.

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

##### Stage: 3 and 4 Challenge Level:

Learn how to use Excel to create triangular arrays.

### Excel Investigation: Fraction Combinations

##### Stage: 3 and 4 Challenge Level:

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

### Excel Technique: Conditional Formatting

##### Stage: 3 and 4 Challenge Level:

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

### Excel Investigation: Ring on a String

##### Stage: 3 and 4 Challenge Level:

This investigation uses Excel to optimise a characteristic of interest.

### Cola Can

##### Stage: 3 Challenge Level:

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

### Training Schedule

##### Stage: 4 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 Technique: Composite Bar Charts

##### Stage: 3 and 4 Challenge Level:

Learn how to use composite bar charts in Excel.

### Patio

##### Stage: 3 Challenge Level:

A square patio was tiled with square tiles all the same size. Some of the tiles were removed from the middle of the patio in order to make a square flower bed, but the number of the remaining tiles. . . .

### Excel Investigation: Number Pyramids

##### Stage: 3 and 4 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 Investigation: Multiples of Three

##### Stage: 3 and 4 Challenge Level:

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

### Excel Investigation: Pascal Multiples

##### Stage: 3 and 4 Challenge Level:

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

### Excel Investigation: Target Decimal

##### Stage: 3 and 4 Challenge Level:

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

### Pythagoras’ Comma

##### Stage: 4 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.

##### Stage: 3 and 4 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.

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

##### Stage: 3 and 4 Challenge Level:

Learn how to make a simple table using Excel.

### Excel Investigation: Pythagorean Triples

##### Stage: 3 and 4 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.

### Time of Birth

##### Stage: 3 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 Interactive Resource: Make a Copy

##### Stage: 3 and 4 Challenge Level:

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

### Excel Investigation: Planks

##### Stage: 3 and 4 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

##### Stage: 3 and 4 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?

### Getting to Know Excel

##### Stage: 3 and 4 Challenge Level:

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

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

##### Stage: 3 and 4 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. . . .

### Excel Investigation: Power Crazy

##### Stage: 3 and 4 Challenge Level:

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

### Excel Technique: Inserting an Increment Button

##### Stage: 3 and 4 Challenge Level:

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

### Odd Differences

##### Stage: 4 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

##### Stage: 4 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 ?

### Unusual Long Division - Square Roots Before Calculators

##### Stage: 4 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?

### What's the Weather Like?

##### Stage: 3 Challenge Level:

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

### Substitution Cipher

##### Stage: 3 Challenge Level:

Find the frequency distribution for ordinary English, and use it to help you crack the code.

### Zeller's Birthday

##### Stage: 4 Challenge Level:

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

### Sending a Parcel

##### Stage: 3 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?

### Excel Interactive Resource: Fraction Multiplication

##### Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

### The Fire-fighter's Car Keys

##### Stage: 4 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 ?.

### Peaches in General

##### Stage: 4 Challenge Level:

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

##### Stage: 4 Challenge Level:

If a sum invested gains 10% each year how long before it has doubled its value?

### Excel Interactive Resource: Equivalent Fraction Bars

##### Stage: 3 and 4 Challenge Level:

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

### Excel Interactive Resource: Haitch

##### Stage: 3 and 4 Challenge Level:

An Excel spreadsheet with an investigation.

### Excel Interactive Resource: Long Multiplication

##### Stage: 3 and 4 Challenge Level:

Use an Excel spreadsheet to explore long multiplication.