Thursday, 25 August 2011
:: Day 4 -Part or Whole.. Part or Whole.. ::
:
"Ok children, tonight we will be learning about FRACTIONS!"
So ... basically, today’s entry is gonna be just about FRACTIONS apart from many other things that I have learnt last night.
Scenario: Dividing Fractions
Teacher: Ok children. Today we are going to do 3/4 ÷ 1/4. You must first change the division sign to multiply sign. Then invert 1/4 into 4/1. Then you cancel both the 4s and then you get the answer as 3.
Student: But Teacher. Why must change the divide sign to multiply?
Teacher: I don’t know. The rule is like that so just follow. You MUST do it this way!
Sounds familiar???
This is the problem that many of us faced during Math lessons in school many, many years ago. Solutions were given with NO justification. True?
Yesterday’s Fraction activity opened up my eyes. The way Dr yeap introduced the concept was way, way different from those days.
(1) We were told to divide a square paper provided into 4 equal parts. After we are done with that, he invited us to show the product and share if any of us has came up with something special or unique.
(2) He go on to explain that for every parts that are equal, THEY CAN BE NAMED. And for this case, each part is called 1 FOURTH.
*His reason for using the word ‘FOURTH’ was because ‘FOURTH’ is a NOUN. Similar to cookies, apples, cupcakes etc … something that preschoolers and lower primary students can relate easily to.
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Btw have you ever tried drawing a big ‘X’ from one corner of a rectangle to the other corner? And have you ever wonder if they are equal EVENTHOUGH visually the 4 triangles that you see (after puting the ‘X’) doesn’t look equal at all? And IF you think that they are equal, can you PROVE IT?
*They don't look equal right? They seems unidentical*
Anyway...
After much brainstorming, we all were able to prove that the 4 parts of the rectangle are equal using 3 different ways/methods.
Anyway...
After much brainstorming, we all were able to prove that the 4 parts of the rectangle are equal using 3 different ways/methods.
(1) We first began by folding the rectangle paper provided, cut 1 triangle (bottom) into half and place the 2 smaller triangles onto either one of the triangle on the side and amazingly, they can fit! (concrete)
(2) We drew 2 more dotted lines (imaginary lines) to make the ‘fourths’ as ‘eighths’ to serve as a guide (pictorial)
(3) And lastly, at a more advance level, we proof our findings through algebra (abstract).
This is done by finding the Area of each of the triangle by applying this formula: ½ x B x H to make sure all 4 triangles measured to have the same area.
MORAL OF THE STORY:
“BEING EQUAL DOES NOT MEAN IDENTICAL”
–Dr Yeap Ban Har
As the night gets heated up with discussions and ideas, I can’t help but ponder:
Is there really no ONE way to arrive to a solution? Are there really many other possible ways of cracking the ‘code’?
Could it be that we are so used to the rigid way of solving Math problems by memorizing formulas rather than really understanding the concept and looking out for strategies? Or … we are just plain lazy to try other methods as we are so used to being ‘fed’ with answers by our teachers.
SO…
Do we want our children or students to be like us? OR…
Instill in them life-long skill of PROBLEM-SOLVING and ‘Never say Cannot’ attitude?
Take some time to reflect …
-ME-
Blogged @ 22:01 |
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