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Exam answers for FMT3701 for November 2020 received a distinction.
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FMT3701 Examinations Student 49432087Question 1
1.1.1 The most common misconception is that learners classify fractions into the pre-
existing knowledge they have that numbers are natural numbers. This is untrue as
all numbers are not natural numbers, only whole numbers are natural numbers.
Fractions are rational numbers and the denominator and numerator are separate
numbers that form a rational number.
1.1.2
You have to change the denominator to a common denominator, so the 2 and 4
both have 4 as a common factor, so you can multiply the 2 by 2 to get 4 and what
you do to the bottom you must do to the top. In essence you are multiplying by 1,
so you don’t change the value of the fraction.
1.1.3 Natural and rational numbers differ with regards to value. With natural numbers one
number is always linked to one value. In a fraction, value is governed by
relationship between the two numbers in the fraction and the ‘whole’. Its value not
only depends upon whether it is the numerator, the denominator or the whole, but
also upon what the other numbers in the fraction are. It is the relationship between
these three numbers that determines the value.
I would start by using practical examples. Take a round fruit, e.g. orange. Cut this
in half in front of the class. Show that you can out two halves together to get one
whole. Write on the board:
Then cut the one half in half again to make quarters. Show that if you have 2
quarters you can make one half. Write on the board:
Then cut the other half in half as well. Repeat the same sum on the board.
Use the two quarter sums to show as follows:
1 1 1 1 4 1
+ + + = = =1
4 4 4 4 4 1
2 2 4 1
+ = = =1
4 4 4 1
1 1 2 1
+ = = =1
2 2 2 1
The learners needs to understand that you can divide, or break up, parts of a whole
or a whole into parts. The number of parts the whole has been broken up into gets
represented by the denominator, the bottom of the line. The top of the line in the
numerator, how many parts you have of the whole.
, FMT3701 Examinations Student 49432087
In essence fractions are this:
(What I have) ÷ 2 (How many parts there are to make a whole) = 1 ÷ 2 =
Examples:
a) I have a pizza to share between four friends how much of the pizza will each
friend get?
1 ÷4=
Each friend gets one part (numerator) and the pizza gets divided into 4
friends (denominator).
b) Giac has of a popcorn bowl left after the movies and Franco has left.
They decide to share this evenly when they get home with their little sister.
How much does each get?
+ = x + x = + =
Divide the numerator in 3. 9 ÷ 3 = 3 . Then each will receive of the
original bowl.
1.2 The counting error that is taking place is linked to the One-to-One Correspondence
principal. This states that each object in a group can be counted once and only once.
The order of counting doesn’t matter, but each object should be counted at least
once. By skipping blocks the learner has miscounted the total.
The learner might have problems with rote counting and the teacher needs to assess
this first. Have the learner count from 1-10 repeatedly while showing the number on a
number line. You should also have them pick up and place the object in a different
position as they count, that is move the items away once it has been counted.
I would use beads with a number line. As the learner counts have them place one
bead at that specific number. This way when they reach 10, they should have 10
beads placed out.
Have them then count the beads as they remove them from next to the numbers, still
10. This should be repeated a few times and then highlight that the number of beads
stays the same no matter their location. At the number or away from the number.
This activity can be repeated with other objects or even the learners in the class. You
can write the numbers on the floor with a marker and have them stand on a number
as they are counted. Then move away once they are counted again. The number of
children stays the same.
Show the child that no matter which way they count the number stays the same and
that they need to count each one only once.
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