1. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
Name
Math Period ____
Date: _____
Module 1 ‐ Lesson 23 ‐ "Problem Solving
Using Rates, Unit Rates, and Conversions"
23
I. Vocabulary/Informaon
1) Rate ‐ a rate is a rao that compares two quanes measured in different units. For
example, a car travels 100 miles in 2 hours.
3) Constant Rate ‐ A measurement of something happening per unit of me. The me
is always in the denominator or on the BOTTOM when using T ‐ R ‐ F strategy.
4) Unit Rate‐ The value of a quanty when the second quanty is one. When finding
unit rate, the quanty of ONE should be le in the denominator. This will be demonstrated
in the first example.
II. Concepts/Objecves
1) Students solve constant rate work problems by calculang and comparing unit rates.
2) Constant rate problems always count or measure something happening per unit of
me. The me should always be in the denominator.
3) Somemes the units of me in the denominators of two rates are not the same.
When this is the case, one must convert one me measurement to the other before finding
the unit rate.
4) Dividing the numerator by the denominator can be a shortcut in finding unit rate as
opposed to using other strategies. This will be shown in the first example.
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2. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
Lets first tackle this using a strategy that we already know... T ‐ R ‐ F. In the first T ‐ R ‐ F model
we are going to set it up the same way the problem gets read... lawns on top and hours on
the boom of the template.
YOU
LAWNS
_____
HOURS
_____
_____
_____
_____
FRIEND
LAWNS
_____
HOURS
Based on your calculaons, who cuts lawns at a faster rate? Explain why.
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3. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
Now lets see what happens when we reverse the template. This me, we are going to put
hours on top and lawns on the boom in the template
YOU
HOURS
_____
LAWNS
_____
_____
FRIEND
HOURS
_____
LAWNS
_____
_____
Based on your calculaons, who cuts lawns at a faster rate? Explain why.
Even though we essenally get the same answer for different reasons, it is best to use the
first model with me ALWAYS on the boom part of the template (rao) when solving unit
rate problems. Common core wants us to do it this way too and we have to be prepared for
this consistent format when doing state tests. If you think about it, most rates involving
me are expressed this way anyway. Miles per hour for cars is an example. Time will always
be on the boom!
Finally, many of you have already realized that you can easily find unit rate by dividing the
numerator by denominator to find unit rate. As a maer of fact, some of you even
discovered this by accident way back in lesson #10 when finding the value of the rao. Let's
see how it works here. Recall the following rate from the original problem...
You
Friend
3 lawns
5 lawns
5 hours
8 hours
Find unit rate using the shortcut, numerator divided by denominator.
You: ____________ lawns per hour
Friend: _____________ lawns per hour
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4. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
But, can't we also show who is faster by making equivalent raos so we don't have to deal
with decimals at all?
Sure can! Let's do it!
YOU:
FRIEND:
And you can also make tape diagrams too. The point is that there are mulple strategies
you can use to find an answer. That's the whole gist of MODULE 1! You use what works
best.
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5. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
What strategy do you want to use and why?
Let's do it!
What strategy do you want to use and why?
Let's do it!
* If the queson had asked to find how fast each animal runs in ONE second, would that
have changed your strategy? Why or why not?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
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6. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
Example 4: Flying Fingers
The secretary in the main office can type 225 words in 3 minutes, while the
computer teacher can type 105 words in 90 seconds. Who types at a faster
rate?
Before we use a strategy, what issue do you see regarding this problem? What must we do
BEFORE we start to solve it?
Let's divide ourselves into two groups... one group will convert minutes to seconds. One
SLIDE
group will convert seconds to minutes before solving. Then we will compare our answers
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7. Module 1 Lesson 23 Problem Solving Using Rates, Unit Rates, and Conversions.notebook
November 19, 2013
1) In the last problem, did we have to change one me unit?
______________________________
2) What happened if we do not convert one me unit so that they match?
__________________________________________________________
__________________________________________________________
3) Does it maer which one you change?
_______________________________________________________
4) Can you choose the one that makes the problem easier for you?
_______________________________________________________
5) Is there an advantage in choosing one method over the other?
__________________________________________________________
__________________________________________________________
Please take out your exit ticket for Lesson 23, close your
binder, and complete the exit ticket. This will be collected.
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