TOPIC
9
Fractions 2
Strand: Number
Strand unit: Fractions
Curriculum Objectives
612
614
Multiply a fraction by a fraction.
Divide a whole number by a unit fraction.
Looking back: What the 5th class programme covered
1. Multiplying a fraction by a whole number.
Maths skills used in this topic
1. Applying and problem-solving: Plan and implement solutions to problems in a variety of
contexts. Evaluate solutions to problems.
2. Communicating and expressing: Communicate and express mathematical ideas, processes
and results in oral and written form.
3. Integrating and connecting: Make mathematical connections within mathematics itself,
throughout other subjects, and in applications of mathematics in practical everyday contexts.
Concrete materials
1
1 1 1 1 1 1
1
Fraction walls, fractional cubes, fraction wall chart up to 12 in family groups ( 2 , 4 , 5 , 3 , 6 , 9 , 10 ,
1
12 ), unit cubes, tangram sets, playing cards, equivalent fraction cards
Vocabulary
Numerator, denominator, simplify, cross multiplication, fraction of a number, unitary method,
simplify a fraction, a whole number, opposite, invert
Teaching points
Children usually find that the multiplication of fractions is easier than the addition or subtraction of
fractions! They quickly know how to multiply the 2 numerators and the 2 denominators and then
simplify if necessary. The introduction of cross multiplication is a natural progression if the child wishes
to multiply fractions a quicker way. There are children who do not want to make this progression
and they can manage very successfully by multiplying the 2 numerators and the 2 denominators. In a
similar way, the division of fractions will not pose a problem for children when they have grasped the
simple rule for division: invert (the second fraction) and multiply. In the section on ‘Unitary method’
(textbook page 62), children explore value for money. This is a very useful method of introducing
social maths and shows children the relevance to them of this aspect of real-life maths.
Oral and mental activities
Counting stick:
Count in 15 s . How many wholes on the stick? Start at different numbers either whole or mixed,
counting in 12 s, 14 s , 15 s and estimate what the end point will be.
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Fans:
1
of a decade, 16 of a year, etc? Use class books to record what fraction of
What is 17 of a week, 10
the book is 1 page. You can also use jigsaws. Smarties in a box: what fraction are red, yellow, blue,
3 4 5
etc. Find 15 of 45, Find 25 , 5 , 5 , 5 . Repeat with different numbers.
Target board 5:
Add the numbers in the first row, second row, etc. What must I add to each to reach 5, 10, etc. If
a whole is 12, then what does each number on the board represent?
Topic suggestions
1. This card game can help to practise multiplying and dividing fractions. It works best in small
groups with a maximum of 4 children in a group. Each group needs a deck of playing cards
(with the court cards removed).
(a) Deal each player 4 cards.
(b) The children use their cards to make different fractions for each another (choose 1 card to
be the numerator and another to be the denominator).
(c) Player A calls on someone in their group to multiply or divide his/her fraction by Player
A’s. If s/he is not correct, Player A gets both the other player’s fraction cards.
(d) The children continue to take turns among the group so that everyone has a chance to
play.
(e) Whoever ends up with the most cards at the end of the time period given, or whoever
gets all of the cards, wins!
2. Fraction riddles
1
(a) I am a unit of time on our planet. I am 7 of a week. What am I? (a day)
1
1
1
of 60
of 24
of the answer to question 1. What am I?
(b) I am also a unit of time. I am 60
(a second)
(c) I am a fraction. My denominator is 14. I am not just a part of 1 whole thing. I am 1
whole thing! And don’t you forget it! What fraction am I? ( 14
14 )
(d) I am a denominator. The numerator of the fraction that I am part of is 5. That fraction is
equivalent to the answer to question (c). What number am I? (5)
(e) I am a fraction. My numerator is an odd single digit. My denominator is a single digit that
is 4 times greater than my numerator. What fraction am I? ( 28 )
Activity A
Pick out the correct photograph
5
1. Put the number 1 over the illustration that shows 8 shaded. (second from left)
18
2. Simplify 20 . (seventh from left)
3. One quarter of the cake has been eaten! (first from left)
4. Put the number 4 over the illustration showing 11
2 . (fifth from left)
20
5. Show 7 as a mixed number. (fourth from left)
6. This bar has been divided into halves. Now divide the bar into quarters. (sixth from left)
9
as an improper fraction? (third from left)
7. Simplify 12
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Differentiation
Lower attainers:
Separate activity sheet
Higher attainers:
Separate activity sheet
Topic
Topic
9
9
1. Multiply.
(a)
2
5
x
5
8
1. Find the whole number if
(b)
8
9
x
= ____ (b)
7
8
of
= ____
1
4
(c)
5
6
x
= ____ (c)
6
8
of
= ____
3
4
= ____
(d) 6 x
5
6
(e)
2
4
x
= ____ (e)
1
3
of
= ____
4
6
= ____
(a)
5
8
(e)
9
12
= ____
2. Find.
2. Solve.
(a)
3
8
of
5
9
6
11
4
10
= ____ (d)
5
10
of
1
20
1
2
(a)
3. Add.
(a) 2 13 + 3 14 = ____
(d)
4
13
= 24 _____
= 894 _____
(h)
6
17
= 30 _____
(c)
4
9
of 2,196 _____
(d)
5
8
of €9.92 _____
4. Maria had €32 going shopping. She met her sister, Grace who also had money. Grace had
when he had seen
3
7
of the movie. How much of the movie did he miss? ______________
3
4
of
the amount which Maria had.
4
5
÷ 5 = ____
(e)
2
3
÷ 9 = ____
(f)
2
3
÷ 7 = ____
(b)
3
7
of €14.28 = ____
(a) How much money had Grace? ______________
(c)
3
5
÷ 6 = ____
(d)
8
9
÷ 6 = ____
(c)
3
5
of 2,250 ¬ = ____ (d)
2
5
of €2,055 = ___
(b) How much money did they have between them? ______________
5. If a motorbike travels at
of 96 = ____
= 6,558 ___ (b)
2
5
= €400 ___ (c)
1
2
= 163 ___
(d)
4
7
of a kilometre per minute, how far will it travel in 9 minutes?
of a kilogram of flour to make a cake. How many cakes can he make from 10
7
9
= 945 ___
(e)
2
5
= 20 ___
7. Each child at a party gets
5
7
of a litre of orange juice. If there were 14 children at the party, how
many litres of oranges juice were consumed? ______________
(c) 20 _____ (d) 25 _____
(e) 3 _____
(f) 2 _____
8. A painter uses
8
9
of a litre of paint per door. If he paints 18 identical doors, how many litres of
paint does he use? ______________
9. What fraction of €12 is
(a) €10 _____ (b) €6 _____
5
6
kilograms of flour? ______________
8. What fraction of 30 is
(a) 10 _____ (b) 15 _____
4
9
______________
6. A baker uses
7. Find the whole number if
3
5
of 1,632 _____
= 2,355 _____
6
8
(d) 4 34 – 1 78 = ____
6. Solve.
11.
8
12
5
7
7
(c) 5 25 – 1 10
= ____
(b)
10. William spent
(b)
(c)
(g)
9
(b) 6 12 – 2 10
= ____
÷ 2 = ____
3
5
of 1,092 _____
= 2,700 _____
= 945 _____
3. David had to leave the cinema early, as he felt sick. The movie was 133 minutes long but he left
3
4
(a)
7
9
3
(d) 6 12
+ 4 26 = ____
(a)
2
3
9
11
(f)
5
(c) 4 34 + 2 12
= ____
4. Subtract.
(a) 4 14 – 1 12 = ____
(b)
= 3,690 _____
3
(b) 3 45 + 2 10
= ____
5. Divide.
(a)
3
7
= 140 _____
(c) €2.50 ____ (d) €6.50 ____ (e) €4 _____
(f) €3 _____
9. Story Maths – Pedro’s Pizzas
Pedro made 4 different pizzas for the party. Each pizza was the same size.
of his money and had €30 left. How much had he at the start? _____________
Pedro cut the Pineapple Pizza into 6 equal slices, the Ham Pizza into 5 equal slices, the
Vegetarian Pizza into 8 equal slices and the Chicken Pizza into 9 equal slices.
of a number is 12. What is the number? _____________
Nina had the largest amount of pizza which was 3 times as much as Liam.
13. Which is better value?
(a) 8 copies for €5.20 or 10 copies for €6.20? _____________
(b) 7 pens for €3.15, 8 pens for €3.12 or 10 pens for €4? _____________
Name: _______________________________________
Date: ___________________
Page 139: Fractions 2
139
Liam had the smallest amount of pizza.
Colm and John ate 2 more slices than Liam.
(a) How many slices of pizza did each person eat? ______________
(b) What fraction of the total pizza did each person eat? ______________
Simply the fractions in the answer.
Name: _______________________________________
Date: ___________________
© Folens Photocopiables
© Folens Photocopiables
12. 5 scrapbooks cost €12.50. How much would 8 scrapbooks cost? _____________
140
Page 140: Fractions 2
Linkage
Number: Operations (multiplication), division, decimals, percentages, problem solving
Measures: Time, money, length, weight, capacity
Integration
Art: Origami – making designs and patterns using fraction cards or pasta shape patterns, making
jigsaws for younger classes, cutting magazine pictures into halves, quarters, thirds, eighths, etc.
SESE Geography: Look at the flags of the world and discuss what fractions appear in them
(colours, etc.)
Cookery: Division of pizzas, cakes, pies, etc.
Music: Values of notes, e.g. 14 beat, 12 beat
Maths at home/parental involvement
Parents can help children by checking if they can cut food items into varying fractions, e.g.
tenths, eighths, twelfths, sixths, etc. as well as distributing required amounts, e.g. cutting a cake
7 of the cake to a plate; counting biscuits in a packet and observing
into tenths and removing 10
varying fractions of the packet, e.g. how many biscuits in 14 of the packet, in a 13 of the packet,
1 2 3
2 , 3 , 4 of the packet, etc.
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