Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
www.everydaymathonline.com
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
848 Unit 11 3-D Shapes, Weight, Volume, and Capacity
Advance PreparationGive 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
Key Concepts and Skills• Estimate weight with and without tools.
[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 ActivitiesStudents 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 Vocabularygram � ounce
MaterialsMath 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)
Updating the World TourMath 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.
Math Boxes 11�1Math Journal 2, p. 288
Students practice and maintain skills
through Math Box problems.
Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 1a. [Geometry Goal 3]
Study Link 11�1Math Masters, p. 327
Students practice and maintain skills
through Study Link activities.
READINESS
Ordering WeightsMath Masters, p. 389
5 objects to weigh � balance or scale
Students order objects by weight.
EXTRA PRACTICE
Estimating Weightsobjects to weigh � scale
Students estimate weights of objects.
EXTRA PRACTICE
5-Minute Math5-Minute Math ™, p. 134
Students convert among units of weight.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
� WeightObjectives To review grams and ounces as units of mass and weight;
and to guide the estimation and measurement of weight in grams
and ounces.
a
848_EMCS_T_TLG2_G4_U11_L01_576906.indd 848848_EMCS_T_TLG2_G4_U11_L01_576906.indd 848 2/16/11 2:32 PM2/16/11 2:32 PM
Lesson 11�1 849
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.
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
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 centimeter cube 10 grams hexagon pattern block 25 grams compass 100 grams 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 milligram ( 1 _ 1,000 gram) and the metric ton (1,000 kilograms). Ask:
● 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
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.
Getting Started
Math MessageA nickel weighs about 5 grams. Look around the classroom. Find objects you think weigh about:
1 gram 10 grams 25 grams 100 grams
Mental Math and ReflexesWrite pairs of fractions on the board. Have students indicate “thumbs-up” if the fractions are equivalent. Suggestions:
1
_ 2 and
2
_ 4 up
1
_ 4 and
25
_ 100
up
1 _ 5 and
3
_ 10
down
1 _ 10
and 20
_ 100
down
3
_ 4 and
6
_ 8 up
4
_ 5 and
9
_ 10
down
2 _ 3 and
3
_ 9 down
7 _ 8 and
70
_ 80
up
14
_ 21
and 2
_ 3 up
12
_ 20
and 2
_ 5 down
8
_ 40
and 1
_ 5 up
18
_ 54
and 1
_ 3 up
849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 849849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 849 3/31/11 11:26 AM3/31/11 11:26 AM
850 Unit 11 3-D Shapes, Weight, Volume, and Capacity
Adjusting the Activity
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.
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 ounce chalk/white board eraser 4 ounces calculator 8 ounces pad of paper; 50 sheets 16 ounces Student Math Journal 32 ounces 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
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
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 � T A C T I L E � V I S U A L
� Setting up a Gram and WHOLE-CLASSDISCUSSION
Ounce MuseumIntroduce 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
ELL
849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 850849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 850 3/16/11 4:26 PM3/16/11 4:26 PM
Estimating Weights in Grams and KilogramsLESSON
11�1
Date Time
A nickel weighs about 5 grams (5 g).
A liter of water weighs about 1 kilogram (1 kg).
In Problems 1–7, circle a possible weight for each object.
1. A dog might weigh about
20 kg 200 kg 2,000 kg
2. A can of soup might weigh about
4 g 40 g 400 g
3. A newborn baby might weigh about
3 kg 30 kg 300 kg
4. An adult ostrich might weigh about
1.5 kg 15 kg 150 kg
5. A basketball might weigh about
0.6 kg 6 kg 60 kg
6. The weight limit in an elevator might be about
100 kg 1,000 kg 10,000 kg
7. A pencil might weigh about
4.5 g 45 g 450 g
8. Choose one of the problems above. Explain why you chose your answer.
140
Sample answer: Problem 7—I thought a pencil would weigh
about the same as a nickel so I chose 4.5 grams.
286-308_EMCS_S_MJ2_G4_U11_576426.indd 286 2/15/11 6:15 PM
Math Journal 2, p. 286
Student Page
Metric and Customary WeightLESSON
11�1
Date Time
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.
Use the number line to give the approximate weight of each object.
1. 2.
About 425 grams About 455 grams
3. 4.
About 3 1 _ 2 ounces About 17 1 _
2 ounces
Use the number line to help you determine which object weighs more. Circle the heavier object.
5.
6.
0 2 4 6 8 10 12 14 16 18 20
ounces
0 100 200 300 400 500
grams
15 ounces 16 ounces
5 ounces 454 grams
Sample answers:
140
225 grams2.3 ounces
100 grams 500 grams
286-308_EMCS_S_MJ2_G4_U11_576426.indd 287 2/16/11 1:33 PM
Math Journal 2, p. 287
Student Page
Lesson 11�1 851
Adjusting the Activity
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.
� Estimating Weights PARTNER ACTIVITY
(Math Journal 2, p. 286)
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.
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
� Converting between Metric and PARTNER ACTIVITY
Customary Weights(Math Journal 2, p. 287; Math Masters, p. 448)
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.
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.
PROBLEMBBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBLBLBLBLBLBLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBBBLELEELEMMMMMMMMOOOOOOOOOBBLBLBLBLBLBBBBLBLOOORORORORORORORORORROO LELELELEEEEEELEMMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINNVINNNVINVINVINNVINVINVINVINVV GGGGGGGGGGGOLOOOOLOOLOLOLOO VVINVINLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINGGGGGGGGGGOOOLOLOLOLOLLOLOOO VVVVVLLLLLLLLLLVVVVVVVVVSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOSOOOSOSOSOSOSOSOSOOOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING
ELL
PROBLEMBBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBLBLBLBLBLBLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROROROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBBBLELEELEMMMMMMMMOOOOOOOOOBBLBLBLBLBLBBBBLBLOOORORORORORORORORORROO LELELELEEEEEELEMMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINNNNNVINVINVINNVINVINVINVINVV GGGGGGGGGGGGOLOOOLOOLOLOLOO VVINVINLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINGGGGGGGGGGOOOLOLOLOLOLLOLOOO VVVVVLLLLLLLLLLVVVVVVVVVVSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOSOOOSOSOSOSOSOSOSOOOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 851849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 851 2/16/11 2:33 PM2/16/11 2:33 PM
852 Unit 11 3-D Shapes, Weight, Volume, and Capacity
Math Boxes LESSON
11� 1
Date Time
1. a. Explain how you know that the pattern
below is an example of a translation.
b. Draw the figure after it is translated
to the right.
2. Find the solution of each open sentence.
a. �6
7� � y � �
4
7� y �
b. �1
3
0� � a � �
1
9
0� a �
c. �3
5� � r � �
1
1
0� r �
d. �3
4� � m � �
7
8� m �
4. Insert parentheses to make each number
sentence true.
a. 14 � 18 � 15 � 42
b. 13 � 6 � 5 � 56 � 21
c. 48 / 6 � 2 � 10 � 4
d. 150 / 10 � 5 � 4 � 4
3. Circle the numbers that are multiples of 6.
Put an X through the numbers that are
multiples of 5.
38
84
150
198
540
3,500
5. If you use an average of 7 sheets of paper
per day, about how many sheets would
you use in
a. 1 week? sheets
b. 4 weeks? sheets
c. 52 weeks? sheets
d. 2 years? sheets
Sample answer: The figure is slid to
the right. It was not turned or flipped.
The size and shape are the same.
�27
�
�160�
�18
�
�150�, or �
12
�
107
55 148
150 47
9
49
5,096,or 5,110
2,548
196
�
( )( )
( )
( )
Math Journal 2, p. 288
Student Page
STUDY LINK
11�1 The World’s Largest Foods
327
140
Name Date Time
Use the information in the table to solve the following problems.
1. The largest apple weighed ounces.
2. A typical hamburger weighs about 4 ounces. The largest hamburger weighed
ounces.
3. Which 2 foods together weigh about a ton? and
4. A kilogram is a little more than 2 pounds. Which 4 foods each weigh more than
1,000 kilograms?
5. On the back of this page, use data from the table to write and solve your own problem.
Answers vary.
Pasta, chocolate bar, hamburger, ice cream sundae
Or, gingerbread man and tacopumpkin
bagel
96,640
59
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
Source: www.guinnessworldrecords.com
Practice
6. �$75 � $25 � 7. � �$45 � (�$30)
8. � �$60 � $60 9. $55 � (�$25) � $30$0
�$75�$50
Math Masters, p. 327
Study Link Master
Ongoing Assessment: Math Boxes
Problem 1a �Recognizing Student Achievement
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.
[Geometry Goal 3]
2 Ongoing Learning & Practice
� Updating the World Tour INDEPENDENTACTIVITY
(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)
Social Studies Link Students follow the established World Tour routine:
� 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.
� Math Boxes 11�1 INDEPENDENTACTIVITY
(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.
� Study Link 11�1 INDEPENDENTACTIVITY
(Math Masters, p. 327)
Home Connection Students convert among ounces, pounds, and tons as they solve problems involving some of the world’s largest foods.
849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 852849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 852 2/11/11 11:15 AM2/11/11 11:15 AM
Lesson 11�1 853
3 Differentiation Options
READINESS SMALL-GROUP ACTIVITY
� Ordering Weights 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 SMALL-GROUP ACTIVITY
� Estimating Weights 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 SMALL-GROUP ACTIVITY
� 5-Minute Math 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.
849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 853849-853_EMCS_T_TLG2_G4_U11_L01_576906.indd 853 2/16/11 2:33 PM2/16/11 2:33 PM