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# Week 7 - 8 Fractions, Decimals and Percentages

National curriculum content

• Solve problems which require answers to be rounded to specified degrees of accuracy
• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

Lesson objectives

1. Decimal and fraction equivalents
2. Fractions as division
3. Understand percentages
4. Fractions to percentages
5. Equivalent fractions, decimals and percentages
6. Order fractions, decimals and percentages
7. Percentage of an amount- one step
8. Percentage of an amount- multi-step
9. Percentages- missing values

What we want children to know

• They will use ‘number of parts per hundred’ alongside the % symbol.
• How to convert fractions to equivalent fractions where the denominator is 100 in order to find the percentage equivalent.
• Use their knowledge of common equivalent fractions and decimals to find the equivalent percentage.
• Convert between fractions, decimals and percentages to enable them to order and compare them.
• Use known fractional equivalences to find percentages of amounts.
• Find multiples of 10% and other known percentages.
• Explore different methods of finding certain percentages e.g. Finding 20% by dividing by 10 and multiplying by 2 or by dividing by 5. They also explore finding 5% by finding half of 10%. Using these methods, children build up to find percentages such as 35%.
• Use their understanding of percentages to find the missing whole or a missing percentage when the other values are given.

What skills we want children to develop

Use knowledge to solve reasoning and problem solving questions such as:

Fill in the missing values to make this statement correct.

Can you find more than one way?

Make up an example/Give further examples

How many ways can you find 45% of 60?

Use similar strategies to find 60% of 45.

What do you notice? Does this always happen? Can you find more examples?

Missing numbers

50% of 40 = ____% of 80

___% of 40 = 1% of 400

10% of 500 = ____% of 100

Ordering

Put the following amounts in order, starting with the largest.

23%, 5/8, 3/5, 0.8

Vocabulary/Mathematical Talk

• What does the word ‘percent’ mean?
• How can you convert tenths to hundredths?
• Why is it easy to convert fiftieths to hundredths?
• What other fractions are easy to convert to percentages?
• How does converting a decimal to a fraction help us to convert it to a percentage?
• How do you convert a percentage to a decimal?
• Can you use a hundred square to represent your conversions?
• Do you prefer to convert your numbers to decimals, fractions or percentages? Why?
• Why do we divide a quantity by 2 in order to find 50%?
• How do you calculate 10% of a number mentally?
• What’s the same and what’s different about 10% of 300 and 10% of 30?
• Is dividing by 10 and multiplying by 5 the most efficient way to find 50%? Explain why.
•  Is dividing by 10 and multiplying by 9 the most efficient way to find 90%? Explain why.
• How many ways can you think of to calculate 60% of a number?
• If we know a percentage, can we work out the whole?
• If we know the whole and the amount, can we find what percentage has been calculated?
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