Alvin pp

 Knowledge of the 4 basic math operations.
 Knowledge of decimals.
 Knowledge of the various units of
measurements and their conversion
(sometimes merged with the teaching of the
topic of average).
 Knowledge of the part-whole concept and
unitary method (in solving word problems).

 Interpret average as “total amount ÷ number of
items”.
 Calculate the average number or quantity.
 Find the total amount given the average and
the number of items.
 Solve up to 3-step word problems involving
average.

 AVERAGE = TOTAL AMOUNT or VALUE
NUMBER OF ITEMS

 Derivation of the concept (and formula) of
average, and understand what it means.
 Apply the formula to find average.
 Address some of the common errors and
learning difficulties faced by students.

 Confusion between the concept of sharing (equally) VS
the concept of average, even though both utilizes the
division method.
 Inability to distinguish the category of items from the
number of items.
 Disregard zero or repeated measure/ number as part
of the data set.
 Misconception that the average of a set of data can
ONLY be a whole number.
 Misconception that the average means that every single
individual for example, will have the same value.
 Inept application of the part-whole concept to word
problems involving average.

 Number the individual pupils within their
groups (A-D). Show of hands to confirm
understanding
 A: 1 counter, B: 2 counters, C: 4 counters, D: 5
counters.
 Qn: How to even out all the counters among
the members in the group such that we have a
fair distribution?

 How many counters does each person have
now?
 So, after you have evened out the counters
among yr group members, each of you will
have 3 counters.
 We say that 3 is the average for the set of
numbers 1, 2, 4 and 5.
 Record it down in the table provided.

A: 2 counters, B: 4 counters, C: 5 counters, D: 5 counters

A B C D

 How many counters does each person have
now?
 So, after you have evened out the counters
among yr group members, each of you will
have 4 counters.
 We say that 4 is the average for the set of
numbers 2, 4, 5 and 5.
 Record it down in the table provided.

 Describe the pattern you see. Can you derive a
formula to calculate average in both cases?

A B C D Total counters No. of children Average

Activity 1 1 2 4 5 12 4 3

Activity 2 2 4 5 5 16 4 4

A B C D Total counters No. of children Average

Activity 1 1 2 4 5 12 4 3

Activity 2 2 4 5 5 16 4 4

12 16
4 4

Gerald Rahma Bernard Vani Winnie Jac Total weight No. of children Averag
(kg) t (kg) (kg) kg) (kg) (kg) e
(kg) (kg)
Activity 75.5 82 55.2 58 54.1 44
3
 Now that we have their individual weight listed on the
table, can we use the formula to calculate their average
weight?

 AVERAGE = TOTAL WEIGHT
NUMBER OF CHILDREN

Gerald Rahma Bernard Vani Winnie Jac Total weight No. of children Averag
(kg) t (kg) (kg) (kg) (kg) (kg) e
(kg) (kg)
Activity 75.8 82 55.2 58 54.1 44 368.8 6 61.4
3

 As can be seen, the average weight that we’ve gotten is a decimal figure. So,
banish the misconception that average must be a whole number

 The concept of average involves smoothening out the values to get a figure
that somewhat lies in the middle. As can be seen, the concept of average is
different from that of sharing. At the end of the day, there is no way that we can
divide and share the weight of any one person among the rest of the children.
Their individual weight will still remain the same. The average weight in this
case is simply an indication of the best estimate of their individual weight after
smoothening it out.

Alvin pp

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