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  4. Recognise and classify ordinary

3.1 Recognise and classify ordinary fractions  (Page 2/2)

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ANumber BRounded off to the nearest whole number
E.g. 2 8 10 size 12{2 { { size 8{8} } over { size 8{"10"} } } } {} → 3
1.1 3 1 6 size 12{3 { { size 8{1} } over { size 8{6} } } } {} 5
1.2 3 5 8 size 12{3 { { size 8{5} } over { size 8{8} } } } {} 2
1.3 4 7 9 size 12{4 { { size 8{7} } over { size 8{9} } } } {} 7
1.4 2 2 5 size 12{2 { { size 8{2} } over { size 8{5} } } } {} 3
1.5 6 1 8 size 12{6 { { size 8{1} } over { size 8{8} } } } {} 4
1.6 7 1 4 size 12{7 { { size 8{1} } over { size 8{4} } } } {} 6

Activity 5:

To calculate through selection and use of suitable computations [lo 1.8.3]

1.1 Now answer the following questions:

a) 1 5 + 3 5 size 12{ { { size 8{1} } over { size 8{5} } } + { { size 8{3} } over { size 8{5} } } } {} = .........................

b) 1 1 5 + 2 5 size 12{1 { { size 8{1} } over { size 8{5} } } + { { size 8{2} } over { size 8{5} } } } {} = .........................

c) 2 5 + 4 5 size 12{ { { size 8{2} } over { size 8{5} } } + { { size 8{4} } over { size 8{5} } } } {} = .........................

d) 1 1 5 + 1 5 size 12{1 { { size 8{1} } over { size 8{5} } } + { { size 8{1} } over { size 8{5} } } } {} = .........................

e) Calculate:

2 3 + 7 9 size 12{ { { size 8{2} } over { size 8{3} } } + { { size 8{7} } over { size 8{9} } } } {} ; 4 5 + 9 10 size 12{ { { size 8{4} } over { size 8{5} } } + { { size 8{9} } over { size 8{"10"} } } } {}

5 6 + 2 3 size 12{ { { size 8{5} } over { size 8{6} } } + { { size 8{2} } over { size 8{3} } } } {} ; 7 8 + 3 4 size 12{ { { size 8{7} } over { size 8{8} } } + { { size 8{3} } over { size 8{4} } } } {}

5 8 + 1 2 size 12{ { { size 8{5} } over { size 8{8} } } + { { size 8{1} } over { size 8{2} } } } {} ; 1 4 + 5 8 size 12{ { { size 8{1} } over { size 8{4} } } + { { size 8{5} } over { size 8{8} } } } {}

Activity 6:

To calculate through selection and the use of suitable computations [lo 1.8.3]

To recognise and use equivalent forms of fractions [lo 1.5.1]

To write number sentences in order to describe a problem situation [lo 2.4]

1. Split up into groups of three. Work through the following problems and see if you can find solutions:

a) A farmer transports his fruit to the market by lorry. On arrival he discovers the following: one quarter of the bananas, one eighth of the apples and three eighths of the pears have become spoiled. Which fraction of the fruit could not be off-loaded to be sold at the market?

b) The learners of the Khayelitsha Primary School decided to add some colour to the informal settlement nearby. They painted two fifths of the shacks yellow. Later three tenths of the remaining shacks were painted blue.

i) What fraction of all the shacks was painted?

ii) What fraction still had to be painted?

iii) Which colour would you paint them and why?

c. Mrs Johnny decided to start a soup kitchen in her area.

i) If she gives 5 and seven ninths of the pea soup, and 3 and two thirds of the bean soup to less privileged people on a certain day, what fraction of the soup is eaten altogether on that specific day?

ii) What is your favourite kind of soup?

d. It takes 2 and a half hours to fly from Cape Town to Johannesburg. A flight from Johannesburg to London takes 9 and three quarters of an hour. How long will it take you altogether to fly to London if you depart from Cape Town? Give your answer as a mixed number.

e. Mrs Zuqa makes delicious fruit juices to give to the learners at school during break. She mixes 4 and three quarters of orange juice with 1 and a half litre of pineapple juice. What is the difference between these two quantities?

f. Mrs Sonn helps her friend to bake cakes for the learners. She buys 5 kg of sugar and uses 3 and a third of this quantity. How many kilograms of sugar are left?

2. Your teacher will now ask you to explain one of the above-mentioned problems to the rest of the class.

3. Compare your solutions to those of other groups in the class.

4. Discuss the differences and / or similarities between the different methods that were used.

Assessment

Learning outcomes(LOs)
LO 1
Numbers, Operations and RelationshipsThe learner is able to recognise, describe and represent numbers and their relationships, and counts, estimates, calculates and checks with competence and confidence in solving problems.
Assessment standards(ASs)
We know this when the learner:
1.1 counts forwards and backwards fractions;
1.2 describes and illustrates various ways of writing numbers in different cultures (including local) throughout history;
1.3 recognises and represents the following numbers in order to describe and compare them:
  • common fractions to at least twelfths;
1.5 recognises and uses equivalent forms of the numbers listed above, including:
1.5.1 common fractions with denominators that are multiples of each other;
1.6 solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • financial (including buying and selling, profit and loss, and simple budgets);

Memorandum

ACTIVITY 1

1.

1.1<1.2>

1.3>1.4<

1.5 = 1.6<

1.7 = 1.8<

1.9>1.10 =

2. 2.1 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} 2.2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

2.3 9 10 size 12{ { { size 8{9} } over { size 8{"10"} } } } {} 2.4 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

2.5 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} 2.6 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {}

CLASS DISCUSSION

First make both nominators the same by finding the smallest common denominator

OR

First simplify the fraction, if you can

3. 3.1>

3.2>

3.3 =

3.4 =

4. 4.1<

4.2<

4.3>

4.4>

Another BRAIN-TEASER!

5 6 size 12{ { { size 8{5} } over { size 8{6} } } } {} ; 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} ; 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} ; 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

ACTIVITY 3

1.

1.1 5 5 size 12{ { { size 8{5} } over { size 8{5} } } } {} 8 9 size 12{ { { size 8{8} } over { size 8{9} } } } {}
1.2 5 5 size 12{ { { size 8{5} } over { size 8{5} } } } {} 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}
1.3 4 4 size 12{ { { size 8{4} } over { size 8{4} } } } {} 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}
1.4 6 6 size 12{ { { size 8{6} } over { size 8{6} } } } {} 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {}
1.5 6 6 size 12{ { { size 8{6} } over { size 8{6} } } } {} 8 9 size 12{ { { size 8{8} } over { size 8{9} } } } {}

ACTIVITY 4

1.

  • 3 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {} → size 12{ rightarrow } {} 3 1.2 3 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {} → size 12{ rightarrow } {} 4

1.3 4 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} → size 12{ rightarrow } {} 5 1.4 2 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {} → size 12{ rightarrow } {} 2

1.5 6 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} → size 12{ rightarrow } {} 6 1.6 7 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} → size 12{ rightarrow } {} 7

BRAIN-TEASER!

9

ACTIVITY 5

1.1

a) 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} ;

b) 1 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {} ;

c) 1 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {} ;

d) 1 2 5 size 12{ { { size 8{2} } over { size 8{5} } } } {}

e) (i) 1 4 9 size 12{ { { size 8{4} } over { size 8{9} } } } {}

(ii) 1 7 10 size 12{ { { size 8{7} } over { size 8{"10"} } } } {}

(iii) 1 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(iv) 1 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {}

(v) 1 1 8 size 12{1 { { size 8{1} } over { size 8{8} } } } {}

(vi) 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

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Source:  OpenStax, Mathematics grade 5. OpenStax CNX. Sep 23, 2009 Download for free at http://cnx.org/content/col10994/1.3
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