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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 ?

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 ?.

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?

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.

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 Technique: Triangular Arrays by Turning Off Zeros

Stage: 3 and 4 Challenge Level:

Learn how to use Excel to create triangular arrays.

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: 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: 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: Logic Tests

Stage: 3 and 4 Challenge Level:

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

Excel Technique: LCM & HCF (or GCD)

Stage: 3 and 4 Challenge Level:

Learn how to use the Excel functions LCM and GCD.

Excel Technique: LOOKUP Functions

Stage: 3 and 4 Challenge Level:

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

Excel Technique: Conditional Formatting

Stage: 3 and 4 Challenge Level:

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

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 ?

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?

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.

Excel Technique: Composite Bar Charts

Stage: 3 and 4 Challenge Level:

Learn how to use composite bar charts in Excel.

Stage: 3 and 4 Challenge Level:

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

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?

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: Target Decimal

Stage: 3 and 4 Challenge Level:

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

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: 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.

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?

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: Inserting an Increment Button

Stage: 3 and 4 Challenge Level:

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

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.

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.

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. . . .

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 ?

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level:

How much peel does an apple have?

Peaches in General

Stage: 4 Challenge Level:

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

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 Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

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

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.

Stage: 4 Challenge Level:

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

Excel Interactive Resource: Long Multiplication

Stage: 3 and 4 Challenge Level:

Use an Excel spreadsheet to explore long multiplication.

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.

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 Interactive Resource: Multiples Chain

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to investigate factors and multiples.

Excel Interactive Resource: Fraction Addition & Fraction Subtraction

Stage: 3 and 4 Challenge Level:

Use Excel to practise adding and subtracting fractions.