TOPIC
7
Fractions 1
Strand: Number
Strand unit: Fractions
Curriculum Objectives
609
610
611
613
Compare and order fractions and identify equivalent forms of fractions.
Express improper fractions as mixed numbers and vice versa and position them
on the number line.
Add and subtract simple fractions and simple mixed numbers.
Express tenths, hundredths and thousandths in both fractional and decimal form.
Looking back: What the 5th class programme covered
1.
2.
3.
4.
5.
6.
7.
8.
9.
Identifying equivalent forms of fractions with denominators 2–12.
Comparing and ordering fractions with denominators 2–12.
Expressing tenths, hundredths and thousandths in decimal form.
Expressing improper fractions as mixed numbers.
Expressing mixed numbers as improper fractions.
Positioning fractions on the number line.
Adding simple fractions and simple mixed numbers.
Subtracting simple fractions and simple mixed numbers.
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
1
Fractional cubes, fraction wall chart up to 12 in family groups ( 2 , 4 , 5 , 3 , 6 , 9 , 10 , 12 ), unit cubes,
3D flats, 3D thousand cubes, squared paper, tangram set
Vocabulary
Fraction, part of a whole, equal parts, numerator, denominator, equivalent fractions, simplify
fractions, cancelling, put fractions in order, mixed number, vice versa, whole number, proper
fraction, improper fraction, correct grouping, compare fractions, order fractions, tenths,
hundredths, thousandths, the same denominators, common denominator, lowest
common denominator, fractional form, biggest fraction, smallest fraction
45
Teaching points
Spend time going through the equivalence of fractions. It can be difficult for children to grasp that
1 = 2 = 3 = 4 and that 1 = 2 = 3 = 4 = 5 = 6 and that 1 = 2 , etc. Completing work on
3
6
9
12
2
4
6
8
10
12
5
10
the fraction wall will prove very useful, as will manipulating concrete materials, such as equivalent
cubes. When the children are very familiar with the equivalence of fractions, they should be able
to compare and order fractions on the number line. Emphasise that in order to
compare, add or subtract fractions, the fractions must be converted to ‘the same
family of fractions’.
Oral and mental activities
Fans:
1
Show 12 , 14 , 13 , 15 , 16 , 18 , 10 of any number. How many 18 s in 32, 15 s in 35 etc? What fraction of an
hour is 20 minutes, 30 minutes,10 minutes, 15 minutes ,1 minute, etc.
Counting stick:
1
. Starting with that fraction, i.e. 12 . Then start at different mixed numbers
Counting in 12 s , 14 s, 12
e.g. 2 12 , 31
2 etc.
1
s for other fractions. Put fraction cards at each point like the clock
Use a hula hoop divided into 12
numbers (use 2-sided Velcro).
Loop game (see Folens Online resources):
Fractions
Target board 8:
How many 14 s in each number? How many 18 s in each number?
Topic suggestions
1. Play Snap with cards showing equivalent fractions. Put the cards face down on the table. Each
player takes a card, looks at it discreetly and puts it face down on the table again. When a
player finds 2 matching cards, they then shout Snap and hold on to those 2 cards. The player
with the most sets of pairs at the end wins.
1
1
1
2. Use the clock to demonstrate 2 an hour, 4 of an hour, 6 of an hour, etc.
3. Write the minutes as fractions of an hour.
4. Make a class timetable and establish what fraction of each day is spent on the various
subjects.
5. This timetable could be extended over a week to give the fraction of each week which
is devoted to each subject. Comparisons between the subjects should prove to make for
interesting discussion, e.g. the fraction of time devoted to PE as opposed to Maths or Irish.
6. Carry out a class survey to see which TV programmes are popular among the children in the
class. What fraction of the class like certain programmes best? The children could make a pie
chart of the results.
Activity A
1. What fraction of the marbles are red? ( 2 or 15 )
10
4
or 25 )
What fraction of the marbles are green? ( 10
1
)
What fraction of the marbles are blue? ( 10
3)
What fraction of the marbles are yellow? ( 10
How many marbles are 15 of the total number of marbles? (2)
How many marbles are 12 of the total number of marbles? (5)
5
or 12 )
What fraction do the green and blue marbles make up altogether? ( 10
6 or 3 )
What fraction do the red and green marbles make up altogether? ( 10
5
Take away 2 green marbles. Now what fraction of the remaining marbles are red? ( 28 or 14 )
2.
3.
4.
5.
6.
7.
8.
9.
Differentiation
Lower attainers:
Separate activity sheet
Higher attainers:
Separate activity sheet
Topic
Topic
7
7
1. Write each of these mixed numbers as improper fractions:
1. Add.
(a) 4 23 _____ (b) 7 35 _____
(c) 5 16 _____
(d) 9 47 _____
(e) 3 12 _____
(f) 6 34 _____
(g) 2 45 _____ (h) 3 56 _____
(i) 7 34 _____
(j) 4 58 _____
(k) 6 14 _____
(l) 2 57 _____
(a)
1
2
+
5
6
3
= _____
2
(e) 5 4 + 4 3 = _____
(b) 35 +
2
10
= _____
6
1
(f) 5 7 + 4 3 = _____
(c)
5
8
+
3
4
5
= _____
4
5
(d)
2
+
9
20
7
(g) 4 6 + 5 3 = _____
= _____
3
(h) 5 8 + 4 4 = _____
2. Write each of these improper fraction as mixed numbers:
(a)
15
4
_____
(g)
19
8
_____
(b)
(h)
17
6
_____
13
2
_____
(c)
35
8
_____
(i)
19
5
_____
(d)
41
7
_____
(e)
28
9
_____
(f)
26
3
2. Subtract.
_____
(j)
42
6
_____
(k)
33
7
_____
(l)
100
9
_____
(d)
7
21
_____
(e)
4
16
_____
(f)
10
15
9
(d)
4
7
(h)
10
11
(a)
_____
(a)
6
10
_____
(b)
3
9
_____
8
12
(c)
(a)
2
6
=
5
6
=
12
30
(b)
5
7
(f)
6
11
=
21
=
24
(c)
3
4
=
(g)
8
9
=
3
4
1
3
7
8
_____
2
5
(b)
3
4
= _____
2
27
12
=
9
10
2
3
7
(b) 8 –
1
4
3
= _____
11
(f) 6 4 – 3 12 = _____
(c)
3
4
–
7
20
= _____
7
10
(d)
9
(g) 7 25 – 2 10
= _____
–
15
30
(h) 8 13 – 3 25
= _____
= _____
3. Circle the greater fraction. By how much is it greater?
(a)
1
3
1
2
(d)
7
9
2
3
__________
(b)
__________
(e)
5
9
1
3
__________
(c)
7
12
3
4
__________
5
8
1
4
__________
(f)
1
10
5
12
__________
=
4. Maria had
5. Put these fractions in order, starting with the biggest:
(a)
–
1
_____
4. Write these equivalent fractions:
(e)
4
5
(e) 7 4 – 4 3 = _____
3. Simply each of the following fractions:
_____
(c)
4
5
7
8
3
4
2
3
of a litre of water and
3
5
litre of cranberry juice.
(a) Which drink had the greater quantity? _________________
_____
(b) By how much was this drink greater than the other drink? ___________________
6. Add.
(a)
5
6
(e)
3
12
+
2
3
+
5
6
= _____
(b) 38 +
1
4
= _____
(c)
1
10
= _____
(f) 47 +
2
3
= _____
(g)
5
6
+
= _____
(d)
5
8
+
1
4
= _____
2
3
= _____
(h)
3
4
+
3
5
= _____
+
2
5
5. Peter cut a plank of wood into two pieces, one measuring 2 45 m long and the other measured
7
3 10
m long. What was the original plank of wood before it was cut into two pieces?
7. Subtract.
_________________
(a)
1
2
–
1
4
= _____
(b) 12 –
1
3
= _____
(c)
2
3
–
1
12
= _____
(d)
1
2
–
4
10
= _____
(e)
8
9
–
5
18
= _____
(f) 23 –
5
9
= _____
(g)
5
6
–
2
3
= _____
(h)
4
5
–
2
3
= _____
6. Philip lives 9 14 km from his job. On Monday he got a lift for 2 38 km and travelled by bus for 5 34 km.
He walked the rest of the way. How far did he walk? _____________________
8. Add.
(a) 4 34 + 2 45 = _____
(e) 3 12 + 4 34 = _____
(b) 2 13 + 6 56 = _____
(f) 4 12 +
2
3
3
(c) 4 10
+ 1 25 = _____
(d) 1 12 + 2 23 = _____
5
(h) 3 14 + 2 12
= _____
(b) 4 12 – 2 14 = _____
(c) 5 23 – 2 34
= _____
6
(d) 5 45 – 3 10
= _____
(e) 7 56 – 4 12
18 = _____
(f) 4 34 – 1 25 = _____
(g) 7 23 – 2 78
= _____
(h) 6 23 – 2 79
= _____
7. What is the difference between 6 15 and 4 34 ?
did he walk? __________________
11. Louise bought 1 34 kg of mince and 2 15 kg of chicken. What was the total weight of the meat which
Louise bought? __________________
Name: _______________________________________
Date: ___________________
Page 135: Fractions 1
© Folens Photocopiables
= _____
10. Michael lived 6 23 km from school. He went 3 16 km by bus and walked the rest of the way. How far
8. By how much is the sum of 4 23 and 5 45 greater than 9?
9. Two family-sized lasagnes were divided among the guests. Each lasagne was divided into 8 pieces.
If all the lasagne was eaten except for three pieces, what fraction of the lasagne was consumed?
_______________________
Name: _______________________________________
Date: ___________________
© Folens Photocopiables
(g) 3 13 + 2 58 = _____
7
(a) 9 35 – 8 10
= _____
9. Subtract.
135
Linkage
Measures: Money, length, weight, capacity, time
Number: Decimals, percentages, problem solving, operations (division)
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, twelfths, etc.
SESE Geography: What colours/shapes make up the flags of the world
Cookery: Division of pizzas, cakes, pies
1
1
Music: Values of notes, e.g. 2 beat, 4 beat
47
Maths at home/parental involvement
1. See how many regular bowls of cereal you can get out of the box of cereal. What fraction
of the total packet fits into 1 regular-sized cereal bowl? Weigh the regular bowlful first.
How many bowls of cereal can you have from 1 box of cereal?
2. Examine a box of chocolates. Look at each type of chocolate in the box. Find out what
fraction of all the chocolates is each different type in the box.
3. Weigh a dishwasher tablet. Weigh the total number of dishwasher tablets in the box. What
fraction of the total box weight is each tablet?
Notes
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
48