Wednesday, July 15, 2015

Modeling Volume Measurements using the Metric System

When a kid can't get the hang of their math lesson, then I know it's time to bring out the manipulatives.

Normally, I try to introduce each mathematical concept using manipulatives right at the beginning, but sometimes they sneak up on me. In Will's Math Mammoth, for instance, she was tooling along in decimals, and I'd shown her how to model decimals using Base Ten blocks, how to round decimals using a number line with tenths and hundredths marked, how to divide decimals using blank hundred grids as models, etc., but then I went to print out her lesson for the day one morning and boom! Here's a lesson on the metric system, all of a sudden!

I let the lesson go by, then, just handing it over to Will, but she just could not wrap her head around the concept of metric conversions. Grams to centigrams? Kilometers to meters? Hectoliters to liters to milliliters? Forget it! It made no sense to her, even when I gave her a conversion chart for reference.

The next day, then, we had a different type of math lesson. I had bought this set of graduated cylinders marked in liter measurements a while ago--like, a year and a half!--and had never opened them. This day, however, was finally the day for the graduated cylinders to come out to play!

I made Will a chart that consisted of seven rows, each with the conversion chart from kiloliter to milliliter typed out. Her job was to be two-fold:
1. Model each liter unit from milliliter to liter, and
2. Write out the complete conversion chart when the entry for each unit is 1. For example, what is the complete conversion chart for 1 milliliter? 1 decaliter?
Lastly, I provided a set of Base Ten blocks to use for modeling. My own goals for this lesson were to:
1. Provide Will with a visual reference of each unit from milliliter to liter.
2. Give Will practice making these conversions.
3. Have her create her own reference sheet to use in future lessons.
4. Let her have plenty of practice looking at that conversion chart, to help with memorizing it.
First, I asked Will to model one milliliter:

I would have liked for her to have used the 1 centiliter graduated cylinder for this, just because, but for each unit that she modeled, she kept choosing to use the largest cylinder that still had markings for her particular measurement:

It spoiled part of the activity that I had planned, because I'd wanted her to photograph each measurement to serve as a visual reference, but photos of cylinders of different sizes, each with water barely covering its bottom, doesn't make much of a comparative reference. Ah, well...

Will normally loathes manipulatives, but surprisingly, she LOVED this activity! Perhaps it was the way that it involved not tiny little pieces of things to fiddle with, but large movements that you can make with your whole body:

It was more of a problem-solving activity than a simple modeling one, as well, which also helped.

For the first couple of measurements--1 milliliter, and 1 centiliter--I used the Base Ten blocks to show her how the conversions work exactly as they do with decimals. If the cm cube represents 1 milliliter, then the ten-bar represents 1 centiliter. What decimal represents the place that one cm cube holds in a ten-bar? In a hundred flat, for the deciliter? In a thousand cube, for the liter?

After the first couple Will could easily see the pattern that emerges, and could fill in all the others herself:

Here's what her finished chart looks like:

This activity turned out to be the key that unlocked the metric system for Will. As she filled out the chart, she said, in passing, "I understand this." All the yays!

Of course, this is the best hot summer day celebration of the liter!

We're about to begin a two-week break from school, so this might not happen for a while, but I did have Matt buy a giant bag of cheap rice so that Will can do this same activity with grams--for that, I plan to have her put her measurements in sandwich baggies and label them, so that she CAN have a permanent visual reference for it.

And I suppose I should also start reading ahead in Math Mammoth...