Weight
Objectives To review grams and ounces as units of mass and weight;
and
to guide the estimation and measurement of weight in grams
a
and ounces.
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Ongoing Learning & Practice
Key Concepts and Skills
Updating the World Tour
• Estimate weight with and without tools. Math Journal 2, pp. 329–331, 340,
and 341
Student Reference Book, pp. 276, 277,
281, 292, 293, 297, and 302–305
Math Masters, pp. 419–421 (optional)
Students continue the World Tour,
traveling to Region 5.
[Measurement and Reference Frames Goal 1]
• Describe relationships among metric
units of mass and weight. [Measurement and Reference Frames Goal 3]
• Convert between metric and customary
units of mass and weight. [Measurement and Reference Frames Goal 3]
• Extend numeric patterns. [Patterns, Functions, and Algebra Goal 1]
Key Activities
Students review measuring weight in ounces
and grams and start a classroom Gram and
Ounce Museum. They estimate weights
and practice converting between grams
and ounces.
Ongoing Assessment:
Informing Instruction See page 851.
Key Vocabulary
Math Boxes 11 1
Math Journal 2, p. 288
Students practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Curriculum
Focal Points
Differentiation Options
READINESS
Ordering Weights
Math Masters, p. 389
5 objects to weigh balance or scale
Students order objects by weight.
EXTRA PRACTICE
Estimating Weights
objects to weigh scale
Students estimate weights of objects.
EXTRA PRACTICE
5-Minute Math
5-Minute Math ™, p. 134
Students convert among units of weight.
Use Math Boxes, Problem 1a. [Geometry Goal 3]
Study Link 11 1
Math Masters, p. 327
Students practice and maintain skills
through Study Link activities.
gram ounce
Materials
Math Journal 2, pp. 286 and 287
transparency of Math Masters, p. 448
(optional) balance or scale standard
masses index cards nickels pennies
and quarters (optional) liter bottles of
water (optional) chart paper (optional)
Advance Preparation
Give each student a nickel to use in the Math Message. In preparation for the Gram and Ounce Museum
in Part 1, gather different kinds of scales, balances, and standard mass sets. See the note on page 850
for additional information.
Teacher’s Reference Manual, Grades 4–6 pp. 13, 44–46, 216–218, 225, 236, 237
848
Unit 11
3-D Shapes, Weight, Volume, and Capacity
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP2, SMP4, SMP5, SMP6, SMP7
Getting Started
Content Standards
4.MD.1, 4.MD.2
Mental Math and Reflexes
Math Message
Write pairs of fractions on the board. Have students indicate “thumbs-up” if the
fractions are equivalent. Suggestions:
A nickel weighs about
5 grams. Look around the
classroom. Find objects
you think weigh about:
1
2
_
and _ up
2
4
25
1
_
_
and 100 up
4
3
1
_
and _
down
5
10
20
1
_
and _
down
10
100
3
6
_
and _ up
4
8
9
4
_
_
and 10 down
5
3
2
_
and _
down
3
9
7
70
_
and _
up
8
80
14
2
_
and _ up
21
3
2
12
_
and _ down
5
20
8
1
_
_
and 5 up
40
18
1
_
and _
up
54
3
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Demonstrate or have students demonstrate how to use a scale or
balance to weigh some of the objects identified by students for the
weights given. For example:
1 gram
10 grams
25 grams
100 grams
centimeter cube
hexagon pattern block
compass
calculator
For greater accuracy in weighing small objects, weigh several at
once and divide to find the weight of a single object.
Review the relationship betwen grams and kilograms (1,000
grams = 1 kilogram) and other metric units of mass, including the
1
milligram (_
gram) and the metric ton (1,000 kilograms). Ask:
1,000
●
What might be measured in milligrams? Sample answer:
medicine
●
In grams? Sample answer: food
●
In kilograms? Sample answer: body weight
●
In metric tons? Sample answer: whale
1 gram
10 grams
25 grams
100 grams
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
NOTE In everyday language, the terms
weight and mass are used more or less
interchangeably. One may, for example,
try to lose weight in order to improve one’s
body mass index. But in technical and
scientific contexts, weight and mass are quite
different. In such contexts, weight refers to the
force of gravity on an object, whereas mass
is a measure of the amount of matter in an
object. Mass and weight are proportional—
an object with twice the mass, for example,
weighs twice as much—so the distinction
between them is subtle and was not
understood even by scientists until relatively
recently. So, for example, units such as
grams and pounds, which have been in use
for hundreds of years, are often used for both
mass and weight, and the context must be
used to sort out what is being measured. See
Section 14.6 of the Teacher’s Reference
Manual for a further discussion of the
differences between weight and mass.
Discuss the difference between weight and mass. Ask questions
such as the following:
●
If you went to the moon and weighed yourself, would you weigh
more or less than you do on Earth? less Why? Gravity is weaker
on the moon than it is on Earth.
●
If your weight on the moon is not the same as on Earth, what
does remain the same? mass
●
Would you rather have a bowling ball dropped on your toe on
Earth or on the moon? Explain. On the moon, because the
weight of the bowling ball is less on the moon so it would hurt
less.
Lesson 11 1
849
NOTE The distinction between mass and
weight is tricky, so do not expect students to
grasp it right away. Return to questions such
as these throughout this unit as the occasion
arises.
●
Can you think of an activity where your weight changes but
your mass stays the same? Sample answers: skydiving; jumping
off a diving platform; riding on an elevator that is either
starting to move or coming to a stop
●
Would an astronaut be able to move a large satellite easily
since it is weightless in outer space? No, because the satellite is
still massive and resists being moved.
Review ounces by asking students to name objects that weigh
about 1, 4, 8, 16, and 32 ounces. Have students use the scale or
balance to weigh some of the objects they suggest. For example:
1
4
8
16
32
ounce
ounces
ounces
ounces
ounces
chalk/white board eraser
calculator
pad of paper; 50 sheets
Student Math Journal
Student Reference Book
Review the relationship between ounces and pounds (16 ounces =
1 pound) and pounds and tons (2,000 pounds = 1 ton). Ask:
●
What might be measured in ounces? Sample answer: letters
●
In pounds? Sample answer: body weight
●
In tons? Sample answer: trucks
Adjusting the Activity
ELL
Display a poster in the classroom to remind students of weight
equivalencies and approximate comparisons. Consider adding pictures of
items for the weights listed to provide a reference for students. For example:
Metric Units
1 gram (g) = 1,000 milligrams (mg)
1 kilogram (kg) = 1,000 grams
1 metric ton (t) = 1,000 kilograms
NOTE Use a variety of measuring tools for
the Gram and Ounce Museum (for example, a
bathroom scale, a diet scale, and a spring
scale) so students can measure a range of
weights. The minimum equipment is a rocker
balance or pan balance and a set of standard
masses. Use commercial standard masses, or
for metric standard masses, use nickels
(about 5 grams each) and pennies dated
1983 or later (about 2.5 grams each).
for customary standard masses, use
quarters (about 0.2 ounce each).
To make larger standard masses for weighing
heavier objects, coins, washers, or other
objects can be taped together or placed in
resealable plastic bags.
850
U.S. Customary Units
1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2,000 pounds
Rules of Thumb
1 kilogram equals about 2.2 pounds.
1 ounce equals about 30 grams.
A U D I T O R Y
K I N E S T H E T I C
Setting up a Gram and
T A C T I L E
V I S U A L
WHOLE-CLASS
DISCUSSION
Ounce Museum
Introduce a project to create a museum of objects of different
weights measured in grams and ounces. Use index cards to label
objects in the museum and record their weights. The measuring
tools available determine the range of weights you can display. For
example, if you are limited to one balance and coins as standard
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Student Page
masses, then aim for a modest weight range (possibly up to
500 grams or 16 ounces). If you also have a scale or a balance
that can accommodate larger weights, then expand the range
of weights.
Discuss the goals for the collection, the kinds of objects to be
collected, and the procedures for adding objects to the museum.
For example, if you have a scale that is precise enough to weigh
objects to the nearest gram, you might decide to try to find an
object for every number of grams from 1 to 100. Because this will
be a large collection, you might focus on common items like rocks.
The procedure for adding items should probably be managed by
students. Ask students to bring in objects for the museum over
the next week or two. To ensure accuracy and to assess students’
skill in weighing different objects, require that every item added
to the museum be weighed by two or three students working
independently.
Date
Time
LESSON
Estimating Weights in Grams and Kilograms
11 1
A nickel weighs about 5 grams (5 g).
A liter of water weighs about 1 kilogram (1 kg).
140
In Problems 1–7, circle a possible weight for each object.
1.
A dog might weigh about
2.
A can of soup might weigh about
3.
A newborn baby might weigh about
20 kg
200 kg
4g
40 g
3 kg
4.
2,000 kg
400 g
30 kg
300 kg
An adult ostrich might weigh about
1.5 kg
15 kg
150 kg
5.
A basketball might weigh about
6.
The weight limit in an elevator might be about
7.
A pencil might weigh about
8.
Choose one of the problems above. Explain why you chose your answer.
0.6 kg
100 kg
4.5 g
6 kg
60 kg
1,000 kg
10,000 kg
45 g
450 g
Sample answer: Problem 7— I thought a pencil would weigh
about the same as a nickel so I chose 4.5 grams.
Estimating Weights
PARTNER
ACTIVITY
(Math Journal 2, p. 286)
PROBLEM
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VIN
IIN
NG
Math Journal 2, p. 286
286-308_EMCS_S_MJ2_G4_U11_576426.indd 286
2/15/11 6:15 PM
Students estimate the weights of different objects. Partners should
discuss the possibilities and come to an agreement about which
measure is the most reasonable for each object.
Adjusting the Activity
ELL
Have a handful of nickels and a couple of liter bottles of water available
so students have an opportunity to hold the different weights, compare them,
and use this information to make better estimates.
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
Student Page
Converting between Metric and
Customary Weights
PARTNER
ACTIVITY
PROBLEM
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VIN
IIN
NG
(Math Journal 2, p. 287; Math Masters, p. 448)
Date
Time
LESSON
11 1
The number line below has ounces on the top and grams on the bottom.
It shows, for example, that 7 ounces are about equal to 200 grams.
0
2
0
4
6
100
8
200
10
12
14
300
16
400
18
20
500
Use the number line to give the approximate weight of each object.
Sample answers:
1.
2.
15 ounces
About
425
16 ounces
grams
3.
About
455
grams
About
17_12
ounces
4.
100 grams
Ongoing Assessment: Informing Instruction
Watch for students who do not notice that the ounces number line has a different
scale than the grams number line. Have students cover the grams portion of the
double-scale number line with a sheet of paper while they label the tick marks on
the ounces number line. Then have them reverse the procedure.
140
ounces
grams
Students use a double-scale number line to convert between
grams and ounces. Use a transparency of Math Masters,
page 448 to demonstrate how to use the number line.
Metric and Customary Weight
500 grams
_1
About
32
ounces
Use the number line to help you determine which object weighs more. Circle the heavier object.
5.
225 grams
2.3 ounces
6.
5 ounces
454 grams
Math Journal 2, p. 287
286-308_EMCS_S_MJ2_G4_U11_576426.indd 287
2/16/11 1:33 PM
Lesson 11 1
851
Student Page
Date
Time
LESSON
䉬
夹
2 Ongoing Learning & Practice
Math Boxes
11 1
Explain how you know that the pattern
below is an example of a translation.
1. a.
Draw the figure after it is translated
to the right.
b.
Sample answer: The figure is slid to
the right. It was not turned or flipped.
The size and shape are the same.
2.
Find the solution of each open sentence.
6
a. ᎏ7ᎏ
4
⫺ y ⫽ ᎏ7ᎏ
3
ᎏ
b. ᎏ
10
⫹a⫽
2
ᎏᎏ
7
6
ᎏᎏ
10
y⫽
9
ᎏᎏ
10
a⫽
3
c. ᎏ5ᎏ
⫺ r ⫽ ᎏ1ᎏ
0
r⫽
3
d. ᎏ4ᎏ
⫹ m ⫽ ᎏ8ᎏ
7
m⫽
1
5
ᎏᎏ
10,
1
ᎏᎏ
8
107
Circle the numbers that are multiples of 6.
Put an X through the numbers that are
multiples of 5.
3.
150
540
3,500
55 148
4.
Insert parentheses to make each number
sentence true.
(
5.
)
14 ⴱ 18 ⫺ 15 ⫽ 42
a.
Social Studies Link Students follow the established World
Tour routine:
84
198
If you use an average of 7 sheets of paper
per day, about how many sheets would
you use in
a.
(13 ⫺ 6)ⴱ 5 ⫽ 56 ⫺ 21
48 / (6 ⫹ 2)⫽ 10 ⫺ 4
d. 150 / (10 ⫹ 5)⬍ 4 ⴱ 4
9
b.
b.
c.
c.
d.
150
49
196
4 weeks?
2,548
52 weeks?
5,096,
2 years?
or 5,110
1 week?
sheets
sheets
sheets
sheets
INDEPENDENT
ACTIVITY
(Math Journal 2, pp. 329–331, 340, and 341; Student Reference Book,
pp. 276, 277, 281, 292, 293, 297, and 302–305; Math Masters,
pp. 419–421)
38
1
ᎏᎏ
2
or
Updating the World Tour
They update the Route Map by drawing a line segment
connecting Beijing, China, and Mexico City, Mexico.
They use the World Tour section of the Student Reference Book
to locate facts about Mexico and Mexico City, and fill in the
Country Notes pages for this country and capital.
If they are keeping a Route Log, they update it.
47
Math Journal 2, p. 288
Math Boxes 11 1
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 288)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 11-3. The skill in Problem 5
previews Unit 12 content.
Ongoing Assessment:
Recognizing Student Achievement
Date
STUDY LINK
Time
The World’s Largest Foods
11 1
䉬
Use Math Boxes, Problem 1a to assess students’ ability to describe a
translation. Students are making adequate progress if they state that the
pattern is an example of a translation because the original figure moved or
slid to the right, without being turned or flipped, and that the size and shape
of the figure remained the same. Some students might be able to sketch an
example of a translation in Problem 1b.
Study Link Master
Name
Math Boxes
Problem 1a
140
[Geometry Goal 3]
Food
Weight
Date
Location
Apple
3 pounds 11 ounces
October 1997
Linton, England
Bagel
714 pounds
July 1998
Mattoon, Illinois
Bowl of pasta
7,355 pounds
February 2004
Hartford, New York
Chocolate bar
5,026 pounds
March 2000
Turin, Italy
Garlic
2 pounds 10 ounces
1985
Eureka, California
Gingerbread man
372.13 pounds
November 2003
Vancouver, Canada
Hamburger
6,040 pounds
September 1999
Sac, Montana
Ice cream sundae
22.59 tons
July 1988
Alberta, Canada
Pumpkin
1,337 pounds
October 2002
Topsfield, Massachusetts
Taco
1,654 pounds
March 2003
Mexicali, Mexico
Study Link 11 1
(Math Masters, p. 327)
Source: www.guinnessworldrecords.com
Use the information in the table to solve the following problems.
59
1.
The largest apple weighed
2.
A typical hamburger weighs about 4 ounces. The largest hamburger weighed
3.
Which 2 foods together weigh about a ton?
96,640
4.
ounces.
ounces.
pumpkin
bagel
and
Or, gingerbread man and taco
A kilogram is a little more than 2 pounds. Which 4 foods each weigh more than
1,000 kilograms?
Pasta, chocolate bar, hamburger, ice cream sundae
5.
On the back of this page, use data from the table to write and solve your own problem.
Answers vary.
Practice
6.
8.
⫺$75 ⫹ $25 ⫽
$0
⫺$50
⫽ ⫺$60 ⫹ $60
7.
9.
⫺$75
Math Masters, p. 327
852
⫽ ⫺$45 ⫹ (⫺$30)
$55 ⫹ (⫺$25) ⫽
$30
INDEPENDENT
ACTIVITY
327
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Home Connection Students convert among ounces,
pounds, and tons as they solve problems involving some
of the world’s largest foods.
3 Differentiation Options
READINESS
Ordering Weights
SMALL-GROUP
ACTIVITY
15–30 Min
(Math Masters, p. 389)
To explore estimating and ordering weights, have students hold
and compare the weights of five objects and then place them in
order from lightest to heaviest. Ask students to record the
estimated order on an Exit Slip. Then have the group use a
balance or scale to check their estimates and record the actual
order and weights on the Exit Slip.
Discuss how this activity uses the force of gravity as a guide to
ordering objects by weight. In the Space Shuttle, the objects would
be weightless, but their masses would be the same as they are on
Earth. Ask students how they might order a set of objects by mass
in the Space Shuttle. Sample answer: One method would be to give
each object a push to set it in motion. The more an object resists
being set in motion, the more massive it is. So the harder an object
is to push, the more mass it has.
EXTRA PRACTICE
Estimating Weights
SMALL-GROUP
ACTIVITY
15–30 Min
To practice estimating weights of objects with and without tools,
have students estimate the weights of objects by holding them and
by comparing the weights to benchmarks. Then have students use
a scale to determine the actual weight.
Consider having students do this activity in teams. Have students
devise a scoring system to determine the winning team.
EXTRA PRACTICE
5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with units of weight, see
5-Minute Math, page 134.
Planning Ahead
Have models of the following geometric solids available for
Lesson 11-2: rectangular prism, triangular prism, square
pyramid, cylinder, cone, and sphere. Gather examples from
everyday objects or make them from Math Masters,
pages 449–451.
Lesson 11 1
853