Online Investigations

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Welcome to hours of mathematical enjoyment!

(Ages 5-8): Finding Half of Even Numbers (FREE!)

Explore how to find half of 8 by splitting 8 counters into two groups (p2). Explore the two different ways of writing this: 8 ÷ 2 = 4 (p3) and ½ of 8 = 4 (p4). Discuss 12 counters in the same way (pp7/8/9) and then investigate patterns with missing numbers (p12).

Set the children to find half of some other numbers (p5,6,10,11,13) and investigate examples and patterns of their own (pp14/15).

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(Ages 5-8): Double and Half Small Numbers (FREE!)

Explore doubling first by looking at the idea of 2 lots of (p2), at then at multiplying by 2 (p6). Next look at halving (p10) and how this is the same as dividing by 2 (p14). Along the way, practise each of the four skills using numbers within 20, including missing number problems.

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(Ages 6-9): Double and Half with Multiples of Ten (FREE!)

Explore how to double multiples of ten building on knowledge of simple doubles facts. Extend to halving where the answer is a multiple of ten.

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(Ages 6-9): Finding Halves of Numbers to 100 (FREE!)

Explore how to find halves of simple numbers using doubles facts in reverse.

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(Ages 6-9): Quartering Numbers in the 4x Table (FREE!)

Make sure you are confident with the 4x table before you try this one!

Explore how to find a quarter of 12 by splitting 12 counters into four groups (p2). Explore the two different ways of writing this: 12 ÷ 4 = 3 (p3) and ¼ of 12 = 3 (p4).

Build a pattern dividing numbers by 4 and note the link with the 4x table (p5). Discuss the two different ways of quartering mentally: either halving and halving again or dividing by 4 (p6).

Set the children to find a quarter of some other numbers (pp7/8/9), explore patterns and problems with missing numbers (pp10/11/12) and investigate examples and patterns of their own (pp13/14).

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(Ages 6-9): Fractions of Twelve (FREE!)

Work with 12 counters to explore what happens when you divide them into two groups (halves) (p2) and then four groups (quarters) (p4). Discuss the idea of one quarter, two quarters three quarters and four quarters of twelve (p6). Practise with mixed examples. Investigate thirds (p9) and then sixths (p14) of twelve in the same way.

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(Ages 7-10): Finding Quarters with Remainders (FREE!)

Builds on Finding Quarters, looking first at quartering larger numbers and then at quartering numbers that do not quarter!

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(Ages 7-10): Counting with Halves (FREE!)

Get a metre stick, turn it over to the blank side and discuss where the half metre point is. Mark it with blu-tac. Discuss the fact that two halves make one whole. Explore how to write one half (½), two halves, zero halves.

Can you get three halves? What about four halves? Introduce a second metre stick and put them end to end. Explore! Then get bits of paper and write on the numbers 0, ½, 1, 1½, 2, 2½ etc.

Draw a line on the board. Mark 0 at one end and 4 at the other. Ask the children if there are any numbers in between. (See Numbers between Numbers for a full development of this idea.) Through discussion, mark on ½, 1, 1½, 2, 2½ etc and explore the equivalences with 3/2, 4/2, 5/2 etc.

Consider what happens if you start at 0 and keep adding ½. Then try counting backwards. Discuss how you could show how many halves you would need to make different numbers using the multiplication sign (se pp12/13).

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(Ages 7-10): Metres and Centimetres with Two Kinds of Halves (FREE!)

Investigate half metres and their equivalences with centimetres using a metre stick.

Turn the stick over and put blu-tac on the back to show where half a metre is. Discuss what numbers of centimetres will match with this. Check. Can you get three halves? What about four? Use a second metre stick to investigate. Discuss different ways of expressing fractions (three halves = one and a half 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): 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): Find Unit Fractions using Multiplication Facts (FREE!)

Consolidate the link between finding ½ and dividing by 2, and between finding ¼ and dividing by 4. Then explore how to find one third, one fifth and other unit fractions.

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

Investigate where you would have to cut to chop a metre stick into 2 equal pieces (halves), ten equal pieces (tenths) and five equal pieces (fiths).

Through discussion/investigation establish the fact one tenth is smaller than one half; one fifth is bigger than one tenth.

Discuss how you can use the centimetre equivalents for different fractions to compare their sizes and then investigate equivalences between halves, fifths and tenths of 1 metre.

This investigation builds nicely on Counting in 20s. (see Counting section)

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

Explore the links between tenths, fifths and decimals on a metre stick.

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(Ages 8-11): Equivalent Fractions for Halves and Quarters: Part 1 (FREE!)

Use fractions strips to explore families of fractions that are equivalent to one half and one quarter.

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(Ages 8-11): Half 3-digit multiples of 10 (FREE!)

Explore how to use the skill of halving 2-digit numbers such as 74 to halve 3 digit numbers such as 740.

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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): Find a Fraction of a Whole Number (without remainders) (FREE!)

Investigate how to find any fraction of a number. Start by exploring quarters and fifths. Then move on to tenths and eighths. Use the open-ended pages to explore fractions with other denominators.

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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): 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): Equivalent Fractions for Fifths (FREE!)

Use fraction strips to explore the different fractions that are equivalent to one fifth, two fifths, three fifths etc.

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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): Halves, Fifths and Tenths on a Number Line (FREE!)

Investigate the sequence of fifths and tenths between zero and one and then continue into improper fractions.

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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): 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): 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): 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): 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): Twentieths, Twenty-fifths and Fiftieths on a Number Line (FREE!)

Challenge pupils to sequence fractions on a number line. Revise tenths and fifths and then move on to twentieths, fiftieths and twenty-fifths.

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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 10-13): Multiply a Fraction by a Whole Number (FREE!)

Investigate how to multiply fractions by whole numbers.

Get pupils exploring 1 x ¼, 2 x ¼, 3 x ¼ etc and they will quickly discover the rules that for multiplication you multiply the numerator and for division you multiply the denominator.

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(Ages 10-13): Divide a Fraction by a Whole Number (FREE!)

Investigate how to divide fractions by whole numbers.

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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 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): Fraction, Decimal, Percentage Equivalences (FREE!)

A summary of all the skills you need to switch between fractions, decimals and percentages, with links to the other investigations that teach each skill.

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(Ages 11-14): Multiply by a Fraction (FREE!)

Investigate how to multiply a whole number or a fraction by a unit fraction (such as one quarter or one fifth). Then investigate multiplying by other fractions.

Multiplying by a fraction is where things get interesting. Pupils are used to thinking that multiplying a number by something will make it bigger. But when fractions are around, all that changes!

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(Ages 11-14): Divide by a Unit Fraction (FREE!)

Investigate how to divide a whole number or a fraction by a unit fraction (such as one quarter or one fifth).

Dividing anything (whole number or fraction) by a fraction is the same as multiplying by the reciprocal of the fraction.

Dividing by ¼ is the same as multiplying by 4!

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(Ages 11-14): Divide by Any Fraction (FREE!)

Explore how to divide a whole number or fraction by any fraction using the idea of reciprocals.

Discover how dividing by 5 eighths is the same as multiplying by 8 fifths and vice versa.

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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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