I like to introduce maths in a visual, concrete way, so I took out two manipulatives that have been tucked away in the cupboards from Tiger's preschool days and let him play around with them for a bit:

The Equivalency Cubes can also be used to teach concepts of of percentages and decimals. The main purpose of them this week, however, is for Tiger to become familiar with the concept of equivalent fractions.

After Tiger has played with the cubes for a while, we started on our fraction activity. I gave them three sheets of papers, each printed with three circles to be divided into smaller fractions. For example, the first sheet consists of three circles that have been divided into halves by a line drawn through the centre of the circle. The idea is to have the first circle remained as halves, and have the student further divide the other two circles into fourths and eighths. The second set of circles are: thirds (already drawn), sixths, and twelves; the third set consists of: fifths (already drawn), tenths, and twentieths.

After the division of the circles into smaller fraction parts is done, Tiger cut them out and glued them onto a piece of construction paper (together with each circle's corresponding labels) to make "The Dangerous Fraction Garden", as Tiger puts it. This step is not strictly necessary to learn the maths concept, but we wanted to have a laugh so we did it.

We then proceeded to understand Fractions of a Set. Using the printed sheets of incremental stacks of 4x5 squares, we first determined the total of each set. Then, we talked about how much one-fourth of each set would be -- this is quite simple, given that the sets are designed in four rows each. Finally, from one-fourth of each set, Tiger could easily determine three-fourths of each set by multiplying by three.

When the colouring is done, we glued both sheets of paper together to have an overall view of all our three-fourths. It provides a clear visual sense of what three-quarters of an incremental total looks like:

While Tiger has labelled under each set its non-simplified three-quarters fraction (15/20, 30/40, 45/60, 60/80, 75/100, 90/120), I showed him how to simplify them by finding the common factor of both numerator and denominator, so that each fraction eventually reduces to 3/4.

Tiger then worked through some of the problems in the Fractions section at Khan Academy. We found the drills to be adequate for practice.

The word problems on fractions present an interesting way to apply what Tiger has learned so far, so that is well worth a try. When he had enough of drills, he played the Fractions and Coins Game.

Finally, we also learned not to get too hung up about getting perfect scores, especially when in France:

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Great hands on activity as always. It's funny, fractions seem to be one concept the girls understood straight away (yay!)

ReplyDeleteAs an aside, what do you think of the Khan academy? I've been hearing bits about it recently and wondered if it was worth looking into?

It's wonderful to know that the girls understand fractions straightaway. Sometimes it's a matter of being to visual the concept, and the girls clearly can do it with fractions. That's excellent news! :-)

ReplyDeleteWe've dipped into Khan academy from time to time. I think it's very good as an alternative to workbooks as the system is designed such that it recognises the registered user's progress, as there is a log that tells the user how he is doing in each section, eg 'struggling' or 'practised' or 'mastery', etc. When the user gets stuck on any question, there is always a corresponding video to explain the concept. It can work successfully as a self-paced online learning class. Overall, I think it's very useful, and it's free to use.

Those manipulatives look very helpful. How do you use Khan Academy? Do you just select lessons from the fractions section?

ReplyDeleteMy son has been using Khan Academy for the past two months. I looked into it a few years ago and from what I remember, there has been a ton of improvement in the math section in particular. He logged in and took a pre-test. Now Khan Academy feeds him lessons to do. It works great for him since he is a figure-it-out kind of kid. Some days he spends 30 minutes on one lesson and other days he finishes 3 or 4 lessons in that time. One day he spent 30 minutes completely not understanding a concept, so I had him shut it down and try again the next day. He got it right away. I'm very impressed with Khan Academy. Although we don't use it exclusively, or every day, once or twice per week it has been very useful for us.

Tiger uses it pretty much the same way as you son does, Julie. Mostly we use Khan Academy to practise drills, to reinforce his understanding of a concept that we are learning. I don't use it exclusively either -- we mostly just dip into it when we need to. I often sit with Tiger when he watches the video, to see whether he understands the concept when it is explained in a different way from mine.

ReplyDeleteAnd yes, the maths section is continuously improving, in my opinion. It seems that most of their development budget goes into the maths section.

Now this is how to learn maths!

ReplyDeleteThank you, Fiona. That's a very kind compliment. :-)

ReplyDeleteFantastic! I love manipulatives...I just saw a photo floating around FB yesterday with legos being used to show fractions! :)

ReplyDeleteWe also had a "visual maths" moment for rounding up (we ended up with number lines! ) - they've drastically overhauled the way they teach maths in the UK since I was at school but "visual" learning seems so much more beneficial.

ReplyDeleteWhere did you get your fraction circles manipulative?

ReplyDeleteThe fraction circles was bought years ago from the Early Learning Centre.

ReplyDeleteHwee,

ReplyDeleteI love your hands-on approach to maths. Yes, concepts have to be presented in a concrete way. Paper printouts seem to be a great alternative to expensive manipulatives.

We also dip into Kahn Academy from time to time. My girls like Sal's conversation as he explains the lessons. (Have I got his name right? I can't remember!)

Thanks for stopping by, Sue. I try to present maths as concrete as possible before going into the abstracts, since I think my son has a better understanding of the concepts this way. Using Khan Academy is like having a maths tutor explain the concepts right there with you. It is a very useful tool. :-)

ReplyDelete