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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.
  • 5 2 + 3 4 size 12{ { { size 8{2+3} } over { size 8{4} } } } {} = 5 5 4 size 12{ { { size 8{5} } over { size 8{4} } } } {} = 1 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {}

1.2 1 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {} + 2 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}

3 15 + 16 24 size 12{ { { size 8{"15"+"16"} } over { size 8{"24"} } } } {} = 3 31 24 size 12{ { { size 8{"31"} } over { size 8{"24"} } } } {} = 4 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

1.3 3 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} + 2 1 5 size 12{ { { size 8{1} } over { size 8{5} } } } {}

5 5 + 4 20 size 12{ { { size 8{5+4} } over { size 8{"20"} } } } {} = 5 9 20 size 12{ { { size 8{9} } over { size 8{"20"} } } } {}

2.

  • 4 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
  • 5 19 20 size 12{ { { size 8{"19"} } over { size 8{"20"} } } } {}

2.3 5 10 21 size 12{ { { size 8{"10"} } over { size 8{"21"} } } } {}

BRAIN TEASER!

1 + 1 2 size 12{ { {1} over {2} } } {} = 1 1 2 size 12{ { {1} over {2} } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} = 1 size 12{ { size 8{3} } wideslash { size 8{4} } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + 1 8 size 12{ { {1} over {8} } } {} = 1 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + 1 8 size 12{ { {1} over {8} } } {} + 1 16 size 12{ { {1} over {"16"} } } {} = 1 15 16 size 12{ { { size 8{"15"} } over { size 8{"16"} } } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + 1 8 size 12{ { {1} over {8} } } {} + 1 16 size 12{ { {1} over {"16"} } } {} + 1 32 size 12{ { {1} over {"32"} } } {} = 1 31 32 size 12{ { { size 8{"31"} } over { size 8{"32"} } } } {}

CLASS DISCUSSION

4 Make denominators the same

4 Find lowest common multiple

4 Make all improper fractions

4 First subtract whole numbers

Leaner section

Content

Activity: to solve problems in context [lo 1.6.2]

1. Pair up with a friend and work together to solve the following problem:

1.1 Mom uses 2 1 2 size 12{2 { {1} over {2} } } {} cups of sugar in one recipe and 3 3 4 size 12{3 { {3} over {4} } } {} cups of sugar in Altogether how many cups of sugar does she use?

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_____________________________________________________________________

1.2 At a birthday party, Rafiek and his friends eat one and five eighths of the ham and salami pizzas. They also eat two and two thirds of the ham and pineapple pizzas. What fraction of the pizzas did they eat altogether?

_____________________________________________________________________

_____________________________________________________________________

1.3 Rafiek and his friends also drank three and a quarter litres of Coke and two and one fifth litres of Cream Soda. What fraction of the cold drink did they drink?

_____________________________________________________________________

_____________________________________________________________________

2. Calculate the following by yourself:

2.1 2 5 6 size 12{ { {5} over {6} } } {} + 1 2 3 size 12{ { {2} over {3} } } {}

2.2 3 3 4 size 12{3 { {3} over {4} } } {} + 2 1 5 size 12{ { {1} over {5} } } {}

2.3 4 1 7 size 12{ { {1} over {7} } } {} + 1 1 3 size 12{ { {1} over {3} } } {}

PUZZLE THIS OUT!

  • Are you able to complete the fraction pattern?

1 + = 1 1 2 size 12{ { {1} over {2} } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} = 1 3 4 size 12{ { {3} over {4} } } {}

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + = 1

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + + = 1

1 + 1 2 size 12{ { {1} over {2} } } {} + 1 4 size 12{ { {1} over {4} } } {} + + + = 1

  • Are you able to complete this magic square?
5 2 size 12{ { {5} over {2} } } {} 3
2 4
1

CLASS DISCUSSION

  • What has to be done before fractions can be subtracted from one another?

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What must I do when the denominators of two fractions that have to be

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  • What is the simplest method for calculating the difference between two mixed numbers?

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  • Which other methods can be used?

_____________________________________________________________________

REMEMBER THIS!

When fractions are used in subtraction, we only subtract the numerators. The denominator is kept as it is.

REMEMBER THIS AS WELL!

If the answer is in the form of an improper fraction, it must be converted to a mixed number.

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 1.6: We know this when the learner 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:

1.6.2 measurements in Natural Sciences and Technology contexts.

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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