Calorie Use
Objectives To estimate calorie use per day; and to practice
solving
rate problems.
s
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Apply place-value concepts to round
decimals to the nearest tenth. [Number and Numeration Goal 1]
• Use unit fractions to find the whole,
given fractions of the whole. [Number and Numeration Goal 2]
• Estimate products of decimal and
whole numbers. [Operations and Computation Goal 5]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Using Unit Fractions
to Find the Whole
Math Journal 2, p. 291
Students find the whole when a
fractional part is given.
Math Boxes 8 4
Math Journal 2, p. 294
Students practice and maintain skills
through Math Box problems.
Study Link 8 4
• Write an open sentence from
cross products. [Operations and Computation Goal 6]
Math Masters, p. 251
Students practice and maintain skills
through Study Link activities.
Curriculum
Focal Points
Differentiation Options
READINESS
Converting within Measurement Systems
Student Reference Book, p. 371
Math Masters, p. 424
Students use rate tables to convert between
various units of capacity, weight, and time.
EXTRA PRACTICE
Solving Calorie Use Problems
Math Journal 2, p. 292
Math Masters, p. 252
Students calculate the number of calories a
sixth grader uses in a triathlon.
• Use a method to solve equations. [Patterns, Functions, and Algebra Goal 2]
Key Activities
Students refer to a calorie-use chart to
estimate their calorie use in a typical
24-hour day.
Ongoing Assessment:
Recognizing Student Achievement
Use Mental Math and Reflexes. [Operations and Computation Goal 6]
Ongoing Assessment:
Informing Instruction See page 714.
Key Vocabulary
calorie
Materials
Math Journal 2, pp. 290, 292, and 293
Study Link 8 3
calculator
Advance Preparation
Continue adding nutrition labels that students bring to school to the Rates and Ratios Museum or Rates
in Our World bulletin board.
Teacher’s Reference Manual, Grades 4–6 pp. 64–68, 161, 307
710
Unit 8
Rates and Ratios
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6
Content Standards
Getting Started
6.RP.2, 6.RP.3, 6.RP.3b, 6.RP.3d
Mental Math and Reflexes Math Message
Solve Problems 1–5 on journal page 290.
Students use unit rates, rate tables, or proportions to solve simple
rate problems on their slates. Suggestions:
A car goes
316 miles on
10 gallons of
gas. How far
does it go on
1 gallon?
31.6 miles
A total of
6 candy bars
costs $3. How
much does
1 candy bar
cost? $0.50
Ongoing Assessment:
Recognizing Student Achievement
Melinda runs
5 miles in
1
47_
2 minutes.
What is her
average time
per mile?
1
9_
2 minutes
Study Link 8 3 Follow-Up
See Part 1 for the Study Link 8-3
Follow-Up discussion.
Mental Math
and
Reflexes
Use Mental Math and Reflexes to assess students’ ability to use unit
rates, rate tables, or proportions to solve simple rate problems.
[Operations and Computation Goal 6]
1 Teaching the Lesson
▶ Study Link 8 3 Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Masters, p. 249)
Algebraic Thinking Discuss the answers to the problems. Because
this lesson involves finding unit costs, make sure students
understand how to solve Problems 1 and 2. Pose additional
unit-cost problems as needed.
Ask students who chose the correct answer in Problem 6 to defend
their choices. This is a two-step problem.
Step 1 Find the cost per pound by multiplying 16.8 cents by 16,
the number of ounces in 1 pound. 268.8 cents per pound
Step 2 Divide the cost of 1 pound by 502 pieces of candy.
0.535 cents , or a little more than _
1 cent per piece
_
2
1 piece
Discuss the following strategies for solving Problem 7. Be sure
to point out how to keep track of the units as you discuss
each strategy.
Strategy 1: Corresponding parts of a proportion must have the
same unit, so convert gallons (gal) to fluid ounces (fl oz). Then
convert minutes (min) to hours (hr). (See Strategy 1 in margin.)
Strategy 1:
Convert gal to fl oz.
1 gal = 128 fl oz
128 fl oz
12 gal ∗ _ = 1,536 fl oz
1 gal
Set up a proportion.
Cross multiply.
Solve for x.
(fl oz) _
1,536
1.6
_
=_
x
(min) 1
1.6x = 1,536
x = 960 min
960 min 960 min ∗ 1 hr
Convert
=
= 16 hr
60 min
60 min
min to hr.
1 hr
Solution: The car will run out of gas in 16 hours.
Lesson 8 4
711
Strategy 2: Calculate the number of fluid ounces of gasoline used
in 1 hour. Then, using the number of fluid ounces in 12 gallons,
calculate the number of hours before the car runs out of gas.
(See Strategy 2 in margin.)
Strategy 2:
fl oz
fl oz
_
Convert _
min to hr .
1.6 fl oz _
60 min
_
∗
= 96 fl oz/hr
1 min
1 hr
Strategy 3: Express fluid ounces used per hour as gallons used
per hour. (See Strategy 3 in margin.)
(fl oz) 96
1,536
Set up the proportion. _ _
=_
h
(hr) 1
Cross multiply.
96h = 1,536
▶ Math Message Follow-Up
h = 16
Solve for h.
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 290)
Stategy 3:
Find gal/hr.
1 gal
96 fl oz
128 fl oz
96 fl oz ∗ _
_
÷_
=_
1 hr
1 gal
1 hr
128 fl oz
96
gal
3
=_=_
gal/hr
4
128 hr
3
_
(gal) _
4
12
_
=_
h
(hr) 1
3
_
h = 12
4
3
_
h = 12 ÷
4
Set up the proportion.
Cross multiply.
h = 16
Algebraic Thinking Ask students to share their number models.
Spend a few minutes comparing different number models for the
same problem.
All the problems on journal page 290 involve rates of distance over
time. Students may have written number models of the form r ∗ t
= d, where r is the given rate, t is the given time, and d is the
unknown distance. They should be made aware that such number
models are based on proportions. For example the proportion for
60 = _
m . Using cross multiplication, 4 ∗ 60 = 1 ∗ m.
Problem 1 is _
1
4
Students should understand that proportions are also number
models. Note that in Problem 5 students must convert inches
to feet.
In the previous two lessons, students have been using proportions
to solve rate problems. The problems in this lesson can be modeled
by equations of the form r ∗ t = d, although they involve calorie
use over time rather than distance over time.
▶ Examining a Table
of Calorie Use
LESSON
8 4
Time
Rate ∗ Time = Distance
Health Link Briefly discuss nutrition and ask students to
define calorie. Mention the following points:
110–112
Math Message
For each problem, make a rate table. Then write a number model and solve it.
1.
Grandma Riley drove her car at 60 miles per hour
for 4 hours. How far did she travel?
60 ∗ 4 = m
Number model
240
Answer: She traveled
miles
miles
60
240
hours
1
4
inches
8
56
days
1
7
The body uses the materials in food to produce energy. Energy
keeps the body warm and moving. Energy also builds and
repairs muscles and tissues.
in 4 hours.
2.
A bamboo plant grows 8 inches per day.
How tall will it be after 7 days?
8 ∗7=i
56
Answer: The plant will be
Number model
3.
A calorie is a unit for measuring the amount of energy a food
will produce when it is used by the body. Calories are not
substances in food.
inches tall.
A rocket is traveling at 40,000 miles per hour.
How far will it travel in 168 hours?
40,000 ∗ 168 = m
Answer: The rocket will travel 6,720,000
miles
Number model
40,000 6,720,000
hours
1
168
miles
in 168 hours.
4.
Amora can ride her bicycle at 9 miles
per hour. At this rate, how long will it take
her to ride 30 miles?
miles
9
hours
1
30
3 _1
Australia is moving about 3 inches per year
with respect to the southern Pacific Ocean.
How many feet will it move in 50 years?
inches
3
150
Number model 3
years
1
50
9 ∗ t = 30
3 _13
It will take her
Number model
Answer:
ride 30 miles.
5.
3
hours to
∗ 50 = i; i / 12 = f
12.5
feet
Math Journal 2, p. 290
278_323_EMCS_S_G6_U08_576442.indd 290
Unit 8
2/26/11 1:15 PM
Rates and Ratios
The average adult should consume about 2,000 calories per
day, but individuals may need more or fewer, depending on
their size, metabolism, and activity levels. Calorie information
on nutrition labels assumes that an average adult eats food
that supplies about 2,000 calories per day.
Language Arts Link Write the following on the board:
French, calorie; Czech, kalorie; Spanish, caloría. Students
should recognize the words’ meanings without prompting. Explain
that the word calorie is so similar in these languages because
they all come from the same Latin root calor, which means heat.
Answer: Australia will move
in 50 years.
712
PROBLEM
PRO
PR
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VI
VIN
IN
NG
G
(Math Journal 2, p. 292)
Student Page
Date
WHOLE-CLASS
DISCUSSION
Student Page
Take a few minutes to discuss the calorie-use table on journal
page 292. Note that calorie use is reported in two ways—calories
per minute and calories per hour. Include the following questions
in your discussion:
Date
8 4
䉬
●
How Many Calories Do You Use Per Day?
The amount of energy a food will produce when it is digested by the body is measured
in a unit called the calorie. A calorie is not a substance in food.
How do you convert a number of calories per minute to a
number of calories per hour? Multiply the number of calories
per minute by 60.
The following table shows the number of calories used per minute and per hour by the
average sixth grader for various activities. Complete the table. Round your answers for
calories per minute to the nearest tenth and calories per hour to the nearest ten.
Calorie Use by Average Sixth Graders
Calories/Minute
(to nearest 0.1)
Calories/Hour
(to nearest 10)
Sleeping
0.7
40
Studying, writing, sitting
1.2
70
Eating, talking, sitting in class
1.2
70
Activity
How do you convert a number of calories per hour to a number
of calories per minute? Divide the number of calories per hour
by 60.
Standing
Dressing, undressing
Watching TV
Have students use calculators to find the missing numbers in the
table. They should round answers for calories per minute to the
nearest tenth and round answers for calories per hour to the
nearest ten. Discuss the wide range in calorie use for various
activities. Ask: Are you surprised by any of the data?
80
90
1.0
60
3.0
180
Doing housework, gardening
2.0
120
Playing the piano
2.7
160
Raking leaves
3.7
220
5.0
300
Bicycling (6 mph)
2.8
170
Bicycling (13 mph)
4.5
Bicycling (20 mph)
8.3
270
500
Running (5 mph)
Running (7.5 mph)
6.0
360
9.3
560
Swimming (20 yd/min)
3.3
200
Swimming (40 yd/min)
5.8
350
Basketball, soccer (vigorous)
9.7
580
Volleyball
4.0
240
Aerobic dancing (vigorous)
6.0
360
Bowling
3.4
200
Math Journal 2, p. 292
NOTE The term calorie used in talking about food is actually a unit scientists
call the kilocalorie, or Calorie. It is 1,000 times as large as the metric unit called
the calorie.
Calorie Consumption
1.3
1.5
Walking (briskly, at 3.5 mph)
Shoveling snow
Point out that walking, running, bicycling, and swimming are
listed more than once. Calorie use varies for these activities,
depending on the speed. Because the number of calories used
during an activity also depends on a person’s weight, the calorie
data for adults will be greater than that of sixth graders.
▶ Estimating Total Daily
110–112
Your body needs food. It uses the materials in food to produce energy—energy to keep
your body warm and moving, to live and grow, and to build and repair muscles and tissues.
1.
●
Time
LESSON
Adjusting the Activity
Extend the activity by having
students do research on rates of calorie
consumption for favorite activities not listed
on journal page 292.
PARTNER
ACTIVITY
PROBLEM
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
ING
AUDITORY
KINESTHETIC
TACTILE
VISUAL
(Math Journal 2, pp. 292 and 293)
Briefly go over journal page 293. Students list all their activities
and indicate how long they engage in each during a typical
24-hour day on which they attend school. They refer to the table
on journal page 292 to calculate the number of calories used for
each activity and the total number of calories used in a day.
Student Page
Date
Time
LESSON
How Many Calories Do You Use Per Day?
8 4
2.
Estimates need not be precise, so suggest that students round
times to the nearest 15 minutes. In filling out the Calorie Rate
column, students should choose the rate that is appropriate for the
duration of the activity. For example, if they swim for 15 minutes,
they should record the rate as a per-minute rate; if they sit for
4 hours, they should record a per-hour rate.
continued
Think of all the things you do during a typical 24-hour day during which you
go to school.
a.
List your activities in the table below.
b.
Record your estimate of the time you spend on each activity (to the
nearest 15 minutes). Be sure the times add up to 24 hours.
c.
For each activity, record the number of calories used per minute or per
hour. Then calculate the number of calories you use for the activity.
110–112
Example:
Suppose you spend 8 hours and 15 minutes sleeping.
Choose the per-hour rate: Sleeping uses 40 calories per hour.
Multiply: 8.25 hours ∗ 40 calories per hour = 330 calories
Answers vary.
My Activities during a Typical School Day (24 hr)
If an activity is not listed in the calorie-use table, students can
use the calorie rate listed for a similar activity. For example,
playing a musical instrument might require about the same
amount of energy as eating or talking. Bring the class together
to compare their results.
Activity
3.
Time Spent
on Activity
Calorie Rate
(cal/min or cal/hr)
Calories Used
for Activity
After you complete the table, find the total number of calories you use in 24 hours.
In a typical 24-hour day during which I go to school, I use about
Answers calories.
vary.
Math Journal 2, p. 293
Lesson 8 4
713
Student Page
Date
Ongoing Assessment: Informing Instruction
Time
LESSON
Using Unit Fractions to Find a Whole
8 4
81 82
Watch for students who have difficulty with rates given as calories per minute
and calories per hour. Suggest that they use calories per minute throughout.
Example 1:
Alex collects sports cards. Seventy of the cards feature basketball players. These
2
70 cards are 3 Alex’s collection. How many sports cards does Alex have?
2
1
If 3 the collection is 70 cards, then 3 is 35 cards.
3
Alex has all the cards—that’s 3 the cards.
Therefore, Alex has 3 º 35, or 105 cards.
Example 2:
2
Barb’s grandmother baked cookies. She gave Barb 12 cookies, which was 5 the
total number she baked. How many cookies did Barb’s grandmother bake?
If
2
5
the total is 12 cookies, then
1
5
2 Ongoing Learning & Practice
is 6 cookies.
5
Barb’s grandmother baked all the cookies —that’s 5 the cookies.
She baked 5 º 6, or 30 cookies.
1.
Clue
Six jars are filled
with cookies. The
number of cookies
in each jar is not
known. For each
clue given in the table,
find the number of
cookies in the jar.
1
2
2
8
3
5
3
8
4
7
3
11
62
40
60
56
112
165
jar contains 10 cookies.
jar contains 36 cookies.
jar contains 21 cookies.
jar contains 64 cookies.
jar contains 45 cookies.
Jin is walking to a friend’s house.
6
He has gone 10 the distance in
48 minutes. If he continues at the
same speed, about how long will
the entire walk take?
2.
Number of Cookies in Jar
jar contains 31 cookies.
cookies
cookies
cookies
cookies
cookies
cookies
INDEPENDENT
ACTIVITY
to Find the Whole
(Math Journal 2, p. 291)
Students solve problems in which they find the whole when a
fractional part is given. Pose problems such as the following:
1 of a set, how many counters are in the set?
If 12 counters are _
80 minutes
3
A candle burned 8 the way down in
36 minutes. If it continues to burn at the
same rate, about how many more minutes
will the candle burn before it is used up?
3.
▶ Using Unit Fractions
60 minutes
5
5 ∗ 12 = 60
Math Journal 2, p. 291
3 of a book, how many pages are in the book?
If 30 pages are _
8 the book)
1
_ the book = 308÷ 3, or 10; the whole book (_
8
8
= 8 ∗ 10 = 80.
Discuss the two examples at the top of journal page 291 with the
class. The examples show the following two-step solution method:
1 the whole.
Step 1 Find the number of objects in _
n
Step 2 Find the number of objects in the whole by multiplying the
1
number of objects in _
n the whole by n.
Review answers and solution strategies as a group.
▶ Math Boxes 8 4
Student Page
Date
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-2. The skills in Problems 4 and 5
preview Unit 9 content.
Math Boxes
8 4
2.
The formula d r t gives the distance
d traveled at speed r in time t. Use this
formula to solve the problem below.
Which formula is equivalent to d
Choose the best answer.
r
d
t
r
d
r
t
d
r
3.
(Math Journal 2, p. 294)
Time
LESSON
1.
r
Solve.
Solution
t?
a.
6
p
b.
f
2
4
c.
15
t
t
d
p 21
f 0.5
x 45
w 9
y 1.75
2
7
3
12
12
x
d.
24
36
6
w
e.
7
8
y
2
246
111
Of the 330 students at Pascal Junior High, 45 run track and 67 play basketball.
Twenty-two students participate in both sports.
Use this information to complete the Venn diagram below. Label each set (ring).
Write the number of students belonging to each individual set and the
intersection of the sets.
Pascal Junior High Students
Track
22 Basketball
45
23
263 264
240
4.
Solve.
a.
b.
c.
32
2
5.
75
15
( 9)2 ( 1)5
68
112
10
11
Fill in the blanks. (Hint: For decimals,
think fractions.)
a.
7
3
b.
0.01
c.
0.5
81
18
247
Math Journal 2, p. 294
714
INDEPENDENT
ACTIVITY
Unit 8
Rates and Ratios
3
7
100
2
1
1
93
1
Study Link Master
Name
▶ Study Link 8 4
INDEPENDENT
ACTIVITY
Date
STUDY LINK
84
(Math Masters, p. 251)
Time
Food Costs as Unit Rates
111 112
Visit a grocery store with a parent or guardian. Select 10 different items and record the cost
and weight of each item in Part A of the table below.
Select items that include a wide range of weights.
Select only items whose containers list weights in pounds and ounces or a
Home Connection Students complete Parts B and C of
the table. If a grocery store posts a unit price, students
record and verify that price.
combination of pounds and ounces, such as 2 lb 6 oz.
Do not choose produce items (fruits and vegetables).
Do not choose liquids that are sold by volume (gallons, quarts, pints, liters,
milliliters, or fluid ounces).
Answers vary.
1.
Complete Part A of the table at the store.
2.
Complete Parts B and C of the table by
converting each weight to ounces and pounds.
calculating the unit cost in cents per ounce and in dollars per pound.
Example: A jar of pickles weighs 1 lb 5 oz and costs $2.39.
3 Differentiation Options
Convert Weight
▶ Converting within
5
= 1.31 lb
to pounds: 1 lb 5 oz = 1_
16 lb
$1.82
$2.39
=_
in dollars per pound: _
1lb
1.31 lb
Part A
Part B
Cost
Weight
Shown
Weight in
Ounces
Part C
Cents per
Ounce
Weight in
Pounds
Dollars per
Pound
p
Item
py g
15–30 Min
$2.39
11.4 cents
in cents per ounce: _ = _
21 oz
1 oz
g
SMALL-GROUP
ACTIVITY
READINESS
Calculate Unit Cost
to ounces: 1 lb 5 oz = 21 oz
Measurement Systems
(Student Reference Book, p. 371; Math Masters, p. 424)
To provide experience with measurement conversions, have
students use rate tables and proportions to convert measurements.
Students can use the capacity, weight, and time charts on page 371
of the Student Reference Book if needed to help them identify
equivalent units.
Example: 64 days =
Math Masters, p. 251
246-284_EMCS_B_G6_MM_U08_576981.indd 251
2/28/11 1:02 PM
weeks
days
7
64
weeks
1
w
7 =_
64
_
1
w
7w = 64
1
w = 9_
Teaching Master
7
Name
1 weeks
64 days = 9_
7
84
Suggestions:
Capacity
2.25 gal
9 qt = _____
Date
LESSON
Time
Calorie Use for a Triathlon
In a triathlon, athletes compete in swimming, cycling, and running races. In a short-course
triathlon, athletes go the distances shown in the table below. Tevin is a fit sixth grader who
plans to compete in the short-course triathlon. He estimates his rate of speed for each event
to be as shown.
Weight
48 oz
3 lb = _____
Time
24 min
0.4 hr = _____
5 pt _____
2.5 lb = 40 oz 270 min = _____
4.5 hr
80 fl oz = _____
3.5 d
56 c 0.75 lb = _____
12 oz
3.5 gal = _____
84 hr = _____
1. a.
b.
2. a.
3. a.
b.
▶ Solving Calorie Use Problems
PARTNER
ACTIVITY
15–30 Min
(Math Journal 2, p. 292; Math Masters, p. 252)
Physical Education Link Students calculate how many
calories a sixth grader uses in a triathlon. They convert
between customary and metric units of linear measure.
Miles
Tevin’s Estimated Times
1
40 yards per minute
Cycling
25
20 miles per hour
Running
6.2
7.5 miles per hour
Refer to the information above and the table on journal page 292 to answer these questions.
b.
EXTRA PRACTICE
Event
Swimming
About how long will it take Tevin to swim the mile?
(Hint: Find the number of yards in a mile.)
About how many calories will he use?
About 44 minutes
About 255 calories
About 1 hr 15 min
About 625 calories
About how long will it take Tevin to cycle 25 miles?
About how many calories will he use?
About 50 minutes
About 465 calories
About how long will it take Tevin to run 6.2 miles?
About how many calories will he use?
4.
About how many calories will Tevin use to complete the triathlon?
5.
Use the following equivalencies to express the distance of each event and Tevin’s
estimated times in kilometers.
About 1,345 calories
1 mi is about 1.6 km.
1 m is about 39 in.
1 yd is about 0.9 m.
Event
Kilometers
(approximate)
Swimming
1.6
Cycling
40
10
Running
Tevin’s Estimated Times
36
32
12
meters per minute
kilometers per hour
kilometers per hour
Math Masters, p. 252
246-284_EMCS_B_G6_MM_U08_576981.indd 252
2/28/11 1:02 PM
Lesson 8 4
715
=
=
424
Copyright © Wright Group/McGraw-Hill
=
Time
Date
Name
Rate Tables
=