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Percentages for Key Stage 4

Stage: 4 Challenge Level:

A group of interactive resources to support work on percentages Key Stage 4.

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.

Excel Interactive Resource: Fraction Addition & Fraction Subtraction

Stage: 3 and 4 Challenge Level:

Use Excel to practise adding and subtracting fractions.

Excel Interactive Resource: Interactive Division

Stage: 3 and 4 Challenge Level:

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

Excel Interactive Resource: Multiples Chain

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to investigate factors and multiples.

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 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: Number Grid Functions

Stage: 3 and 4 Challenge Level:

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

Excel Interactive Resource: the up and Down Game

Stage: 3 and 4 Challenge Level:

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

Excel Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

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 ?

Stage: 4 Challenge Level:

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

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 ?.

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?

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.

Substitution Cipher

Stage: 3 and 4 Challenge Level:

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

Cola Can

Stage: 4 Challenge Level:

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

Negative Power

Stage: 4 Challenge Level:

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

Succession in Randomia

Stage: 5 Challenge Level:

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?

Farey Approximation

Stage: 5 Short Challenge Level:

Use Farey sequences to obtain rational approximations to irrational numbers.

Any Win for Tennis?

Stage: 5 Challenge Level:

What are your chances of winning a game of tennis?

What's the Weather Like?

Stage: 3 and 4 Challenge Level:

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

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: Conditional Formatting

Stage: 3 and 4 Challenge Level:

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

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?

Peaches in General

Stage: 4 Challenge Level:

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

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.

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level:

How much peel does an apple have?

Excel Investigation: Ring on a String

Stage: 3 and 4 Challenge Level:

This investigation uses Excel to optimise a characteristic of interest.

Excel Technique: Composite Bar Charts

Stage: 3 and 4 Challenge Level:

Learn how to use composite bar charts in Excel.

Time to Evolve 2

Stage: 5 Challenge Level:

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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?

Euler's Squares

Stage: 4 Challenge Level:

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

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.

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 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 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.

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.

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. . . .

Getting to Know Excel

Stage: 3 and 4 Challenge Level:

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

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?

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.

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 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.

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.

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.

Excel Investigation: Target Decimal

Stage: 3 and 4 Challenge Level:

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