Online Investigations

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Welcome to hours of mathematical enjoyment!

(Ages 8-11): How do Percentages Work? (FREE!)

Use a metre stick to recap on what tenths (p2) and hundredths (p4) of a metre are as decimals. Explain the equivalence between one hundredth and 1% (p7) and extend the pattern to other hundredths such as 0.04 = 4% (p9).

Recap on the location of 0.1m on the metre stick and extablish the equivalence with 10% (p12). Explore other equivalences such as 0.3m = 30% (p14).

Recap on the decimal equivalences for quarters of a metre (p17) and investigate the percentage equivalences (p19).

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(Ages 8-11): Easy Percentages of Harder Numbers (FREE!)

Explore how to find 50%, 25% and 75% of 2-digit numbers and then three digit multiples of 10 using doubling and halving skills.

First recap on the meaning of 100%, 50%, 25% and 75% (p1). Then use halving to find 50% of various numbers (p4) then halve 50% to find 25% (p8). Finally explore alternative ways of finding 75% (p12).

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(Ages 9-12): Fractions, Decimals, Percentages and Factors of 100 (FREE!)

Recap on factors of 100 (p2), and create the factor rainbow for 100 (p4). Using a metre stick, discuss unit fractions and consider which can be changed easily to decimals or percentages (p5).

Explore the decimal and percentage equivalents for 1/2, 1/4 and 1/10 (p6). Then consider how 1/5 (p9) and 1/20 (p10) compare with 1/10 and what the equivalences will be. Link these facts to the factor rainbow (p13). Next explore 1/100, 1/50 and 1/25 (p14).

Discuss paired number facts such as 20%=1/5 and 5%=1/20 (p15). Finally consolidate all the facts explored (p20).

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(Ages 9-12): Change between Tricky Decimals and Percentages (FREE!)

Explore how to convert 2, 3 or 4 place decimals to percentages, and what happens with percentages beyond 100%.

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(Ages 9-12): Fractions to Percentages Using Factors of 100 (FREE!)

This activity closely parallels Change Straightforward Fractions to Decimals (above). It uses a metre stick to explore fraction-percentage equivalences where the denominator is a factor of 100.

Use the stick to first recap on the percentage equivalvents for ¼ and ¾ (p4). Explore different numbers of tenths in the same way (p6), next explore fifths (p10) and then look at the equivalences between tenths and fifths and percentages (p13).

Continuing to use the metre stick as a visual aid, move on to investigate different numbers of twentieths (p14), then twenty-fifths (p17) and finally fiftieths (p20).

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(Ages 10-13): Find Any Percentage of a Number (FREE!)

Investigate different ways of finding a percentage of a number. Explore how to use simple percentages like 10% and 1% to find 20%, 5%, 2% and 0.5%, and then move on to finding general percentages.

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(Ages 10-13): Percentage Increase and Decrease (FREE!)

Investigate how to calculate percentage increases and decreases both mentally and using a calculator.

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(Ages 10-13): The Connection between Of and Times (FREE!)

Explore the idea that multiplying by (eg) ¼ is the same as finding ¼ of something which, in turn, is the same as dividing by 4. This investigation introduces the fraction triangle, a powerful little tool for exploring this idea.

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(Ages 10-13): Expressing Things as a Fraction or Percentage: Part 1 (FREE!)

Discuss the mark 17 out of 20 in a test. Agree that this would be 17 twentieths of the total mark (p2).

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(Ages 10-13): Expressing Things as a Fraction or Percentage: Part 2 (FREE!)

Explore how to express something out of something as a percentage if the numbers do not divide exactly.

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(Ages 10-13): Change Percentages to Fractions (FREE!)

Change percentages to fractions.

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(Ages 10-13): Tricky Fractions to Decimals or Percentages - Part 1 (FREE!)

Recap on how to convert easy fractions. Investigate eighths, based on them being half of quarters. Then consider fortieths and eightieths as being ten times smaller.

Next explore examples with other denominators where you first have to simplify the fraction to create a denominator that you can handle.

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(Ages 10-13): Fraction, Decimal, Percentage Triangle Magic (FREE!)

Explore the link between finding a % of something and expressing something AS a percentage.

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(Ages 11-14): Percentage Increase & Decrease Using Scale Factors (FREE!)

Investigate quick methods for working out percentage increases and decreases using a calculator.

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(Ages 11-14): Percentage Increase & Decrease Backwards! (FREE!)

Investigate how to solve percentage increase and decrease problems that ask you to work backwards to find the starting number.

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