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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. Three of the numbers that he found are a = 18530, b=65570, c=45986. Find the fourth number, x. You. . . .

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.

Stage: 4 Challenge Level:

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

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?

Excel Interactive Resource: Multiples Chain

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to investigate factors and multiples.

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 Interactive Resource: Haitch

Stage: 3 and 4 Challenge Level:

An Excel spreadsheet with an investigation.

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: Number Grid Functions

Stage: 3 and 4 Challenge Level:

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

Excel Interactive Resource: Fraction Addition & Fraction Subtraction

Stage: 3 and 4 Challenge Level:

Use Excel to practise adding and subtracting fractions.

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.

Percentages for Key Stage 4

Stage: 4 Challenge Level:

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

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 ?

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: Long Multiplication

Stage: 3 and 4 Challenge Level:

Use an Excel spreadsheet to explore long multiplication.

Excel Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

Litov's Mean Value Theorem

Stage: 3 Challenge Level:

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

Small Change

Stage: 3 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?

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.

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. . . .

Under the Ribbon

Stage: 4 Challenge Level:

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

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?

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 ?

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?

Peaches in General

Stage: 4 Challenge Level:

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

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 ?.

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?

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 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: 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?

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?

Excel Technique: Composite Bar Charts

Stage: 3 and 4 Challenge Level:

Learn how to use composite bar charts in Excel.

Excel Technique: Conditional Formatting

Stage: 3 and 4 Challenge Level:

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

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?

What's the Weather Like?

Stage: 3 and 4 Challenge Level:

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

Excel Investigation: Ring on a String

Stage: 3 and 4 Challenge Level:

This investigation uses Excel to optimise a characteristic of interest.

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level:

How much peel does an apple have?

Excel Investigation: Target Decimal

Stage: 3 and 4 Challenge Level:

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

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 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: 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.

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.

Substitution Cipher

Stage: 3 and 4 Challenge Level:

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

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.

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?

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 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.