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### Peaches in General

##### Age 14 to 16Challenge Level

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

### Unusual Long Division - Square Roots Before Calculators

##### Age 14 to 16Challenge 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?

##### Age 14 to 16Challenge Level

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

### Training Schedule

##### Age 14 to 16Challenge 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?

### Time of Birth

##### Age 11 to 14Challenge 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?

### Litov's Mean Value Theorem

##### Age 11 to 14Challenge Level

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

### Odd Differences

##### Age 14 to 16Challenge 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.

### Excel Investigation: Target Decimal

##### Age 11 to 16Challenge Level

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

### Minus One Two Three

##### Age 14 to 16Challenge 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 Investigation: Fraction Combinations

##### Age 11 to 16Challenge Level

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

### Excel Technique: Logic Tests

##### Age 11 to 16Challenge Level

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

### The Legacy

##### Age 14 to 16Challenge 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?

### Excel Technique: LOOKUP Functions

##### Age 11 to 16Challenge Level

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

### Excel Investigation: Ring on a String

##### Age 11 to 16Challenge Level

This investigation uses Excel to optimise a characteristic of interest.

### Excel Investigation: Happy Numbers

##### Age 11 to 16Challenge 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: Triangular Arrays by Turning Off Zeros

##### Age 11 to 16Challenge Level

Learn how to use Excel to create triangular arrays.

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

##### Age 11 to 16Challenge Level

Learn how to use the Excel functions LCM and GCD.

### Excel Technique: Composite Bar Charts

##### Age 11 to 16Challenge Level

Learn how to use composite bar charts in Excel.

### Excel Investigation: Pascal Multiples

##### Age 11 to 16Challenge 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 16Challenge 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: Conditional Formatting

##### Age 11 to 16Challenge Level

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

### Excel Investigation: Multiples of Three

##### Age 11 to 16Challenge Level

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

##### Age 11 to 16Challenge Level

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

### Excel Investigation: Planks

##### Age 11 to 16Challenge 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 Technique: Inserting an Increment Button

##### Age 11 to 16Challenge Level

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

##### Age 11 to 16Challenge 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

##### Age 11 to 16Challenge Level

Learn how to make a simple table using Excel.

### Excel Interactive Resource: Make a Copy

##### Age 11 to 16Challenge Level

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

### Negative Power

##### Age 14 to 16Challenge Level

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

### Pythagoras’ Comma

##### Age 14 to 16Challenge 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.

### Excel Investigation: Difference Tuples

##### Age 11 to 16Challenge 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: Power Crazy

##### Age 11 to 16Challenge Level

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

### Take Ten Sticks

##### Age 11 to 16Challenge 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?

### Zeller's Birthday

##### Age 14 to 16Challenge Level

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

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

##### Age 11 to 16Challenge 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. . . .

### Getting to Know Excel

##### Age 11 to 16Challenge Level

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

### Excel Investigation: Pythagorean Triples

##### Age 11 to 16Challenge 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.

### Euler's Squares

##### Age 14 to 16Challenge Level

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

### Tree Tops

##### Age 14 to 16Challenge Level

Can you make sense of information about trees in order to maximise the profits of a forestry company?

### The Fire-fighter's Car Keys

##### Age 14 to 16Challenge 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 ?.

### Under the Ribbon

##### Age 14 to 16Challenge Level

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

### Excel Interactive Resource: Interactive Division

##### Age 11 to 16Challenge Level

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

### Excel Interactive Resource: Number Grid Functions

##### Age 11 to 16Challenge Level

Use Excel to investigate the effect of translations around a number grid.

### Excel Interactive Resource: the up and Down Game

##### Age 11 to 16Challenge Level

Use an interactive Excel spreadsheet to explore number in this exciting game!

### Excel Interactive Resource: Equivalent Fraction Bars

##### Age 11 to 16Challenge Level

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

### Excel Interactive Resource: Long Multiplication

##### Age 11 to 16Challenge Level

Use an Excel spreadsheet to explore long multiplication.

### Excel Interactive Resource: Multiples Chain

##### Age 11 to 16Challenge Level

Use an interactive Excel spreadsheet to investigate factors and multiples.

### Excel Interactive Resource: Fraction Addition & Fraction Subtraction

##### Age 11 to 16Challenge Level

Use Excel to practise adding and subtracting fractions.