Online Investigations

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Welcome to hours of mathematical enjoyment!

(Ages 7-10): How Decimals Work - Tenths (FREE!)

Explore the key ideas behind how decimals work using a counting stick.

Explore that idea that each whole metre is divided into ten bits. Each bit is one tenth of a metre. A tenth of a metre is also called a decimetre. (dec = 10 - decade, decimal etc) Introduce the idea that a measurement can be written as a whole number of metres, followed by a decimal followed by the number of bits (tenths). Explore the different ways of writing one tenth (1/10 and 0.1), two tenths etc. Explore mixed numbers with tenths. (12 tenths = 1 & 2 tenths = 1.2 etc.)

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(Ages 7-10): Decimal Halves (FREE!)

Recap that a 1 metre counting stick is divided 10 tenths (p1) and that this can be written as 0.5 (p2).

Use multiple sticks to establish what happens when you count in 0.5s (p5), by adding half a stick each time. Explore the equivalences of these decimals with mixed numbers (2.5 = 2½ etc)(p7) and with improper fractions (3 halves = 1.5 etc)(p9).

Investigate what happens when you multiply 0.5 by 2, 3, 4, 5 etc (p15).

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(Ages 7-10): Decimal Tenths and Halves (FREE!)

Draw a line on the board from zero to 1 and ask if there are numbers in between. Discuss ½, 0.5 etc as appropriate.

Discuss where you would cut to chop a metre stick in into tenths and what these would be as decimals (0.1m, 0.2m etc). Count in 0.1s and explore equivalences between decimal tneths of metres and centimetres (eg 1.9m = 190cm etc).

Recap on where you would cut to chop a metre stick in half, and that ½m = 50cm.

Use two metre sticks to explore that 1½m = 150cm. Recap that ½ = 0.5 and explore 1½ = 1.5. Then explore equivalences between decimal half metres and centimetres (eg 1.5m = 150cm etc).

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(Ages 7-10): Metres and Centimetres with Many Tenths (FREE!)

Explore the link between metres, centimetres and tenths beyond one whole metre.

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(Ages 7-10): Add and Subtract 0.5 (FREE!)

Explore what happens when you add or subtract 0.5 to and from other numbers.

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(Ages 7-10): Add and Subtract 0.1 (FREE!)

Explore what happens when you add or subtract 0.1 to and from whole numbers and other unit decimals.

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(Ages 8-11): How Decimals Work - Hundredths (FREE!)

Explore the second place of decimals using a counting stick.

Recap the idea that each whole metre is divided into ten bits. Note that each bit (tenth) can be divided into ten little pieces. These are called hundredths and are also called centimetres. (cent = 100 - century, centipede etc) Explore the different ways of writing one hundredth (1/100 and 0.01), two hundredths etc. Explore how measurements can be written as a whole number of metres, followed by a decimal followed by the number of bits (tenths) and then the number of little pieces (hundredths).

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(Ages 8-11): Divide and Multiply by 10 with Decimals - Part 1 (FREE!)

Explore what happens if you try to divide a number by 10. Learn the rule for moving numbers relative to the decimal point.

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(Ages 8-11): Tenths, Hundredths and Decimals Bigger than 1 (FREE!)

Use a metre stick to explore where 1 tenth, 3 tenths and 5 tenths would be and what these would be as decimals (p2). Consider whether you could get 12 tenths. What would this be as a decimal (p4)? Investigate other numbers of tenths (p6).

Consider where 1 hundredth, 3 hundredths and 8 hundredths would be and what these would be as decimals (p7). What would 16 hundredths be (p9)? Consider whether you could get 16 hundredths. What about other numbers of hundredths (p11)?

Consider whether you could get 120 hundredths. What would this be as a decimal (p12)?

Investigate other numbers of tenths (p15) and hundredths (p16).

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(Ages 8-11): Decimal Tenths, Hundredths and Quarters (FREE!)

Use a metre stick to consolidate learning about tenths and hundredths and use this to explore decimal equivalences for halves and quarters.

Use a metre stick to recap on tenths and hundredths. Establish the position of 0.1, 0.2 etc and 0.05, 0.15, 0.25 etc. Turn the stick over and put blu-tac on the back to show where the halves and quarters would be. Recap that ¼m= 25cm etc. Establish that this would be 0.25m using decimals. What about ¾?

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(Ages 8-11): Decimals for Many Halves and Quarters (FREE!)

Revise basic facts (½ = 0.5, ¼ = 0.25 etc). Then build on these to explore decimal equivalences for larger numbers of halves and quarters.

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(Ages 8-11): Decimal Fifths and Twentieths (FREE!)

Explore how fifths and twentieths work with decimals.

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(Ages 8-11): Change Fifths and Twentieths to Decimals (FREE!)

Use a metre stick to consider how 1 fifth compares with 1 tenth. What would the decimal equivalents be for 1 fifth, two fifths and three fifths? (p4). Consider whether you could get 6 fifths. What would this be as a decimal (p6)? Investigate other numbers of fifths (p8).

Consider how 1 twentieth compares with 1 tenth. What would the decimal equivalents be for 1 twentieth, two twentieths and three twentieths? (p11). What about larger numbers of twentieths (p13)? Consider whether you could get 21 twentieths or 24 twentieths (p14). What about other numbers of twentieths (p16)?

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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 Decimals Using Factors of 100 (FREE!)

This activity builds on Fractions, Decimals, Percentages and Factors of 100 (above). It uses a metre stick to explore fraction-decimal equivalences where the denominator is a factor of 100.

Use the stick to first recap on the decimal 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 decimals (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 9-12): Metres, Centimetres, Millimetres with Decimals (FREE!)

Use a metre stick and explore patterns to help with decimal metric conversions within 1 metre.

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(Ages 9-12): Multiply and Divide Decimals by 10, 100, 1000 (FREE!)

Build understanding step by step from simple examples (6 x 10) to more complicated ones (0.22 x 1000).

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(Ages 10-13): Fractions, Division and Decimal Equivalents (FREE!)

Discover the amazing fact that ½ = 1 ÷ 2 = 0.5, ¾ = 3 ÷ 4 = 0.75 and go on to explore what happens with other fractions.

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(Ages 10-13): Mixed Metric Equivalences with Decimals (FREE!)

Establish that milli-metres/litres/grams are 1000 times smaller than metres/litres/grams and kilm-oetres/grams are 1000 times larger. Consolidate the understanding that since millimetres are smaller you will need more of them, km are larger so you will need fewer. Explore the idea that changing between these measurements is then just a matter of multipiying or dividing by 1000, by moving numbers relative to the position of the decimal point.

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

Change percentages to fractions.

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

Change decimals to fractions.

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(Ages 10-13): How Can Multiplication Make Things Smaller? (FREE!)

Investigate how multiplying by certain numbers (eg 0.5, 0.1, 0.2, a half, a tenth, a fifth etc) makes a number smaller.

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(Ages 10-13): How Can Division Make Things Bigger? (FREE!)

Investigate why some divisions give answers that are larger than the starting number.

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(Ages 10-13): Multiply and Divide by a Decimal (FREE!)

Weird things start to happen when you multiply and divide by decimals. Things that should get bigger get smaller!

Investigate how to multiply and divide by 0.1 and by 0.01. Then go on to investigate multiplying and dividing by other easy decimals such as 0.2, 0.02, 0.4, 0.04, 0.5, 0.05

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(Ages 11-14): Recurring Decimals and Fractions (FREE!)

Investigate the patterns of digits in recurring decimals arising through division and how this links to fractions decimal equivalences.

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(Ages 11-14): Tricky Fractions to Decimals or Percentages - Part 2 (FREE!)

Recap on how to divide 8 by 5 and 5 by 8. Explore how changing thirds to decimals by dividing gives a recurring answer. Repeat with sixths and ninths.

Next explore 30ths, 60ths, 15ths, 90ths and 18ths.

Finally look at fractions like 29ths using a calculator!

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