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Mathematics

Common and decimal fractions

Common fractions

Educator section

Memorandum

INTRODUCTION

The learning programme for grade six consists of five modules:

1. Number concept, Addition and Subtraction

2. Multiplication and Division

3. Fractions and Decimal fractions

4. Measurement and Time

5. Geometry; Data handling and Probability

  • It is important that educators complete the modules in the above sequence, as the learners will require the knowledge and skills acquired through a previous module to be able to do the work in any subsequent module.

COMMON AND DECIMAL FRACTIONS (LO 1; 2 AND 5)

LEARNING UNIT 1 FOCUSES ON COMMON FRACTIONS

  • This module continues the work dealt with in grade 5. Addition and subtraction of fractions are extended and calculation of a fraction of a particular amount is revised.
  • Check whether the learners know the correct terminology and are able to use the correct strategies for doing the above correctly.
  • Critical outcome 5 (Communicating effectively by using visual, symbolic and /or language skills in a variety of ways) is addressed.
  • It should be possible to work through the module in 3 weeks.
  • ** Activity 17 is designed as a portfolio task. It is a very simple task, but learners should do it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.
  • LEARNING UNIT 2 FOCUSES ON DECIMAL FRACTIONS
  • This module extends the work that was done in grade 5. Learners should be able to do rounding of decimal fractions to the nearest tenth, hundredth and thousandth. Emphasise the use of the correct method (vertical) for addition and subtraction. Also spend sufficient time on the multiplication and division of decimal fractions.
  • As learners usually have difficulty with the latter, you could allow 3 to 4 weeks for this section of the work.

** Activity 19 is a task for the portfolio. The assignment is fairly simple, but learners should complete it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.

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Leaner section

Content

Activity: to recognise and use equivalent forms of decimal fractions [lo 1.5.2]

ARRANGEMENT OF DECIMAL AND COMMON FRACTIONS

Earlier in the module you had to decide whether relationship signs were filled in correctly. Work with a friend to examine the following question and the solutions::

1. Two painters wanted to know who was painting the longer wall: one wall measured 9,3 m and the other 9 1 4 size 12{9 { {1} over {4} } } {} m.

x 4

  • x 4 I work it out like this: 9,3 = 9 3 10 size 12{9 { {3} over {"10"} } } {} 3 10 size 12{ { {3} over {"10"} } } {} = 12 40 size 12{ { {"12"} over {"40"} } } {}

x 10 9 3 10 size 12{9 { {3} over {"10"} } } {} = 9 12 40 size 12{9 { {"12"} over {"40"} } } {}

x 10 9 1 4 size 12{9 { {1} over {4} } } {} = 9 10 40 size 12{9 { {"10"} over {"40"} } } {} 1 4 size 12{ { {1} over {4} } } {} = 10 40 size 12{ { {"10"} over {"40"} } } {}

The 9,3 m wall is longer.

1.2 I first change the 9 1 4 size 12{9 { {1} over {4} } } {} m to a decimal fraction.

x 25x 25 9 1 4 size 12{9 { {1} over {4} } } {} = 1 4 size 12{ { {1} over {4} } } {} = 25 100 size 12{ { {"25"} over {"100"} } } {}

9,3 =

Whose method do you prefer?

  • Why?

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2. ANOTHER COMPETITION!

This time the girls are competing against the boys! You now have two minutes to fill in the correct relationship sign. Your educator will then ask any boy or girl to read out the right answers.

2.1 0,09 9 100 size 12{ { {9} over {"100"} } } {}

2.2 4,02 4 2 5 size 12{4 { {2} over {5} } } {}

2.3 0,016 16 100 size 12{ { {"16"} over {"100"} } } {}

2.4 0 0,8

2.5 0,20 . 1 5 size 12{ { {1} over {5} } } {}

2.6 1,4 1 8 20 size 12{1 { {8} over {"20"} } } {}

2.7 3 210 1 000 size 12{ { {"210"} over {1`"000"} } } {} 3,22

2.8 0,494 1 2 size 12{ { {1} over {2} } } {}

2.9 2,006 2 6 100 size 12{2 { {6} over {"100"} } } {}

2.10 0,025 1 4 size 12{ { {1} over {4} } } {}

  • Who has won this time?
  • How many of your answers are correct?

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.5: We know this when the learner recognises and uses equivalent forms of the numbers listed above, including:

1.5.2 decimal fractions to at least 2 decimal places.

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Source:  OpenStax, Mathematics grade 6. OpenStax CNX. Sep 10, 2009 Download for free at http://cnx.org/content/col11030/1.1
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