Cooking With Numbers (Page 2 of 4) in pdf

Step 3 : Conversion background

Discuss with students instances when converting between units would be necessary. Examples include going from metric

to the U.S. system, but also within each system: feet to inches, minutes to hours, ounces to cups, grams to kilograms, centimeters

to meters….These conversions would be necessary if you are adding together the lengths of multiple small items. Each item may

be measured in centimeters, but if you have thousands of them, the overall length may be given in meters or even kilometers. Or

you may be adding together lengths or volumes in different units and you need them to be the same unit in order to add them. In

a recipe, for example, if you have measuring cups that are strictly “cups,” you will need to convert anything in the recipe that calls

for quarts or gallons.

Step 4 : Metric Conversions

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(I do) Give them the Conversion Factors handout. Conversions in the metric system are the easiest to begin with as all

conversions will include multiplying or dividing by a power of ten. Start by writing down some common metric prefixes:

Milli-, Centi-, Deci-, and Kilo-. Students may be familiar with centimeters, decimeters, and kilograms, so the prefixes

might not be entirely new. Since we’ll be working with volume later, write down the metric unit for volume: liter. Now

fill in some metric conversions: 1 liter = 1000 milliliters, 1 liter = 100 centiliters, 1 liter = 10 deciliters, and 1000 liters = 1

kiloliter. It may be a good idea to let them know this works for meters and grams as well, as milliliter is probably the only

common term there.

1. For the first conversion, you will do it, making sure to think aloud as you go so the students can follow your thought

process when solving the problem. Tell them you want to know how many milliliters are in a kiloliter. First, set this

up as an equation: 1 kiloliter = x milliliters. As part of the understanding the problem step, you know you need to

find a conversion factor to go from kiloliters to milliliters. This means your number should be larger than one as

you’ll be using a smaller unit of measurement to measure the same amount. Make sure you stress that keeping the

units is extremely important (they can treat them as if they are variables).

2. Next, look at the conversion factors. We don’t have one that will immediately take us from milliliters to kiloliters, so

we’ll have to go in steps. We do know that 1 kiloliter = 1000 liters. We also know that we can multiply anything by

1, or a fraction equal to 1, and not really change the value in our equation. Our strategy here, then, is to multiply by

fraction(s) equal to one until we get to the appropriate units.

3. Manipulate the conversion factor equation so that we have: 1 = (1000 liters)/(1 kiloliter), making sure to explain that

you wanted the desired units in the numerator. Carry out the next step by multiplying by this fraction in the

equation we are trying to solve. (Make sure to explain about cancelling out units!) We now have a new equation:

1000 liters = x milliliters. Next, we use the conversion factor 1 liter = 1000 milliliters. Once again, think aloud as you

go through the same steps again. Find a fraction equal to 1: 1000 milliliters/1 liter. Multiply by that and cancel out

units to get 1,000,000 milliliters = x milliliters.

4. Thus, 1,000,000 milliliters = 1 kiloliter. We have the correct units and we did get a number larger than 1, so our

review of the solution seems to be okay. Show them that this could have been done in one step by multiplying by

two fractions: 1 kiloliter *

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(We do) Next, for the entire class, pose the problem of wanting to know how many liters are in 175 centiliters. This time,

instead of just thinking aloud, you will want the class to give as much input as possible and only interject to help them

reach a solution.

1. We want to go from centiliters to liters, which is a larger unit of measure, so our number should decrease. If we set

up an equation, we get 175 centiliters = x liters this time.

2. Again, we want to multiply by fractions equal to one. I have a conversion factor involving centiliter and liters: 1 liter

= 100 centiliters. Since my desired units are liters, I will manipulate this to become: 1 = 1 liter/ 100 centiliters.

3. Now I take my fraction that is equivalent to 1 and multiply it by 175 centiliters to get that 175 centiliters is the same

as 1.75 liters.

4. Since our number decreased as we expected from step 1, our solution makes sense.

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(You do) This time, the students will work alone and you will provide guidance only if necessary as you check in with each

student. Pose the problem that we want to know how many milliliters are in a half of a kiloliter.

Step 5: Finding U.S. Customary Unit Conversion Factors

Using the measuring tools, the class will find out the conversion rates among cups, pints, quarts, and gallons. Start with

the two smallest: cups and quarts. It should be visually clear that the quart is bigger. Fill the cup container with the dry fill and

then dump it into the pint. Keep track of how many times the cup container must be filled and dumped into the pint container

before the pint container is full. Write the equivalence relation down: ___ cups = 1 pint. If there are enough materials, hand

them out for students to find the rest of the equivalence relations. Otherwise, have a few come up to demonstrate finding some

for the rest of the class. At the end, there should be the following relations:

2 cups = 1 pint

Cooking With Numbers Page 2

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