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?

A B C D

A B C D

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 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 B C D

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

A B C D

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

4

€

16

4

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 (kg)

Rahmat (kg)

Bernard (kg)

Vani(kg)

Winnie kg)

Jac(kg)

Total weight (kg)

No. of children

Average (kg)

Activity 3

75.5

82 55.2 58 54.1

44

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.

Gerald (kg)

Rahmat (kg)

Bernard (kg)

Vani(kg)

Winnie (kg)

Jac(kg)

Total weight (kg)

No. of children

Average (kg)

Activity 3

75.8

82 55.2 58 54.1 44 368.8 6 61.4