Understanding fractions Functional Maths Understanding fractions

Let’s talk about fractions. Work in a small group. Talk about what you know about fractions. When do we see fractions in everyday life? What is a fraction?

Fractions in every day life When telling the time (e.g. ¼ past). In shop sales (e.g. a 1/3 off, ½ price). When measuring (e.g. ½ a metre). When sharing something(e.g. 1 pizza) In recipes (e.g. half a dozen In statistics

Drawing fractions

Draw ¼

A ¼ can be shown like this…

Draw 1 in 3 different ways 5

Draw 2 in 3 different ways 3

Finding a fraction of - a quantity - an amount

Sharing a pizza To share a pizza between two, cut it into two equal pieces. Each piece is ½ of a whole pizza. ½ ½

Sharing a pizza To share a pizza between three, cut it into three equal pieces. Each piece is 1/3 of a whole pizza. 1/3 1/3 1/3

Sharing a pizza To share a pizza between four, cut it into four equal pieces. Each piece is 1/4 of a whole pizza. ¼ ¼ ¼ ¼

Sharing a pizza To share a pizza between five, cut it into five equal pieces. Each piece is 1/5 of a whole pizza. 1/5 1/5 1/5 1/5 1/5

Sharing a pizza To share a pizza between five, cut it into five equal pieces. Each piece is 1/5 of a whole pizza. 1/5 1/5 1/5 1/5 1/5

How much pizza has been eaten? How much pizza is left?

How much pizza has been eaten? How much pizza is left?

Need more practice? If you want more practice at visualising fractions, try these online activities http://www.bbc.co.uk/skillswise/game/ma17frac -game-fractions-of-something http://www.softschools.com/math/fractions/ga mes/matching_fractions_game/ http://www.softschools.com/math/fractions/pict ure_fractions/ Read more about fractions on the maths is fun website http://www.mathsisfun.com/fractions.html

Sharing a pizza A pizza costs £4.80

Sharing a pizza £4.80 If two people share the pizza, how much do they each pay? ½ ½ ½ of £4.80

Sharing a pizza £4.80 If three people share the pizza, how much do they each pay? 1/3 1/3 1/3 1/3 of £4.80

Sharing a pizza £4.80 If four people share the pizza, how much do they each pay? ¼ ¼ ¼ ¼ 1/4 of £4.80

Sharing a pizza £4.80 If five people share the pizza, how much do they each pay? 1/5 1/5 1/5 1/5 1/5 1/5 of £4.80

Sharing a pizza £4.80 Tom eats two slices. Ali eats three slices. How much do they each pay? 1/5 1/5 1/5 1/5 1/5

Sharing a pizza £4.80 1/5 1/5 1/5 1/5 1/5 Tom eats 2/5 of the pizza. Ali eats 3/5 of the pizza. Tom = 4.80 ÷ 5 x 2 = 1.92 Ali = 4.80 ÷ 5 x 3 = 2.88 1/5 1/5 1/5

Solution: Calculate the price for one part (divide by how many parts we have) Pieces of pizza Price Whole pizza = 5 pieces £4.80 1 slice 4.80 ÷ 5 96p 2 slices £1.92 3 slices £2.88 4 slices £3.84

¼ ¼ ¼ ¼ Sharing a pizza £4.80 What is the price of 1 slice 2 slices

Sharing more pizzas 1/5 1/5 1/5 1/5 1/5 Five friends share two pizzas. How much do they each eat? How much do they each pay? 1/5 1/5 1/5 1/5 £4.80 each 1/5

To calculate a fraction of an amount/quantity What is 2/5 of £4.80? £4.80

To calculate a fraction of an amount/quantity What is 2/5 of £4.80? £4.80 Divide the total amount / quantity by the total number of parts. 4.80 ÷ 5. Multiply by how many parts you need 4.80 ÷ 5 x 2 = £1.92

Word problems Jo earns £324 per week. She spends 2/3 of her wage on rent. How much rent does she pay? How much does she have left after she has paid her rent? In a recent survey of 1200 people over 65 three quarters of those asked said that they were worried about their heating bills. How many people is that? Orange juice is on offer in your local supermarket at buy one get one half price. One bottle costs £2.50. You want two bottles. How much will you save? How much will you pay in total for two bottles?

Word problems An FE college has been looking at its enrolment figures and foundout that 3/5 of the 6,450 students are female. A) What fraction are male? B) How many male students are there? C) How many more female students are there than male students? In an attempt to recruit more male students, it visits a local secondary school to conduct a survey. They asked 48 boys in year 11. Two thirds of the boys said that are not interested in attending the college. Of these 1/3 wanted to get an apprenticeship and 2/3 wanted to stay on at school. How many boys are a) interested in college? b) interested in an apprenticeship? c) intending to stay in sixth form?

Comparing fractions

Which one is the biggest? You can think of a shape Divide it into parts Which part is bigger? Which one is the biggest? 1/2 1/3 1/4 1/5 You could use a number line If you are good with decimals, you could convert the numbers to decimals. You could use a number 100 ÷2 = 50, 100 ÷3 = 33, 100 ÷4 = 25. 100 ÷5 = 20

You can use a fraction wall It’s easy to compare fractions with a fraction wall.

+ = A fraction of an amount 1/4 of the students in a maths class are single. 1 4 4 + 3 4 =

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 28 students in the class 1 4 + 3 4 4 = If you given this, you can work out the other two values

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 28 students in the class 1 4 + 3 4 4 = How many are single? If you given this, you can work out the other two values

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 28 students in the class 1 4 + 3 4 4 = How many are not single? If you given this, you can work out the other two values

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 6 single students in the class 1 4 + 3 4 4 = If you given this, you can work out the other two values

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 6 single students in the class 1 4 + 3 4 4 = How many are not single? If you given this, you can work out the other two values

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 6 single students in the class 1 4 + 3 4 4 = How many are there all together ? If you given this, you can work out the other two values

If you given this, you can work out the other two values A fraction of an amount 1/4 of the students in a maths class are single. There are 16 married students in the class 1 4 3 4 4 + = How many single students are there? How many are there all together ? If you given this, you can work out the other two values

A fraction of an amount ¾ of a primary school class of 24 children are boys. How many boys are there? How many girls? 2/3 of a primary school class are boys. There are 18 boys. How many girls are there? How many children are there all together?

A fraction of an amount 1/5 of the 1400 people interviewed in a survey about healthy eating said they never eat vegetables? How many people is that? 240 people responded to a survey about healthy eating. This is only 1/20 of the surveys sent out. How many surveys were sent out?

A fraction of an amount You see a jumper with a ticket price of £25. How much money will you save? How much will you pay? You buy a jumper in the sale. It cost £21. What was the original price? How much money did you save?

Word problems An FE college has been looking at its enrolment figures and found out that 1400 of the 3,500 students are female. A) What fraction is female? B) What fraction is male? In a survey of student satisfaction, 1250 if the 1750 people asked said that they were happy with the course. A) What fraction is happy? B) What fraction is mot happy?