Length Measures

Monday 11/3/08

Do-now: Determining the conversion rules

I've given your group a plastic bag with three different types of length units in it. Figure out the conversion rules, and write them out in the space below. On your desk, lay out the units in a way that proves the rules you came up with.

Converting a mixture of units into greens

Now that we know the conversion rules, we can convert any measurement made with these units into other units. In this section, you will make your measurements using a mixture of units, whatever is convenient, and then you will convert everything into greens.

a =      greens +      yellows +      purples =

b =      greens +      yellows +      purples =

c =      greens +      yellows +      purples =

d =      greens +      yellows +      purples =

e =      greens +      yellows +      purples =

f =      greens +      yellows +      purples =

g =      greens +      yellows +      purples =

h =      greens +      yellows +      purples =

Converting into larger units

If I ask you to measure out a line whose length is a large number of greens, you are much better off converting that first into a mixture of larger units. For each of the problems below, first show, step by step, how to convert the number of greens into as large units as you can. Then, lay out on your desk a combination of units that will be that many greens long. You can go on to the next problem while you wait for me to come by and check your work.

12 greens =

21 greens =

25 greens =

17 greens =

29 greens =

19 greens =

31 greens =

39 greens =

What to study for the test

What we have done today is to go through, with a new type of measuring unit, the whole process that we have applied to all the different units we worked with. So, if you understand what we did today, you are in good shape for the test.

First, we had to figure out how to measure with the units we were given.
I measure something by counting how many of some unit fit into it.
What it means to count how many units fit in depends on the type of unit. With area units, this meant that the shape had to be covered. With water, this meant dumping in water from the unit until the container was filled, or pouring out into units until the container was empty.

The measurement is always written as a math sentence that says that the object is some number of a unit, as in "soda bottle = 9 cups." Sometimes, a measurement is a combination of different units, in which case there are "+" signs to show that they are all combined together.

Because there are many different units to measure with, measuring any given thing may produce several different numbers depending on what units I measure it with.
When I measure with a smaller unit, I will get a bigger number.
This is true because a smaller unit will fit more times into the same object.

Instead of measuring the same object over and over in different units, we can figure out how to "convert" any measurement into different units, if I can find out how many of one unit I can trade for another.
I figure out the conversion rule by measuring one unit with another.
The conversion rule is written as a math sentence saying that some number of one unit is the same amount as some number of another unit, as in "2 cups = 1 pint."

Once you know the conversion rules for the units you are working with, it is possible to take any measurement that you have written down and figure out what it would be in other units, without having to measure it all over again.
A conversion rule tells me that I can trade some number of one unit for some number of another.
By trading in according to my rules, I can get the measurement into the units I want, and I can be sure that the measurement still represents the same amount, just in different units.