Download Strand: Number Fractions

TOPIC
Strand: Number
Fractions
7
509
510
1.
2.
3.
4.
5.
Compare and order fractions and identify equivalent forms of fractions with
denominators 2–12.
Express improper fractions as mixed numbers and vice versa and position them
on the number line.
Identifying fractions and equivalent forms with denominators 2, 3, 4, 5, 6, 8, 9, 10 and 12.
Comparing and ordering fractions on the number line.
Calculating a fraction of a set.
Calculating a number given a unit or multiple fraction of the number.
Expressing a number as a fraction of another number.
1. Understanding and recalling: Understanding and recalling equivalent fractions.
2. Applying and problem-solving: Applying and recognising equivalence in diagrammatic forms
and on the number line.
3. Integrating and connecting: Using diagrams and number lines to demonstrate understanding.
4. Reasoning: Investigating patterns in equivalent fractions.
5. Implementing: Using procedures to change improper fractions to mixed numbers and vice
versa.
Counters, piece of A4 paper, fraction walls
Fraction, equivalent, equivalence, compare, mixed number, proper fraction,
improper fraction, numerator, denominator, whole, unit, halves, thirds, quarters,
fifths, sixths, sevenths, eighths, ninths, tenths, elevenths, twelfths, twentieths,
hundredths
1. It is important that students fully understand the concept of a fraction. Ask
students to divide continuous (a piece of paper) and non-continuous sets
(a set of counters) into fractions.
2. Use paper folding as a practical means of investigating equivalence.
3. Students may find the terminology introduced in this chapter confusing.
It is important that they can accurately use and comprehend the language introduced as it is
repeated in the Fractions 2 unit (Topic 8).
Fans:
Show how many 12 s, 13 s, 14 s, 15 s are in whole numbers. For example, how many 14 s
in 4?
Target board 5:
Change each fraction to quarters, 12ths, etc.
Counting stick:
Count in 12 s, 14 s, 15 s starting at different numbers. Start at 5 and count in 14 s, what number do you
finish on?
1. Calculate fractions using data from students in the class, e.g. fraction of children who come to
school by car, who have brown hair, who are vegetarians.
2. Calculate fractions involving quantities of time, e.g. fraction of the day/week spent watching TV,
doing homework, sleeping, reading.
3. Using the 7 tangram pieces, make a square. Explore what fraction of the square is comprised of
each individual piece.
4. Explore fractions in the environment, such as on a ruler, ingredients in a recipe, in music
(semibreve, minim, crotchet, quaver, semiquaver).
1. In box 1, what fraction of the group is wearing a red T-shirt? ( 14 )
2. In box 2, what fraction of the jug is empty? ( 67 )
3. What fraction of the counters is unshaded in box 3? (2/11)
4. True or false: Three-fifths of the cubes are shaded in box 4. (true)
5. True or false: Daniel got one-sixth of his spellings wrong in his test. (true)
6. In box 6, what fraction of the dogs have white coats? ( 13 )
7. True or false: The glass in box 7 is approximately one-third empty. (false)
3
8. What fraction of the squares are shaded in box 8? ( 10 )
9. What fraction of the family in box 9 is female? ( 12 )
10. In box 10, what fraction is represented by the X? ( 56 )
Lower attainers:
Extra practice on equivalence, changing improper fractions to mixed numbers and
vice versa.
Higher attainers:
1. Stretcher activities involving number lines, evaluating fractions and equivalent fractions.
2. ‘Challenge Yourself’ and Activity A on page 48 may prove challenging.
Topic
Topic
7
7
1. Put in the correct sign: < = >
1. Write at least three fractions that are equivalent to:
(a)
1
2
___
1
3
(b)
2
3
___
7
12
(c)
1
3
___
3
12
(d)
1
5
___
3
10
(e)
5
6
___
8
9
(f)
9
10
___
4
5
(a)
(d)
(g)
1
4
8
=
21
(b)
1
3
=
6
=
6
8
=
12
(e)
5
6
=
12
=
4
6
=
12
=
3
3
=
(c)
9
(a)
1
2
(b)
1
4
(c)
3
4
(d)
1
5
(e)
4
12
(f)
6
8
(b)
5
4
(c) 2 23 ___
7
3
(f) 3 56 ___
23
6
2. Put in the correct sign: < = >
2. Fill in the missing numbers on each of these equivalent fractions.
(f)
1
5
=
4
8
=
9
10
=
(a) 1 12 ___
5
10
(d)
17
10
3
2
___ 1 12
___ 1 12
1
(e) 2 12
___
27
12
3. Put each of these amounts into the correct place on this number line:
1 1 5
4, 2, 8,
3. Convert each improper fraction to a mixed number.
(a)
11
2
(b)
12
7
(c)
22
10
(d)
17
6
(e)
50
3
(f)
41
6
(g)
81
8
1 18 ,
11
8,
1 12 , 74 ,
15
8
0
1
2
4. Convert each mixed number to an improper fraction.
(a) 2 13
(b) 1 45
7
(c) 2 10
(d) 3 12
(e) 4 58
(f) 5 45
4. Put each of these amounts into the correct place on this number line:
1 5 4 10
3, 9, 6, 9 ,
1 13 ,
13
9,
1 23 ,
17
9
(g) 5 89
5. Fill in the fractions missing on the number line.
0
1
8
1
8
2
5
8
0
7
4
2
1
5. Put each of these amounts into the correct place on this number line.
1
1 2 1 7 11 13
5 , 5 , 2 , 10 , 10 , 10 ,
1 25 , 35 ,
19
10
6. Fill in the fractions, improper fractions and mixed numbers missing on the number line.
1
2
8
Name: _______________________________________
2
1
5
5
25
Date: ___________________
3
0
Name: _______________________________________
1
Date: ___________________
2
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Measures: Money – Calculating a fraction of an amount of money
Measures: Length – Using fractions of measures in length
Measures: Weight – Using fractions of measures in weight
Measures: Capacity – Using fractions of measures in capacity
Decimals and Percentages: Understanding the relationship between decimals, fractions and
percentages
Chance: Calculating and expressing chance
Data: Pie charts
Visual arts: Using origami in construction, using patterns in print, painting and colour
English: Using the language of fractions to describe mathematics in the environment, e.g. in the
context of surveys in newspapers
Children should be encouraged to investigate the occurrence of fractions in their home
environments, for example: Fractions of measurement (e.g. 1 litre, 12 litre, 14 litre of milk – how
many millilitres is that? Fractions of a continuous quantity (e.g. cake or pizza) – what fraction
would each person get if it was shared equally among a certain number of people, how many
1
2 kg bags can be filled from a 5kg sack of flour?