rules, tables, and graphs: part 1 › em-crosswalk › ... · of values and make line graphs from...
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Lesson 10�4 803
Advance PreparationDisplay the rates and ratios you have collected for the Rates and Ratios Museum. Invite students to add to the
museum over the next few days.
Teacher’s Reference Manual, Grades 4–6 pp. 64–68, 164, 278–289
Key Concepts and Skills• Use table data to create line graphs.
[Data and Chance Goal 1]
• Represent functions with tables, graphs,
and formulas.
[Patterns, Functions, and Algebra Goal 1]
• Extend patterns in graphs and tables
to solve problems.
[Patterns, Functions, and Algebra Goal 1]
Key ActivitiesStudents review the concept of rates and
practice representing rates with formulas,
tables of values, and graphs.
Ongoing Assessment: Recognizing Student Achievement Use journal pages 348 and 349. [Data and Chance Goal 1]
Key Vocabularyrate � formula � variable � line graph
MaterialsMath Journal 2, pp. 346–349
Student Reference Book, pp. 78 and 225
Study Link 10�3
slate � straightedge
Math Boxes 10�4Math Journal 2, p. 345
Students practice and maintain skills
through Math Box problems.
Study Link 10�4Math Masters, p. 301
Students practice and maintain skills
through Study Link activities.
ENRICHMENTSolving Rate ProblemsMath Masters, p. 302
Students use a formula to solve rate
problems in which the rate or the unit is
not known.
EXTRA PRACTICE
Graphing “What’s My Rule?” TablesMath Masters, p. 303
Students use rules to generate tables
of values and make line graphs from the
table data.
EXTRA PRACTICE
Analyzing Two RatesMath Masters, p. 300B
Students use rules, tables, ordered pairs,
and graphs to analyze data.
ELL SUPPORT
Describing Exhibits in the Rates and Ratios MuseumStudents describe rate situations and
different representations of rates in the
Rates and Ratios Museum.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
�
Rules, Tables, andGraphs: Part 1
Objective To develop representational forms for rates.
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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Speed and DistanceLESSON
10 �4
Date Time
Math Message
1. A plane travels at a speed of 480 miles per hour. At that rate, how many miles will it travel in 1 minute? Write a number model to show what you did to solve the problem.
Number model: Distance per minute: miles
Rule for Distance Traveled
2. For an airplane flying at 8 miles per minute (480 mph), you can use the followingrule to calculate the distance traveled for any number of minutes:
where d stands for the distance traveled in miles and t for the time of travel inminutes. For example, after 1 minute, the plane will have traveled 8 miles (8 º 1).After 2 minutes, it will have traveled 16 miles (8 º 2).
3. Use the rule d � 8 º tto complete the table at the right.
8480 � 60
Time (min) Distance (mi)(t ) (8 � t )
1 8
2 16
3 244 325 406 487 568 649 7210 80
Distance traveled � 8 � number of minutesor
d � 8 � t
Math Journal 2, p. 346
Student Page
804 Unit 10 Using Data; Algebra Concepts and Skills
Getting Started
Mental Math and Reflexes Describe number relationships. Have students identify the mystery numbers. Suggestions:
My number times 25 will equal 100. What is my number? 4
15 divided by my number will equal 6. What is my number? 2.5
Let y represent my number. 3y = 60; y = 20
Math MessageComplete the problem at the top of journal page 346.
Study Link 10�3 Follow-UpHave partners share answers and resolve differences. Discuss students’ solution strategies for Problems 3 and 4.
1 Teaching the Lesson
▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION
(Math Journal 2, p. 346)
Algebraic Thinking Remind students that a rate describes a relationship between two quantities. Point out that the two quantities that make up a rate have different units, for example, miles and hours, dollars and pounds, days and months. A rate tells how many of one type of thing there are for a certain number of another type of thing. To support English language learners, write the important ideas and examples regarding rates on the board.
A basic example for rates is speed. A speed tells how many units of distance there are for a given unit of time. Sixty miles per hour, for example, is a rate that says a distance of 60 miles is traveled for each hour of time.
Rates are often expressed with phrases that include the word per, as in 480 miles per hour, $2 per pound, and 10 rainy days per month. Rates can also be expressed as fractions: 3 apples
_ 89¢ , 12 inches _ 24 hours , 36 inches _ 1 yard . Ask students to give other examples of rates they have seen or used.
Have students share their solution strategies to the Math Message problem. Because there are 60 minutes in 1 hour, divide 480 by 60. Thus the distance traveled in 1 minute is 8 miles.
480 miles per hour and 8 miles per minute are equivalent rates. Ask volunteers to suggest an equivalent rate for 36 inches per 1 yard. 12 inches per foot
ELL
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Speed and Distance continuedLESSON
10 �4
Date Time
4. Complete the graph using the data in the table on page 346. Then connect the dots.
Use your graph to answer the following questions.
5. How far would the plane travel in 1 �12
� minutes?
6. How many miles would the plane travel in
5 minutes 24 seconds (5.4 minutes)?
7. How long would it take the plane to travel 60 miles?
12 miles(unit)
(unit)
(unit)
43.2 miles, or about 43 miles
7.5 minutes
1 2 3 4 5 6 7 8 9 10
10
30
20
40
50
60
70
80
90
Dis
tan
ce
(m
i)
Time (min)
00
Math Journal 2, p. 347
Student Page
Lesson 10�4 805
NOTE Continuous quantities can be divided
into smaller and smaller amounts. Measures,
such as the height or the weight of a student
in your class, are continuous quantities.
Discrete quantities are countable things that
cannot be broken up into smaller amounts.
The number of students in your class is a
discrete quantity.
The rates in this lesson can be represented
by line graphs because most of the variables
represent continuous, not discrete, quantities.
▶ Displaying a Rate of Speed
WHOLE-CLASS ACTIVITY
(Math Journal 2, pp. 346 and 347)
Algebraic Thinking Pose problems based on the rate 8 miles per minute:
● At 8 miles per minute, how far will a plane travel in 10 minutes? 80 miles In 2 1 _ 2 minutes? 20 miles
Ask students to share their solution strategies. To calculate the distance traveled, multiply the number of minutes of travel by 8. Explain that the solution can be expressed by the rule:
Distance traveled = 8 ∗ number of minutes
or, in abbreviated form, by d = 8 ∗ t. Remind students that this kind of rule is called a formula and the letters d and t are called variables. Variables used in formulas describe relationships.
Assign Problems 2– 4 on journal pages 346 and 347. Students use the formula d = 8 ∗ t to build a table of values and then display these values on a line graph. Circulate and assist.
When students have finished, discuss Problems 5–7 on journal page 347 as a class. Ask volunteers to use these problems to explain how to obtain values from the graph. For example:
� Problem 5
To find out how far the plane would travel in 1 1 _ 2 minutes, move along the horizontal axis to 1 1 _ 2 , which is halfway between 1 and 2 minutes, and mark the point on the line that is directly above 1 1 _ 2 . Then move left from there to 12 on the vertical axis. Thus, the plane would travel 12 miles in 1 1 _ 2 minutes.
10
30
20
40
50
60
0
Dis
tanc
e (m
i)
1 2 3 4 5 6 7 80
Time (min)
� Problem 7
To find out how long it would take the plane to travel 60 miles, reverse the procedure. Start at 60 on the vertical axis, move right to the line, and then work down to 7 1 _ 2 on the horizontal axis. It would take the plane 7 1 _ 2 minutes to travel 60 miles.
Point out that the table of values on journal page 346 is an example of a “What’s My Rule?” table. Also point out that when the dots on the graph are connected, they form a straight line.
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Representing Rates LESSON
10 �4
Date Time
$44
�Complete each table below. Then graph the data and connect the points.
1. a. Andy earns $8 per hour. Rule: Earnings = $8 ∗ number of hours worked
b. Plot a point to show Andy’s
earnings for 5 1 _ 2 hours.
How much would he earn?
2. a. Red peppers cost $2.50 per pound. Rule: Cost = $2.50 ∗ number of pounds
b. Plot a point to show the cost
of 8 pounds. How much would
8 pounds of red peppers cost?
10
20
30
40
50
Earn
ings (
$)
1 2 3 4 5 6 7
Time (hr)
00
$20 4 8 12
10
20
30
Cost ($
)
Weight (lb)
00
Time (hr) Earnings ($) (h) (8 ∗ h)
1 8 2 16 3 24 5 40
7 56
Weight (lb) Cost ($) (w) (2.5 ∗ w)
1 2.50 2 5.00 3 7.50 6 15.00
12 30.00
333-368_EMCS_S_G5_MJ2_U10_576434.indd 348 2/22/11 5:21 PM
Math Journal 2, p. 348
Student Page
Representing Rates continuedLESSON
10 �4
Date Time
3. a. Frank types an average of 45 words per minute.
Rule: Words typed = 45 ∗ number of minutes
b. Plot a point to show the number of words Frank
types in 4 minutes. How many words is that?
4. a. Joan’s car uses 1 gallon of gasoline every 28 miles.
Rule: Distance = 28 ∗ number of gallons
b. Plot a point to show how far the car
would travel on 1.4 gallons of gasoline.
How many miles would it go?
180 words
Nu
mb
er
of
Wo
rds
1 2 3 4 5 6
Time (min)
0
100
200
300
0
Gasoline Used (gal)
1 2 3 4 5 60
Dis
tan
ce
(m
i)
100
200
0
39.2 miles
Time (min) Words (t) (45 ∗ t)
1 45 2 90 3 135 5 225
6 270
Gasoline (gal) Distance (mi) (g) (28 ∗ g)
1 28 2 56 3 84 5 140
5 1 _ 2 154
�
333-368_EMCS_S_MJ2_G5_U10_576434.indd 349 4/6/11 11:02 AM
Math Journal 2, p. 349
Student Page
806 Unit 10 Using Data; Algebra Concepts and Skills
▶ Making Line Graphs from PARTNER ACTIVITY
Tables of Values(Math Journal 2, pp. 348 and 349; Student Reference Book, pp. 78 and 225)
Algebraic Thinking Have partners solve problems involving other rate situations on journal pages 348 and 349. Circulate and assist.
When students have finished, ask questions such as the following:
● For Problem 1 on journal page 348, would you use the graph, the rule, or the table to find out how long it took Andy to earn $42? Explain. Sample answer: It is easy to locate $42 on the graph.
● For Problem 4 on journal page 349, would you use the graph, the rule, or the table to find the distance traveled on 4 3 _ 7 gallons? Explain. Sample answer: It is easiest to use the rule and find 28 ∗ 4 3 _ 7 .
Ask: How could you use the Distributive Property to solve the problem 28 ∗ 4 3 _ 7 ? Refer students to Student Reference Book, pages 78 and 225 as a reminder. 28 ∗ (4 + 3 _ 7 ) = (28 ∗ 4) + (28 ∗ 3 _ 7 ); 28 ∗ 4 = 112; 28 ∗ 3 _ 7 = 12; 112 + 12 = 124 Ask students to solve the Check Your Understanding problems on Student Reference Book, page 78 using the Distributive Property.
Ongoing Assessment: Journal
Pages 348 �and 349Recognizing Student Achievement
Use journal pages 348 and 349 to assess students’ ability to use table data to
plot points on a graph. Students are making adequate progress if their
responses to Problems 1 and 3 are correct.
[Data and Chance Goal 1]
▶ Comparing Three Ways of WHOLE-CLASSDISCUSSION
Representing Rates(Math Journal 2, pp. 346–349)
Algebraic Thinking Point out that tables, formulas, and graphs are simply different ways of representing the same relationships. There are advantages to each way:
� Tables are often the easiest to understand.
� Formulas are the shortest forms of representation. They summarize the relationship and can be used to find other values in the table. (Rules expressed in words or by formulas are very much the same. Formulas are more compact, which can make them easier to use.)
� Graphs can help you understand the relationship, but are not as useful for finding precise values.
� Many relationships do not have formulas and can be reported in tables or graphs only. The sports and financial sections of the newspaper have tables and graphs that are examples of such relationships.
PROBLEMBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEMMBLELLBLEBLLLLBLEBLEBLEBLEBLEBLEEBLEEEMMMMMMMMMMMMMOOOOOOOOOOOBBBBBBBBLBLBBLBLBLLLLPROPROPROPROPROPROPROPROPROPROPROPRPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROROOOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEELELELELEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOOBBBBLBLBLBLBBLBBROOOOROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGLLLLLLLLLLLLLVVINVINVINVINVINNNVINVINNVINVINVINVINV GGGGGGGGGGGOOOOLOLOLOOLOO VINVINVVLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOLOOLOLOLOLOLOLOOO VVVVVLLLLLLLLLLVVVVVVVVVVOOSOSOSOSOSOSOSOSOSOOSOSOSOOOOOSOSOSOSOSOSOSOSOSOSOOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLVVVVVVVVVLLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING
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Lesson 10�4 806A
▶ Analyzing Two Rates WHOLE-CLASSDISCUSSION
(Math Journal 2, p. 349)
Remind students that they can also use tables, formulas, and graphs to compare situations in which there are two different rates. Refer students to Problem 4 on journal page 349. Write the following on the Class Data Pad:
Joan’s car: 28 mi _ 1 g Rule: Distance = 28 ∗ number of gallons
Tom’s car: 42 mi _ 1 g Rule:
Gasoline
(g)
Joan’s Car:
Distance (mi)
Tom’s Car:
Distance (mi)
0 0 0
1 28 42
2 56 84
3 84 126
4 112 168
5 140 210
Ask: What rule describes the distance Tom’s car travels for a given number of gallons of gasoline? Distance = 42 ∗ number of gallons Ask a volunteer to write the rule for Tom’s car next to his rate.
Have volunteers complete the table for Joan’s and Tom’s cars. Then have a volunteer provide the ordered pairs for Tom’s car. (0,0), (1,42), (2,84), (3,126), (4,168), (5, 210)
On journal page 349, Problem 4, ask students to plot the ordered pairs for Tom’s car on the grid. Have students label the respective graphs, Joan’s Car and Tom’s Car.
Gasoline Used (gal)
0 1 2 3 4 5 6
Dis
tance (
mi)
100
200
0
Joan’s carTom
’s ca
r
Ask: For each number of gallons of gasoline greater than 0, how does the distance Tom’s car travels compare with the distance Joan’s car travels? Each distance Tom’s car travels is 1 1 _ 2 times the distance Joan’s car travels. Ask students to explain how they used the rules, table, ordered pairs, and/or graph to help them answer the question. Answers vary.
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Math Boxes LESSON
10 �4
Date Time
4. Circle the figure below that has the same area as Figure A.
1. Make a magnitude estimate for the product. Choose the best answer. 0.4 ∗ 6.5
tenths
ones
hundreds
thousands
ten-thousands
3. a. Mark and label −1.7, 0.8, −1.3, and 1.9 on the number line.
b. What number is 1 less than −1.7? −2.7 c. What number is 1 more than 1.9? 2.9
2. Circle the numbers below that are divisible by 9.
3,735 2,043 192 769 594
-2 -1 0 1 2
-1.7 -1.3 0.8 1.9
A
5. Find the volume of the prism. Circle the best answer.
A 10 ft3
B 30 ft3
C 17 ft3
D 60 ft3
Volume = length ∗ width ∗ height
5 ft
3 ft
2 ft
247–250
92–94
189 197
11
333-368_EMCS_S_G5_MJ2_U10_576434.indd 345 2/23/11 1:09 PM
Math Journal 2, p. 345
Student Page
STUDY LINK
10�4 Representing Rates
301
Gasoline (gal)
Dis
tanc
e (m
i)
0
100
200
300
0 5 10 15
Cos
t ($)
Weight (lb)
00 5 10
5
10
15
20
25
Complete each table below. Then graph the data and connect the points.
1. a. Cherry tomatoes cost $2.50 per pound.
Rule: Cost = $2.50 ∗ number of pounds
b. Plot a point to show the cost of 8 pounds.
How much would 8 pounds of cherry tomatoes cost?
c. Would you use the graph, the rule, or the table to find out how much
50 pounds of cherry tomatoes would cost? Explain.
2. a. Chantel is planning a trip to drive across country.
Her car uses 1 gallon of gasoline every 24 miles.
Rule: distance = 24 ∗ number of gallons
Weight (lb) (w) Cost ($) (2.50 ∗ w)
1 2.50 3 7.50 6 15.00
10 25.00
Gasoline (gal) (g) Distance (mi) (24 ∗ g)
1 24 4 96 7 168
13 312
b. Plot a point to show the distance the car would travel
on 6 gallons of gasoline. How many miles would it go?
c. Would you use the graph, the rule, or the table to find out
how far the car would travel on 9 gallons of gasoline? Explain.
I can easily
are at the same point.
144 mi
$20.00
look for 9 gallons on the graph to see how many miles
103–105124
Name Date Time
Sample answer: I would use the rule because I could
easily multiply 50 pounds by $2.50 to get the cost.
294-322_439_EMCS_B_MM_G5_U10_576973.indd 301 2/22/11 5:44 PM
Math Masters, p. 301
Study Link Master
806B Unit 10 Using Data; Algebra Concepts and Skills
2 Ongoing Learning & Practice
▶ Math Boxes 10�4
INDEPENDENT ACTIVITY
(Math Journal 2, p. 345)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 10-2. The skill in Problem 5 previews Unit 11 content.
Writing/Reasoning Have students write a response to the following: In Problem 2, explain how to determine whether 3,735 is divisible by 9 without actually dividing. Sample
answer: Add the digits together. If the sum is divisible by 9, then the number is divisible by 9.
▶ Study Link 10�4
INDEPENDENT ACTIVITY
(Math Masters, p. 301)
Home Connection Students complete rate tables. They graph the data on line graphs.
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distance = rate ∗ gallons of gas d = r ∗ g
distance = miles per gallon ∗ 14 gallons of gas 357 = 25 1 _ 2 ∗ 14
rate =
LESSON
10�4 Solving Rate Problems
Rate describes a relationship between two quantities with different
units. Rate tells how many of one type of thing there are for a certain
number of another type of thing. Rates are often expressed with
phrases that include the word per. For example, miles per hour,
cost per ounce, or books per student.
One example of rate is speed. A basic formula is distance = rate ∗ time.
Multiplication can be used for many different problems involving rates.
For example, distance = rate ∗ gallons, total cost = rate ∗ ounces, or
total books = rate ∗ students.
To solve a problem using a formula, first replace variables with the known values.
Example:
Maribel can travel 5 miles per hour on her skateboard. How far will she travel in 2 hours?
Maribel can travel 10 miles.
Use the formula to solve the following problem.
1. Samuel’s go-kart can travel 357 miles on 14 gallons of gas. His go-kart
travels how many miles per gallon?
2. Samuel’s go-kart can travel miles per gallon of gas.
Explain your solution.
distance = rate ∗ time d = r ∗ t
distance = 5 miles per hour ∗ 2 hours 10 = 5 ∗ 2
distance = 10 miles
Name Date Time
25 1 _ 2 miles per gallon
Sample answer: The rate is the distance for 1 gallon of
gas, so I divide 357 by 14 to get 25 1
_ 2 miles per gallon.
25 1
_ 2
294-322_439_EMCS_B_MM_G5_U10_576973.indd 302 2/22/11 5:44 PM
Math Masters, p. 302
Teaching Master
LESSON
10�4 “What’s My Rule?”
in out (n) (15 - n)
1 14 2 13 8 7 10 5
18 -3 15 0
in out
4 2
12 6
16 8
2 1 7 3 1
_ 2
310 155
in out
1 1
2 3
3 5
4 7 5 9 10 19
in out
1 3 1
_ 4
2 3 1
_ 2
3 3 3
_ 4
4 4 8 5 16 7
in out (x) ((2 ∗ x) + 3)
2 7 4 11 6 15 8 19
12 27 0 3
Complete each table below according to the rule.
1. Rule: Subtract the in
number from 15.
2. Rule: Triple the
in number.
3. Rule: Double the
in number and add 3.
in out (d) (3 ∗ d)
7 21 12 36 8 24
0.3
1
9
_ 10 , or 0.9
3
_ 2 , 1 1
_ 2 , or 1.5
Complete each table below. Write the rule in words or as a formula. On the
back of the page, graph the data in Problems 4 and 5.
4. Rule:
5. Rule:
6. Make up your own.
Rule:
in by 4 and add 3.
Sample answer: n _ 2 ; Divide
in by 2. Multiply in by 2.
(n ∗ 2) -1;
n _ 4 + 3; Divide
and subtract 1.
231 232
Name Date Time
1 _ 2
294-322_439_EMCS_B_MM_G5_U10_576973.indd 303 2/23/11 4:21 PM
Math Masters, p. 303
Teaching Master
Lesson 10�4 807
3 Differentiation Options
ENRICHMENT
INDEPENDENT ACTIVITY
▶ Solving Rate Problems 5–15 Min
(Math Masters, p. 302)
Algebraic Thinking To apply students’ understanding of the basic rate formula, have students solve problems in which the rate or unit is unknown.
When students have finished, ask them to use the variables in the formula d = r ∗ t and to write two division equations. r = d/t; t = d/r Emphasize that the relationships in the formula also reflect the relationships between operations.
EXTRA PRACTICE
INDEPENDENT ACTIVITY
▶ Graphing “What’s My Rule?” 5–15 Min
Tables(Math Masters, p. 303)
Algebraic Thinking Students use rules to generate tables of values and make line graphs from the table data.
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Name Date Time
Analyzing Two RatesLESSON
10� 4
Each day, Taylor practices the piano 1 1
_ 2 hours and Kim practices
3
_ 4 hour.
1. In the tables below, write a rule for each student that gives the total number
of hours (h) practiced for a given number of days (d ).
2. Complete the tables to show the total amount of time each student practiced
during a 5-day period.
3. Use the data to write a set of ordered pairs in the form
(Days, Hours) for Taylor and Kim. Graph the data, connect
the points for each student, and label each graph.
Taylor Kim
(1,1 1
_ 2 ) (1, 3 _
4 )
(2,3) (2,1 1 _
2 )
(3,4 1 _
2 ) (3,2 1 _
4 )
(4,6) (4,3)
(5,7 1 _
2 ) (5,3 3 _
4 )
4. After each day, how does the total amount of time
practiced by Taylor compare to Kim’s time? Explain.
Sample answer: After each day, Taylor has practiced twice
as long as Kim. This is because his rate is twice as great.
Hou
rs P
ract
iced
Days0 1 2 3 4 5
0
1
2
3
4
5
6
7
8
Taylo
r
Kim
Kim’s Practice
Rule: h = 3
_ 4 ∗ d
Days Hours
1 3 _
4
2 1 1 _ 2
3 2 1 _ 4
4 3
5 3 3 _ 4
Taylor’s Practice
Rule: h = 1 1
_ 2 ∗ d
Days Hours
1 1 1 _
2
2 3
3 4 1 _ 2
4 6
5 7 1 _ 2
300A-300B_EMCS_B_MM_G5_U10_576973.indd 300B 4/6/11 11:12 AM
Math Masters, p. 300B
Teaching Master
808 Unit 10 Using Data; Algebra Concepts and Skills
EXTRA PRACTICE
INDEPENDENT ACTIVITY
▶ Analyzing Two Rates 5–15 Min
(Math Masters, p. 300B)
Students use rules, tables, ordered pairs, and a graph to identify a relationship between corresponding terms based on two rates.
ELL SUPPORT
SMALL-GROUPACTIVITY
▶ Describing Exhibits in the 15–30 Min
Rates and Ratios MuseumTo provide language support for rates, have students look at the Rates and Ratios Museum and describe some of the situations for which rates are used. Have students discuss different representations of rates displayed in the museum. Have them make a list of words associated with the rates in the museum to add to the display.
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Copyrig
ht ©
Wrig
ht G
roup/M
cG
raw
-Hill
Name Date Time
300B
Analyzing Two RatesLESSON
10� 4
Each day, Taylor practices the piano 1 1
_ 2 hours and Kim practices
3
_ 4 hour.
1. In the tables below, write a rule for each student that gives the total number
of hours (h) practiced for a given number of days (d ).
2. Complete the tables to show the total amount of time each student practiced
during a 5-day period.
3. Use the data to write a set of ordered pairs in the form
(Days, Hours) for Taylor and Kim. Graph the data, connect
the points for each student, and label each graph.
Taylor Kim
(1,1 1
_ 2 )
4. After each day, how does the total amount of time
practiced by Taylor compare to Kim’s time? Explain.
Hou
rs P
ract
iced
Days0 1 2 3 4 5
0
1
2
3
4
5
6
7
8
Kim’s Practice
Rule: Days Hours
1 3 _
4
2
3
4
5
Taylor’s Practice
Rule: Days Hours
1 1 1 _
2
2 3
3
4
5
300A-300B_EMCS_B_MM_G5_U10_576973.indd 300B300A-300B_EMCS_B_MM_G5_U10_576973.indd 300B 4/6/11 11:12 AM4/6/11 11:12 AM