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784 Unit 9 Multiplication and Division
Key Concepts and Skills• Compare and order positive and
negative numbers.
[Number and Numeration Goal 6]
• Solve number stories involving the
addition and subtraction of positive and
negative numbers.
[Operations and Computation Goal 2]
Key ActivitiesChildren consider two uses of positive and
negative numbers: relating numbers to a
zero point and recording changes. They
solve number stories about positive and
negative numbers.
Key VocabularyFahrenheit scale � degrees Fahrenheit �
Celsius scale � degrees Celsius
MaterialsMath Journal 2, p. 237
Student Reference Book, pp. 170 and 171
Home Link 9 �12
calculator � slate � display thermometer
(optional)
Making a Line PlotStudent Reference Book, pp. 79–81,
89A, and 89B
Class Data Pad (optional)
Children measure their pencils and
show the data by making a line plot.
Math Boxes 9�13Math Journal 2, p. 238
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 1. [Measurement and Reference Frames
Goal 2]
Home Link 9�13Math Masters, p. 312
Children practice and maintain skills
through Home Link activities.
READINESS
Counting on a Number LineMath Masters, p. 313
Children count on a number line with
positive and negative numbers.
ENRICHMENTSolving Subtraction Number StoriesMath Masters, p. 314
2 each of number cards 0 –10 (from the
Everything Math Deck, if available)
Children explore the importance of order
in solving subtraction problems.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
Positive and NegativeNumbers
Objective To guide children as they investigate positive and
negative numbers.
�������
Advance Preparation
Teacher’s Reference Manual, Grades 1– 3 pp. 64–66
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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Lesson 9�13 785
NOTE See pages 265 and 266 in the
Student Reference Book for directions to skip
counting on a calculator. When skip counting
beginning with a negative number, it is
necessary to enter the start number and then
press the +/–
key to make the numbers
negative. For the Mental Math and
Reflexes problem, the following key sequences
are needed:
TI 20: 20, +/–
, +
, 5,
=
,
=
, …
Casio: 5, +
, +
, 20, +/–
,
=
,
=
, …
Reference Frames
Most thermometers have marks that are spaced 2 degrees apart.
Fahrenheitthermometer
Celsiusthermometer
Student Reference Book, p. 171
Student Page
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
(Student Reference Book, pp. 170 and 171)
Discuss any disagreements about answers. Colder is further down on the temperature scale. If you have a display thermometer in the classroom, ask children to show the pairs of temperatures.
Review the two thermometer scales on page 171 in the Student Reference Book. The Fahrenheit scale, marked in degrees Fahrenheit, is standard in the United States for everyday use. For example, most U.S. newspapers report temperatures only in degrees Fahrenheit, so Fahrenheit is used in the class high/low temperature record. The Celsius scale, marked in degrees Celsius, is standard throughout the rest of the world for everyday use and everywhere, including the United States, for scientific work.
Note the different temperatures on each scale for the same natural phenomena: the freezing and boiling points of water, the freezing point of salt solutions, and room temperature and body temperature.
NOTE For additional practice with Fahrenheit and Celsius thermometer scales,
go to www.everydaymathonline.com.
Getting Started
Math MessageLook at the thermometer on page 171 in your Student Reference Book. Which temperature is colder, -5°C or -10°C? -10°C +1°C or -14°C? -14°C How do you know?
Home Link 9�12 Follow-Up Have children share solution strategies for Problems 4 and 5 with a partner. Briefly review answers.
Mental Math and Reflexes Children skip count on their calculators. They say the
counts as they press
=
on their calculators.
Suggestions:
Start at 12; count down by 4s. 12, 8, 4, 0, -4, -8, -12, ...
Start at –20; count up by 5s. -20, -15, -10, -5, 0, 5, 10, 15, 20, ...
Start at –18; count up by 4s. -18, -14, -10, -6, -2, 2, 6, 10, 14, 18, ...
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786 Unit 9 Multiplication and Division
Adjusting the Activity
NOTE Locations on a reference scale that
are expressed without a negative symbol are
usually assumed to be positive. However, it is
sometimes helpful to be more explicit by using
the + symbol.
� Writing Temperatures above WHOLE-CLASS ACTIVITY
and below ZeroHelp children make connections between temperatures expressed in words and temperatures expressed with numbers and units. Dictate temperatures above and below zero for children to write on their slates. For this exercise, specify that all temperatures are on the Celsius scale. Examples:
● Write the number and unit for 5 degrees below zero. -5°C
● Write the number and unit for 8 degrees above zero. 8°C or +8°C
Explain that thermometers can be thought of as number lines or reference frames. Zero is a reference or beginning point from which positive and negative numbers go in opposite directions. Temperatures are expressed in words as above or below zero, or with symbols as positive or negative numbers.
Have children think in terms of a number line. Ask questions like the
following: What is the distance (how many jumps) between +2 and -2? 4
What is the distance (how many jumps) between +100 and -1,000? 1,100
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
� Using Sea Level as WHOLE-CLASS ACTIVITY
a Zero PointDiscuss what children know about sea level. Sea level is an agreed-upon zero point from which elevations, such as land elevations and depths of oceans, are measured. Just as with the discussion on temperatures, ask higher/lower questions. Examples:
● Which is lower, 100 meters above sea level or 1,000 meters below sea level? 1,000 meters below sea level
● Which is lower, 2 meters above sea level or 2 meters below sea level? 2 meters below sea level
Dictate elevations, and have children write them on their slates as positive or negative numbers. Check that children write a negative sign when needed and the appropriate unit. Examples:
● 977 meters below sea level -977 m
● 4,240 meters above sea level +4,240 m or 4,240 m
ELL
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Adjusting the Activity
Number Stories with Positive & Negative NumbersLESSON
9�13
Date Time
Solve the following problems. Use the thermometer scale, the class
number line, or other tools to help.
1. The largest change in temperature in a single day took
place in January 1916 in Browning, Montana. The
temperature dropped 100°F that day. The temperature
was 44°F when it started dropping.
How low did it go?
2. The largest temperature rise in 12 hours took place in Granville,
North Dakota, on February 21, 1918. The temperature rose
83°F that day. The high temperature was 50°F.
What was the low temperature?
3. On January 12, 1911, the temperature in Rapid City,
South Dakota, fell from 49°F at 6 A.M. to �13°F at 8 A.M.
By how many degrees did the
temperature drop in those 2 hours?
4. The highest temperature ever recorded in Verkhoyansk,
Siberia, was 98°F. The lowest temperature ever recorded
there was �94°F.
What is the difference between
those two temperatures?
5. Write your own number story using positive and
negative numbers.
Sample answer: My cat weighed 16 lb. Then
she got sick and now weighs 13 lb. What was
her weight change? �3 lb.
192°
62°F
�33°F
�56°F
°F
–100
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
10
20
30
40
50
60
70
80
90
100
Math Journal 2, p. 237
Student Page
Lesson 9�13 787
Links to the Future
� Expressing Changes with WHOLE-CLASS ACTIVITY
Positive and Negative NumbersChanges are often expressed with positive and negative numbers. Discuss changes like the following:
● 6-pound loss: -6 lb; 6-pound gain: +6 lb
● 10°C temperature drop: -10°C; 10°C temperature rise: +10°C
● in football, gain of 6 yards: +6 yards; 15-yard penalty: -15 yards
● lose $10: -$10; find $10: +$10
Have children suggest other change situations. Record them on the board with positive and negative numbers.
You and the children then make up number stories involving comparisons. Examples:
● Is it better to owe $5 or to owe $10? Owe $5
● Is it easier to carry my backpack if I put in 3 lb or take out 5 lb? Take out 5 lb
● In football, is it worse for the team to get a 10-yard penalty or a 15-yard penalty? 15-yard penalty
� Solving Number Stories with PARTNER ACTIVITY
Positive and Negative Numbers(Math Journal 2, p. 237)
Children use thermometer scales, number lines, or other tools to find answers to the problems on journal page 237. Bring the class together to share solutions and strategies.
Encourage children to look for patterns on the completed journal page.
For example, how do you find the difference between a positive temperature and
a negative temperature? Add the two numbers as though both were positive.
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
This lesson is an early exposure to adding and subtracting positive and negative
numbers. This early exposure provides a background for work with positive and
negative numbers that will continue through Grades 4, 5, and 6.
Solving problems and number stories involving positive and negative numbers is
a Grade 5 Goal.
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788 Unit 9 Multiplication and Division
000 000
Name Date Time
HOME LINK
9�13
Encourage your child to use the thermometer pictured here to answer questions about thermometer scales, temperature changes, and temperature comparisons. If you have a real thermometer, try to show your child how the mercury moves up and down.
Please return this Home Link to school tomorrow.
Family Note
170–173
1. What is the coldest temperature this
thermometer could show?
a. °F b. °C
2. What is the warmest temperature this
thermometer could show?
a. °F b. °C
3. What temperature is
20 degrees warmer
than -10°C?
4. How much colder is
-9°C than 9°C?
5. Would 30°C be a good
temperature for swimming outside?
For sledding? Explain.
It would be very warm outside.
30° C is about the same as 86° F.
6. Would -6°C be a good
temperature for ice-skating?
For in–line skating? Explain.
Water freezes at 0° C so there
would be ice to skate on. This would
be dangerous for in–line skating.
104220
-40
Yes
No
Yes
10°C
-40
Positive and Negative Temperatures
°F
–40
–30
–20
–10
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220°C
60
70
80
90
100
50
40
30
20
10
0
–10
–20
–30
–40
Water
boils
Body
Temperature
Room
Temperature
Water
freezes
Salt
solution
freezes
18° colder
No
267-318_EMCS_B_MM_G3_U09_576957.indd 312 2/18/11 7:37 PM
Math Masters, p. 312
Home Link Master
5. What 3-D shape is this a picture of?
Fill in the oval for the best answer.
sphere
cylinder
pyramid
What is the shape of the base?
A circle
3. There are 54 candles. A box holds
12 candles. How many full boxes of
candles are there?
Number model:
or ? × 12 = 54
There are 4 boxes of candles.
There are 6 candles
left over.
Date Time
2. Use the partial-products algorithm
to solve.
652× 3
1,800150
+ 61,956
408× 8
3,200+ 643,264
4. Fill in the oval for the best answer.
The degree measure of the angle is
180°.
less than 90°.
less than 270°.
more than 270°.
1. length = 5 units
width = 9 units
area = 45 square
units
2 factors of 45
are 5 and 9 .
Math BoxesLESSON
9�13
37154 156
74259 260
68 69
167 168
118 79 80
�
6. Number of pets children have:
0, 4, 0, 1, 1, 3, 6, 2, 5
Median: 2
Maximum: 6
Minimum: 0
Range: 6
54 ÷ 12 = ?
204-239_EMCS_S_MJ2_G3_U09_576418.indd 238 3/11/11 1:45 PM
Math Journal 2, p. 238
Student Page
2 Ongoing Learning & Practice
� Making a Line Plot INDEPENDENTACTIVITY
(Student Reference Book, pp. 79–81, 89A, and 89B)
Children measure the lengths of their pencils to the nearest 1 __ 2 inch and record the measures on the board or Class Data Pad. Have them copy the measures on paper and order them from shortest to longest. Then they make a line plot with the horizontal scale marked in 1 __ 2 -inch units and show the data. Remind children that since no pencil is 0 inches long, the scale can begin with the shortest pencil length. Circulate to make sure that each child labels the horizontal and vertical axes and gives the line plot a title.
When most children have completed their line plots, have them identify the median, mode, maximum, minimum, and range of their data.
� Math Boxes 9�13 INDEPENDENTACTIVITY
(Math Journal 2, p. 238)
Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 9-9 and 9-11. The skill in Problem 6 previews Unit 10 content.
Ongoing Assessment: Math Boxes
Problem 1 �Recognizing Student Achievement
Use Math Boxes, Problem 1 to assess children’s progress toward finding the
areas of rectangular shapes. Children are making adequate progress if they
find the area of the rectangle. Some children may identify two factors of 45.
[Measurement and Reference Frames Goal 2]
� Home Link 9�13 INDEPENDENTACTIVITY
(Math Masters, p. 312)
Home Connection Children answer questions about thermometer scales, temperature changes, and appropriate temperatures for various activities. Point out the two scales on the thermometer (°F and °C).
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LESSON
9�13
Name Date Time
Negative Numbers on a Number Line
Show
the
jum
ps o
n th
e nu
mbe
r lin
es.
1.
Star
t at 1
0. C
ount
bac
k 13
. Whe
re d
id y
ou la
nd?
2.
Star
t at �
15. C
ount
up
22. W
here
did
you
land
?
3.
Star
t at 4
0. C
ount
bac
k 50
. Whe
re d
id y
ou la
nd?
4.
Do
your
ow
n. S
tart
at
. Cou
nt
. Whe
re d
id y
ou la
nd?
5.
Des
crib
e th
e re
latio
nshi
ps y
ou s
ee b
etw
een
the
thre
e nu
mbe
rs in
eac
h pr
oble
m. W
hen
the
�20
�10
010
2030
4050
Answ
ers
vary
.
�20
�10
010
2030
4050
�10
�20
�10
010
2030
4050
7�
20�
100
1020
3040
50
�3
Try
This
dist
ance
s fro
m 0
to th
e 2
num
bers
on
the
num
ber l
ine
are
adde
d to
geth
er, t
hesu
m is
the
coun
t up
or c
ount
bac
k nu
mbe
r.
Math Masters, p. 313
Teaching Master
314
LESSON
9�13
Name Date Time
Exploring Order in Subtraction
You
will
need
num
ber c
ards
0–1
0 (2
of e
ach)
.
�Pl
ace
the
card
s nu
mbe
r-sid
e do
wn.
�C
hoos
e 2
card
s. R
ecor
d th
e nu
mbe
rs in
the
char
t bel
ow.
�W
rite
2 su
btra
ctio
n nu
mbe
r sen
tenc
es in
the
tabl
e, o
ne in
whi
ch th
e la
rger
num
ber i
s w
ritte
n fir
stan
d on
e in
whi
ch th
e sm
alle
r num
ber i
s w
ritte
n fir
st. U
se th
e nu
mbe
r lin
e at
the
botto
m o
f thi
s pa
geto
hel
p yo
u fig
ure
out t
he d
iffer
ence
s.
�Fo
llow
the
step
s 3
mor
e tim
es.
Answ
ers
vary
.
1.
Look
at t
he n
umbe
r sen
tenc
es y
ou w
rote
. Doe
s th
eor
der o
f num
bers
in a
sub
tract
ion
num
ber s
ente
nce
mat
ter?
2.
How
do
you
know
?
Whe
n th
e sm
alle
r num
ber i
s su
btra
cted
fro
m th
e la
rger
num
ber,
the
diffe
renc
e is
a p
ositi
ve n
umbe
r. W
hen
the
larg
ernu
mbe
r is
subt
ract
ed fr
om th
e sm
alle
rnu
mbe
r, th
e di
ffere
nce
is a
neg
ativ
e nu
mbe
r.
�10
�9
�8
�7
�6
�5
�4
�3
�2
�1
01
23
45
67
89
10
Yes
Sam
ple
answ
er:
Nu
mb
ers
onN
um
ber
Card
sSe
nte
nce
s
Exam
ple
4, 6
6-
4=
2
4-
6=
-2
1__
� _
_ �
__
__ �
__
� _
_
2__
� _
_ �
__
__ �
__
� _
_
3__
� _
_ �
__
__ �
__
� _
_
4__
� _
_ �
__
__ �
__
� _
_
Math Masters, p. 314
Teaching Master
Lesson 9�13 789
3 Differentiation Options
READINESS INDEPENDENTACTIVITY
� Counting on a Number Line 5–15 Min(Math Masters, p. 313)
To provide experience with finding distances between positive and negative numbers on a number line, have children practice counting on a number line. Children record their work on Math Masters, page 313. Have children describe the relationships they found.
ENRICHMENT INDEPENDENTACTIVITY
� Solving Subtraction Number Stories
15–30 Min
(Math Masters, p. 314)
To explore solving subtraction number stories have children follow the steps on Math Masters, page 314. When children have completed the page, discuss the patterns. Sample answers: When the numbers on the cards are the same, the difference between them is always 0. When the numbers are not the same, the differences are opposites. For example, 6 - 2 = 4 and 2 - 6 = -4. 4 and -4 are opposites.
Planning Ahead
For Lesson 10-1, you will need four objects of various shapes, volumes, and weights that can fit into an empty 2- or 3-pound coffee can. A good mix of objects might be a baseball, a tennis ball (or a rubber ball about the size of a tennis ball), a base-10 big cube, and an unopened 16-ounce can of food. Place a label with the name of each object on each item so that children can use consistent names when they list the items.
For the optional Readiness activity in Lesson 10-2, you will need a few rectangular prisms.
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