This topic is new at P5 level and most students have no problem solving question when they were asked to find either the Average of a group or the Total of the group as long as they know the following formulas:
Average -> Total / No. of items
and
Total -> No. of items x Average
How about the following question? Does your child know how to solve such question?
Question
The average height of 3 boys and 5 girls is 1.47 m. The average height of 3 boys is 1.22 m.
What is the average height of 5 girls?
Is the answer 0.25 m (1.47 m - 1.22 m) correct?
OF COURSE, NOT!
This is a common mistake made by most students as they just see the word 'average' between the sentences and they just subtracted the averages to get the average of the other group of item! ;p
WELL ...
The correct and easy- to-understand solution is ...find the TOTALS FIRST! :)
Solution:
Total height of 3 boys and 5 girls-> 1.47m x 8 = 11.76 m
Total height of 3 boys -> 1.22 m x 3 = 3.66 m
Total height of 5 girls-> 11.76 m - 3.66 m = 8.1 m
Average height of 5 girls -> 8.1 m /5 = 1.62 m (answer)
Do highlight to your child his or her mistake if his or her answer obtained was 0.25 m! ;p
Next....
The next type of question that STUMPED most students is ....when the number of items is UNKNOWN (see sample question in the pic below)!
Without one of the parameters, students are lost on how to proceed the next step instead of thinking out of the box!😜
To solve such type of question, 2 methods are available (see below pics)
Average -> Total / No. of items
and
Total -> No. of items x Average
How about the following question? Does your child know how to solve such question?
Question
The average height of 3 boys and 5 girls is 1.47 m. The average height of 3 boys is 1.22 m.
What is the average height of 5 girls?
Is the answer 0.25 m (1.47 m - 1.22 m) correct?
OF COURSE, NOT!
This is a common mistake made by most students as they just see the word 'average' between the sentences and they just subtracted the averages to get the average of the other group of item! ;p
WELL ...
The correct and easy- to-understand solution is ...find the TOTALS FIRST! :)
Solution:
Total height of 3 boys and 5 girls-> 1.47m x 8 = 11.76 m
Total height of 3 boys -> 1.22 m x 3 = 3.66 m
Total height of 5 girls-> 11.76 m - 3.66 m = 8.1 m
Average height of 5 girls -> 8.1 m /5 = 1.62 m (answer)
Do highlight to your child his or her mistake if his or her answer obtained was 0.25 m! ;p
Next....
The next type of question that STUMPED most students is ....when the number of items is UNKNOWN (see sample question in the pic below)!
Without one of the parameters, students are lost on how to proceed the next step instead of thinking out of the box!😜
To solve such type of question, 2 methods are available (see below pics)
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For Method 1, it is best suitable for students who are familiar with ‘Number x Value’ method.
It is solved using the formula that they know, i.e. Total -> No. of items x Average. From the table, they can 'SEE' how the Totals obtained are related the Total of the incoming or outgoing item(s). |
|
For Method 2, it taps on the understanding of Average (i.e. the best estimate value of each item after evening out the Total among the total items) and require some reasoning skill.
I have explained it using a diagram and hope it helps in the understanding on how does the difference of $55 (in view of the new bag bought) resulted to the increase in the Average. |
Just a gentle reminder to parents who are coaching their kids:
REMEMBER! Teach by choosing the best method that suit your child (not you) the most! 😊 Seek clarification if needed 😊
Happy Learning, Everyone!!:)
REMEMBER! Teach by choosing the best method that suit your child (not you) the most! 😊 Seek clarification if needed 😊
Happy Learning, Everyone!!:)