Proportional Reasoning Standards 7RP1 7NS2d 7NS3 7EE4a 7G1 Resource Connected Math Program 2 Comparing and Scaling Investigation 31 Comparing and Scaling Ratio Proportion and Percent ID: 243711
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Focus 1: Proportional Reasoning
Standards: 7.RP.1, 7.NS.2d, 7.NS.3, 7.EE.4a, 7.G.1
Resource: Connected Math Program 2
Comparing and Scaling: Investigation 3.1Slide2
Comparing and Scaling
Ratio, Proportion, and Percent
Investigation #3- CMP2Slide3
Mathematical & Problem-Solving
Learning Goals for Comparing & Scaling Rates
Examine & Connect the idea of unit rate to what you already know about ratios and about linear relationships (3.1)
Further develop understanding of unit rates and how to compute and interpret them
Work with the important application of rates to miles per hour (speed)
Introduce the concept of “average” or “steady” rate of progress
Introduce and formalize the meaning of unit rate and computation strategies for computing unit rates
Relate unit rate to the slope of the line representing the equation of the underlying relationship
Confront the issue of what it means to divide in rate situationsSlide4
Investigation 3.1
Learning Target
Examine and connect the idea of unit rates to what students already know about ratios and about linear relationshipsSlide5
Investigation #3.1Comparing and Scaling Rates
The following examples illustrate situations involving another strategy to compare numbers.
My mom’s car gets 45 miles per gallon on the expressway.
We need two sandwiches for each person at the picnic.
I earn $3.50 per hour baby-sitting for my neighbor.
The mystery meat label say 355 Calories per 6-ounce serving.
My brother’s top running rate is 8.4 kilometers per hour.Slide6
Getting Ready for Problem 3.1
What two quantities are being compared in the rate statements?
Which of the rate statements is different from the others?
In which of the situations is a quantity being compared to one unit of another?
These are examples of rates that are called
unit rates
.
A unit rate tells us how many per unit. Miles per hour tells how many miles are matched with 1 hour of travel and so on. Slide7
What are some other rates that you have encountered?
Does the statement “440 miles traveled on 20 gallons of gas” represent a unit rate?
Can you find a related unit rate?
How did you find that?
Did anyone have a different way to think about this?
Now let’s use this kind of thinking to help solve the challenge of buying calculators.
Slide8Slide9
Vocabulary Term- RATE
Each of these statements compares two different quantities.
A comparison of two quantities measured in DIFFERENT UNITS is a RATE.
For example
, one compares miles to gallons of gas. Slide10
3.1 Technology on Sale
Stores, catalogs, and Web sites often use rates in their ads. The ads sometimes give the cost for several items. You might see an offer like the one shown at the right.
The listed prices are for orders of 10, 15, or 20 calculators. But it’s possible to figure the price for any number you want to purchase.
One way to figure those prices is to build a
rate table
.
Calculators
for School
Fraction:
$120
for
20
Scientific:
$240
for
15
Graphing:
$800
for
10Slide11
Problem 3.1Making and Using a Rate Table
Suppose you take orders over the phone for the calculator company. You should be quick with price quotes for orders of different sizes.
A. Build a rate table like the one below. Fill in prices for each type of calculator for orders of the sizes shown.
Price of Calculators for School
Number Purchased
1
2
3
4
5
10
15
20
Fraction Price
$ 120
Scientific
Price
$ 240
Graphing Price
$ 800Slide12
Use your rate table to answer questions in your Math Workbook
B.
How much does it cost to buy 53 fraction calculators? How much to buy 27 scientific calculators? How much to buy 9 graphing calculators?
C. How many fraction calculators can a school buy it if can spend $390? What if the school can spend only $84?Slide13Slide14
D. How many graphing calculators can a school buy if it can spend $2,500? What if the school can spend only $560
?
E. What arithmetic operation (+, -, x, /) do you use to find the cost per calculator?
UNIT RATE
!!
F. Write an equation for each kind of calculator to show how to find the price for any number ordered
.Slide15Slide16
Explore 3.1Have you thought about?
Can you find out what a single calculator will cost? If so, how?
How can you use your answer to help fill in the rate table?
Do you see any patterns in your rate table? How would you describe them?
Does the unit rate help you to write a rule that will predict the number of miles
m
for any number of gallows of gas
g
? If so, how?
(m= unit rate X g)Slide17
Class Discussion & Sharing
What patterns do you see in the tables?
What would be the shape of the graphs of the data in these tables?
How would the graphs be alike and different?Slide18Slide19
Pre-Algebra Homework
A.C.E
Applications, Connections, & Extensions
#
1, 2
,
13-16
Copy your answers in your math workbookSlide20