 Reduce a fraction to its simplest form by cancelling common factors

Examples of what pupils should know and be able to do
Recognise that:
 a fraction such as $\frac{5}{20}$ can be reduced to an equivalent fraction $\frac{1}{4}$ by dividing both numerator and denominator by the same number
 a fraction such as $\frac{3}{10}$ can be changed to an equivalent fraction $\frac{30}{100}$ by multiplying both numerator and denominator by the same number.
Recognise fractions that are equivalent to $\frac{1}{2}$, $\frac{1}{3}$ and other unit fractions.
 Primary mathematics exemplification: Use fraction notation, recognise the equivalence between fractions and order familiar fractions
Probing questions
 What clues do you look for when reducing fractions to their simplest form?
 How do you know when you have the simplest form of a fraction?
 Give me a fraction that is equivalent to $\frac{2}{3}$ but has a denominator of 18. How did you do it?
What if pupils find this a barrier?
The main barrier for pupils is a lack of understanding of equivalent fractions. Use a counting stick to guide chanting of pairs of multiples, e.g. 1 and 4 (1, 4, 2, 8, 3, 12, etc.). This generates proportional sets and can help form a clearer understanding of the relationship between the numerator and denominator of equivalent fractions. It also enables pupils to build up full sets of equivalent fractions rather than the smaller set generated by doubling.
 Use a fraction as an 'operator' to find fractions of numbers or quantities (e.g. $\frac{5}{8}$ of 32, $\frac{7}{10}$ of 40, $\frac{9}{100}$ of 400 cm)

Examples of what pupils should know and be able to do
What is:
 $\frac{5}{8}$ of 32?
 $\frac{7}{10}$ of 40?
 $\frac{9}{100}$ of 400 cm?
 $\frac{1}{4}$ of 24?
 Primary mathematics exemplification: Find fractions of numbers or quantities
 Assessment example: Equivalent fractions: Aishah, Megan, Peter and Alan (PDF1.5 MB) Attachments
 Assessment example: Jumping problem: Olivia (PDF805 KB) Attachments
Probing questions
 Give me some examples of numbers that are easy to find one fifth of. What about two fifths?
 Is there anything special about these numbers?
 What about numbers that are easy to find three quarters of?
 How would you find five eighths of a number or quantity?
What if pupils find this a barrier?
Use multilink cubes to visualise $\frac{5}{8}$. To find $\frac{5}{8}$ of 32 the whole must represent 32 so each cube must be worth 4. This image will help pupils make links between visual images of fractions and fractions as operators. This will help pupils understand why they are dividing by 8 and then multiplying by 5.
Download Mathematics ITP: Fractions (SWF18 KB) Attachments and use it in the same way as above.
Practise the skills using Partitioning loop cards (PDF89 KB) Attachments , set 12.
 Targeting level 4 lesson: Lesson 3: Using fractions
 Targeting level 4 lesson: Equivalence of fractions
 Understand percentage as the number of parts in every 100 and find simple percentages of small wholenumber quantities

Examples of what pupils should know and be able to do
Use mental methods. For example find:
 10% of £20 by dividing by 10
 5% of £5 by finding 10% and then halving
 15% of 40 by finding 10% then 5% and adding the results together
 $\frac{1}{4}$ of 24.
Use informal written methods, including using jottings. For example find:
 11% of £2800 by calculating 10% and 1% and adding the results together
 70% of 130 g by calculating 10% and multiplying this by 7 or by calculating 50% and 20%.
 Primary mathematics exemplification: Understand percentage as the number of parts in every 100 and recognise the equivalence between percentages and fractions and decimals
 Assessment example: Sorting fractions and percentages: Sam (PDF239 KB) Attachments
Probing questions
 What percentages can you easily work out in your head? Talk me through a couple of examples.
 When calculating percentages of quantities, what percentage do you usually start from?
 How do you use this percentage to work out others?
 To calculate 10% of a quantity, you divide it by 10. So to find 20%, you must divide by 20. What is wrong with this statement?
 Using a 1–100 grid, 50% of the numbers are even. How would you check?
 Give me a question with the answer 20%.
What if pupils find this a barrier?
Help pupils make connections between finding simple percentages of wholenumber quantities by using a spider diagram.
Ask pupils to write, for example, $52=100\%$ in the middle of a piece of paper and then link together other percentages that they can find (e.g. $26=50\%$, $13=25\%$, $5.2=10\%$, etc).
Use the visual image of Mathematics ITP: Number grid (SWF60 KB) Attachments to discuss parts in every 100.
Use Mathematics ITP: Fractions (SWF18 KB) Attachments with the percentages shown.
Practise using Partitioning loop cards (PDF89 KB) Attachments , set 14.
 Targeting level 4 lesson: Fractions and percentages
 Targeting level 4 lesson: Finding percentages of wholenumber quantities
Attachments
Related downloads
 Equivalent fractions: Aishah, Megan, Peter and Alan [ pdf : 1.5 MB ]
 Jumping problem: Olivia [ pdf : 805 KB ]
 Mathematics ITP: Fractions
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 18 KB ]
 Partitioning loop cards [ pdf : 89 KB ]
 Sorting fractions and percentages: Sam [ pdf : 239 KB ]
 Mathematics ITP: Number grid
 [Windows executable]  [ exe : 4.1 MB ]
 [Flash]  [ swf : 60 KB ]
 Download all [ 2.6 MB ]