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Tuesday, March 08, 2016

Learning Fractions: Multiple Models

We'll mark up the models by counting totals, adding numbers
to the Roman Numerals, and noting length and width of number
and ball or circle grid first. 
In order to understand fractions, students need to work with multiple models. Tomorrow we'll explore the models to the right as we study a number of fractions with greater depth.

First we'll study a fractions such as 24/60. We'll first make models of that fraction with the "candy jar" model and clock model. Then we'll discuss how we can simplify that fraction. After simplifying to 2/5. We'll discuss what that same fraction looks like when we have 100 items. We'll discuss what's 2/5 of 100? Then we'll create models with the 100's chart and 100-circles diagram. After that we'll fill in the chart in the middle naming fraction, simplified (lowest terms) fraction, decimal fraction, decimal, and percent.

I'll emphasize that in all models we showed 2/5, but in each model 2/5 was a different amount. With regard to the candy, it was 24 pieces. It was also 24 minutes on the clock. But on the 100's model 2/5 was equal to 40 numbers and on the balls diagram, it was 40 balls.  I'll ask, "How can the same fraction be a different amount on each model." I imagine someone will say, it doesn't have to be the same amount, but it does have to be the same fraction or proportion of the whole. It means dividing the whole set or object into five equal pieces and you have 2/5 or 40% or .40 of the model considered (colored) in each example. For example 40% (2/5) of 60 is 24 while 40% (2/5) of 100 is 40.

If you only use one kind of model, students won't broaden the fraction concepts and understanding in ways that matter. That's why multiple models of whole objects and sets is an important ingredient to teaching fractions well.

Once we've reviewed the models with a couple different fractions, I'll have students complete one model on their own or with partners. Then I'll ask them to think about and use all the models we've created in the past two weeks to complete this equivalency page.

As they complete the independent/partner work, I'll coach individuals and partners.

There's never one way to foster a knowledge path for a group of students. Every year I do it a bit differently depending on the group's interests, experience, and need. So far we've explored a lot and I know we are building a good foundation. I don't want to rush it too much as I know that will hinder deeper learning. With all this in mind, what would you add to this lesson?