Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Tab 10: Weight/Mass
Table of Contents
10-ii
Master Materials List
Does It Matter? A Mathematical Investigation of Weight and Mass
(with PowerPoint slides embedded in trainer notes)
Transparency 1-Mass KWL Chart
Transparency 2-Weight KWL Chart
Transparency 3-Jogging the Gelatin Boxes
Transparency 4/Handout 1-Newton’s 2nd Law of Motion
Transparency 5/Handout 2-How Much Does a Kilogram Weigh?
10-1
10-24
10-25
10-26
10-27
10-28
Does It Matter? A Mathematical Investigation of Weight and Mass
(without PowerPoint slides embedded in trainer notes)
Transparency 1-Mass KWL Chart
Transparency 2-Weight KWL Chart
Transparency 3-Jogging the Gelatin Boxes
Transparency 4/Handout 1-Newton’s 2nd Law of Motion
Transparency 5/Handout 2-How Much Does a Kilogram Weigh?
10-29
10-45
10-46
10-47
10-48
10-49
Foundations for Weight and Mass
Handout 1-Grade Level Expectations for Development
of Attributes of Weight and Mass
Handout 2-Sample Completed Chart for Grade Level
Expectations for Development of Attributes of Weight and Mass*
Transparencies 1 & 2/Handout 3-Clarifications from
TEA Concerning Weight and Mass
10-50
10-61
10-62
10-63
* This document was developed as a resource for trainers, but it may be used with participants at the
trainer's discretion.
Tab 10: Weight/Mass: Table of Contents
10-i
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Tab 10: Weight/Mass
Master Materials List
1 kg mass or other item that
approximates 1 kg
2-4 sandwich bags
Books or plastic shoeboxes
Calculators
Centimeter/gram cubes
Clear container of water placed in an
overflow tray
Empty paper towel roll (cut in half
longwise)
Gallon freezer bag
Golf ball
Gram stackers
Large bag or bucket of sand, rice, or
small gravel with scoop
Large paperclip
Large rubber band
Markers
Masking tape
Mass sets
Meter tape or stick
Pan balance or triple beam balance with
mass sets
Spring scale > 40 newtons
Spring scale ≤ 5 newtons
Sturdy plastic grocery or shoe bag
Two gelatin boxes (one full and one
empty)
Unopened baby food jar
Does It Matter? A Mathematical Investigation of Weight and Mass Transparencies and
Handouts
Foundations for Weight and Mass Handouts and Transparency
The following materials are not within this tab of the notebook, but they can be
accessed by clicking on the links below.
Mathematics TEKS for Grades K-5
Does It Matter? A Mathematical Investigation of Weight and Mass PowerPoint
Tab 10: Weight/Mass: Master Materials List
10-ii
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Activity:
Does It Matter? A Mathematical Investigation of Weight and Mass
(with PowerPoint slides embedded in trainer notes)
TEKS:
See Appendix for Student Version of this Activity with correlated TEKS.
Overview:
This lesson will give teachers the opportunity to further develop the
concepts of weight and mass and to reflect on methods of introducing
each of these concepts to students in grades K-5 based on the newly
adopted elementary mathematics TEKS. (NOTE: This lesson is written for
participants as a review of the concepts of weight and mass as clarified by
TEA. However, most of the activities are easily adaptable to 4th grade,
and the appendix lesson reflects those modifications. Since the lesson is
designed around the SI (metric) system, it is suggested that teachers of
mathematics and science collaborate on the introduction of these
concepts. This lesson would be a prerequisite to many of the 4th grade
science TEKS.)
This activity should be included in all trainings for grades K-5 teachers.
Materials:
Introductory Activity - for demonstration with large group
Balance
Container of water placed in an overflow tray
Waterproof object such as an unopened baby food jar
Transparency 1-Mass KWL Chart (page 10-24)
Transparency 2-Weight KWL Chart (page 10-25)
Markers
Exploration of Mass - for each group
Two gelatin boxes (one full and one empty)
Empty Paper towel roll (cut in half longwise)
Masking tape
Golf ball
Meter tape or stick
Books or plastic shoeboxes
Pan balance
Centimeter/gram cubes
Gram stackers
Mass sets
Calculators
Exploration of Mass - for the trainer
Transparency 3-Jogging the Gelatin Boxes (page 10-26)
Transparency 4/Handout 1-Newton’s 2nd Law of Motion, teacher
training only (page 10-27)
Transparency 1-Mass KWL Chart (page 10-24)
Markers
Exploration of Weight - for each group
Sturdy plastic grocery or shoe bag
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
10-1
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Materials
(cont.):
Large bag or bucket of sand, rice, or small gravel with scoop
Gallon freezer bag
1 kg mass or other item that approximates 1 kg
Spring scale ≤ 5 newtons
Spring scale > 40 newtons
Pan balance or triple beam balance with mass sets
Gelatin boxes from mass activities
2-4 sandwich bags
Calculators
Exploration of Weight - for the trainer
Transparency 5/Handout 2-How Much Does a Kilogram Weigh? (page
10-28)
Transparency 2-Weight KWL Chart (page 10-25)
Markers
Optional Activity or Extension - for demonstration with large group
Unopened baby food jar
Large rubber band
Large paperclip
Spring scale ≤ 5 newtons
Clear container of water placed in an overflow tray
Other materials
Does It Matter? A Mathematical Investigation of Weight and Mass
PowerPoint, optional
Grouping:
Introductory Activity – whole group
Exploration of Mass – groups of four
Exploration of Weight – groups of four
Optional Activity or Extension – whole group
Time:
1 hour
Lesson:
The Does It Matter? A Mathematical Investigation of Weight and Mass
PowerPoint is optional but may be used as a guide during the lesson. If
you choose to use the PowerPoint, please be aware that the participants
are asked to Explore the concepts before the Explanations are given, so
be careful not to “give away” too much by advancing the slides too quickly.
The correlation of the slides and the procedures are referenced within the
trainer notes, along with a screen capture of the slide. For your
convenience, a version of the trainer notes without the PowerPoint
references is available on pages 10-29 – 10-49. Even though the use of
this PowerPoint is optional, all trainers that choose to present the
extension activity should use slides 25, 26, and 27 either as a PowerPoint
or as color transparencies.
1.
Procedures
Introductory Activity (whole group)
Notes
The introductory activity serves as
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Set up the balance and the container of
water so that all participants can see the
demonstration. Introduce the object that will
be the focus of this observation.
Tarleton State University
Notes
a formative assessment by
activating prior knowledge about
matter and the concepts of weight
and mass.
(PowerPoint – show slides 1 and 2)
Does It Matter?
A Mathematical Investigation
of Weight and Mass
Engage
Objects have attributes
and properties that can
be measured.
Demonstrate what happens when the object
is placed on the balance and in the waterfilled container.
a) Have participants predict what will happen
when you place the object on one side of a
zeroed balance. Confirm their prediction and
ask what they can tell you about the object
based on what they just observed.
b) Now predict what will happen when the
object is placed in the container filled with
a) They will probably say it has
mass, but they may say it is
heavy or has weight.
b) They will probably say it takes
up space, i.e. volume. They may
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
water. Confirm their prediction and ask what
else they can tell you about the object from
their observations.
Tarleton State University
Notes
say it displaces an amount of
water equal to its volume.
Remind participants that they have just
described two properties of matter (mass
and volume). They may remember the
definition: “All matter has mass and takes up
space.” In this unit, we will be focusing on
the property of mass and how it relates to
weight.
2.
(PowerPoint – show slides 3 and 4)
Engage
KWL Chart -- Mass
What I
WANT
to Know
What I
LEARNED
What do I Know W stands for
(or think that I
what I Want to
Know)?
learn.
L stands for
what I Learned.
What I
KNOW
ƒBrainstorm,
ƒQuestion, predict,
generate, activate
prior knowledge
set purpose
ƒReview, reflect,
confirm
Engage
KWL Chart -- Weight
What I
WANT
to Know
What I
LEARNED
What do I Know W stands for
(or think that I
what I Want to
Know)?
learn.
L stands for
what I Learned.
What I
KNOW
ƒBrainstorm,
ƒQuestion, predict,
generate, activate
prior knowledge
set purpose
ƒReview, reflect,
confirm
On KWL charts (or use Transparencies 1
and 2, (pages 10-24 – 10-25), record
If participants don’t provide
responses about when or why
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Procedures
Notes
participants’ knowledge statements and
weight and mass are important in
questions about each concept - weight and
our everyday world, pose that
mass. Ask participants to tell you what they
question.
already Know or think they Know about each
concept. Record their comments on each
chart under “What I Know.” Then, ask them
what questions they might have, or what they
expect to learn about each concept and
record those responses under “Want to
Know.” Post charts on the wall to refer to
later.
3.
Exploration of Mass (table groups of four)
Direct participants’ attention to some
identified heavy object (table) and some light
object (pencil) in the room.
(PowerPoint – show slide 5)
Explore
ƒ What can we do to make this table move?
ƒ Would it be easier to move the table or this
You can choose any heavy and
light object on which to focus the
questions (example: table and
pencil).
Note: The PowerPoint assumes
that you chose a table and a
pencil.
pencil? Why?
ƒ Which would require more force to make it
move, the table or the pencil?
Keep these ideas in mind as we do the
next activity….
Ask: How might we make this table move?
(push it or pull it).
Would it be easier to move the table or this
pencil? Why?
(pencil, the table is heavier)
Continue questioning: Will the table or the
pencil take more force to move?
(table)
4.
Provide each group with the golf ball, empty
paper towel roll, gelatin boxes, meter tape,
masking tape, and stack of books or plastic
Emphasize that the system should
be set up the same for each test -the only difference (variable) being
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
shoeboxes.
(PowerPoint – show slide 6)
Explore
ƒ Examine the materials on your table.
ƒ Design and conduct a fair test to answer
this key question:
How far will the golf ball
move each of the gelatin
boxes?
Tarleton State University
Notes
the full or empty gelatin box
Some possible questions to clarify
the task might include:
• What do you notice about the
gelatin boxes?
• What is the role of the golf
ball?
• What function might the empty
paper towel roll perform? The
notebooks? The meter tape?
(PowerPoint – show slide 7)
Explore
ƒ Conduct 3 trials with each gelatin
box.
ƒ Record results to the nearest cm
and find the mean for each box.
5.
(PowerPoint – show slide 8)
Sharing Time
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Chart each group’s results on Transparency
3 (page 10-26). Have participants examine
the data and discuss any patterns and
relationships they observe.
6.
Introduce the word, “mass,” and write it on a
chart. Explain that all matter, whether solid,
liquid, or gas, has mass. Mass is the amount
of stuff in an object. The full gelatin box has
more mass, so it is harder for the golf ball to
push it. The empty box has less mass, so it
is easier for the golf ball to push it.
7.
Have participants think back to the table and
pencil scenario.
Tarleton State University
Notes
They should conclude that the
full/heavier box moved the fewest
cm; the empty/lighter box moved
the greatest number of cm.
(PowerPoint – show slide 9)
Explain
ƒ Mass
ƒ Mass is the amount of matter
(stuff) in an object.
ƒ Using the word “mass,” explain
why it would be harder to move
the table….
8.
Introduce the pan balance. Ask participants
to predict what will happen when the two
gelatin boxes are placed on each side of the
balance. Demonstrate or have them verify
their predictions at their tables. (The pan with
the full box will go down.)
9.
(PowerPoint – show slide 10)
Responses may vary, but they
should explain that the table has
more mass than the pencil, so it is
harder to move.
If available, show different kinds of
balances, i.e., bucket, pan, triple
beam, homemade, etc…. Be sure
that participants know how to zero
a balance before using the
tool/instrument to determine the
mass of objects.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Explain
ƒ A balance is a tool/instrument used to
measure mass.
ƒ An object’s mass is determined by
balancing it with objects of known mass.
ƒ In the SI (metric) system, units of mass
include the kilogram, gram, and milligram.
Tarleton State University
Notes
If needed, talk about the rules for
symbols (abbreviations) in the
metric system and conversion
between units. (For more
information, see internet sites in
Resources at the end of this
activity, (page 10-22.)
Note: Not all centimeter cubes are
gram cubes, such as the base 10
unit cubes.
Examine gram stackers, brass mass sets,
and centimeter/gram cubes as “known
masses.”
10.
(PowerPoint – show slide 11)
Explore
ƒ What is the mass of each gelatin box?
ƒ Work as a team to predict and then
determine the mass of each box. Use at
least two of the types of mass sets.
(PowerPoint – show slide 12)
Sharing Time
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Discuss the results.
11.
Tarleton State University
Notes
The results obtained when using
each of the types of mass sets
may vary by a gram or two.
Emphasize that measurement is
never exact.
(PowerPoint – show slide 13)
Elaborate
Provide Transparency 4/Handout 1 of
Newton’s Second Law (page 10-27).
This handout is designed to be
used with trainers and teachers.
(PowerPoint – show slide 14)
Elaborate
A force (________) causes the object (________) to accelerate (________).
An object’
object’s mass is a measure of its inertia or “unwillingness to move.”
move.” The full
box of gelatin has more ____ or ____ than the empty box.
The more mass something has, the harder it is to accelerate or move. The full
box with more ---_____
---_____ is harder to _____.
The amount of force needed to accelerate an object
is directly proportional to the object’
object’s mass.
mass.
(More, Less)
Less) force is needed to move the box with (more,
(more, less)
less) mass.
The amount of acceleration is inversely proportional to the object
object’’s mass.
The box with (more,
(more, less)
less) mass moves (more,
(more, less).
less).
Have participants relate the objects and
events from the gelatin box investigation with
the concepts of force, acceleration, mass
or measure of inertia or “unwillingness to
move.”
Remember that friction (another
force) acts on the object opposite
to the direction of motion, hence
the box decelerates and
eventually comes to a stop
(Newton’s First Law – The Law of
Inertia).
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Sample Responses:
• The force, (the push from the golf ball),
causes an object (the gelatin box) to
accelerate (move some distance from its
state of rest).
• The object’s mass is a measure of the
amount of matter in an object or its
inertia or “unwillingness to move.”(The
full box has more mass/inertia than the
empty box.)
• The more mass something has, the
harder it is to accelerate. (The full box
with more mass was harder to move than
the empty box).
• The amount of force needed to
accelerate an object is directly
proportional to the object’s mass. (More
force is needed to move the box with
more mass.)
• The amount of acceleration is inversely
proportional to the object’s mass. (The
box with more mass moves less.)
• F=ma, a=F/m
12.
Tarleton State University
Notes
(PowerPoint – show slide 15)
Elaborate
ƒ Mass is constant and does not change
with location.
Reiterate that mass is a measurement of the
amount of matter in an object. Mass is
constant and does not change when the
object’s location changes. Your mass is the
same on Earth as it is on the moon. So, if
your mass is 60 kilograms on Earth, your
mass would be 60 kilograms on the moon.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
One of commonly used units of mass in the
metric (SI) system is the kilogram which is
equal to 1000 grams.
13.
Tarleton State University
Notes
(PowerPoint – show slide 16)
KWL Chart – Mass
Reflection & Closure
At your table, discuss…
discuss…
ƒ What you’
you’ve learned about mass.
ƒ Any misconceptions regarding mass.
ƒ What questions you still have about mass.
ƒ Be ready to share.
Return to Transparency 1-Mass KWL chart.
Have participants reflect on their initial
responses regarding MASS. Elicit
statements about what they have Learned
about MASS and record these on that chart.
14.
Exploration of Weight (table groups of four)
(PowerPoint – show slide 17)
Materials Management
ƒ Organize the materials from this activity.
ƒ Straighten your tables.
ƒ Secure the materials for Part 2: What
Does a Kilogram Weigh?
Provide each group with a sturdy plastic
grocery bag or shoe bag, a kilogram mass or
other object that approximates 1 kg, and a
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
10-11
Mathematics TEKS Refinement 2006 – K-2
Procedures
Tarleton State University
Notes
pan balance.
15.
(PowerPoint – show slide 18)
Explore
Hint: A liter of water has a mass of
1 kilogram. A nickel has a mass
of about 5 grams, etc.
ƒ “What Does a Kilogram Weigh?”
Weigh?”
ƒ Work together as a team.
ƒ Fill your freezer bag with
approximately 1 kilogram of the
material provided.
16.
(PowerPoint – show slide 19)
Explore
A pan balance is sufficient if you
are using a kilogram mass or
other small objects.
ƒ Use a pan balance to check your
estimates.
ƒ Adjust the contents of your bag to
create a more accurate mass of 1
kg.
17.
(PowerPoint – show slide 20)
Explore
Tape over the kilogram/gram side
of the spring scale if it has one.
ƒ Hang your kilogram bag on the
spring scale.
ƒ Read the results to the nearest N.
1 kg on the spring scale is equal
to about 10 (9.8) N.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Procedures
Next, introduce a spring scale (> 40 N) and
have participants hang their bags
approximating 1 kilogram on the spring
scale.
(PowerPoint – show slide 21)
Explain
ƒ A spring scale measures weight –
the force of gravity acting on an
object.
ƒ The SI (metric) unit for weight is
the newton (N).
18.
19.
Say: You now know that a 1 kg mass creates
a force of about 10 N. If you add the kilogram
mass to your bag, what do you predict the
readout will be?
(about 20 N)
What might the readout be if we combine two
tables’ bags? (about 40 N)
Notes
Names of units in the SI (metric)
system are written in lower case. If
the unit is named after a person,
such as Isaac Newton, the first
letter of the symbol is written in
upper case.
When they add the kg mass to
their bags, they will have about 2
kg to hang on the spring scale.
If they combine their table’s bag
with another table’s bag, they will
have about 4 kg.
(PowerPoint – show slide 22)
Explore
ƒ Use the input/output table to record
the weights of 1 kg, 2 kg, 4 kg, etc…
How Much Does a Kilogram Weigh?
Input
Number of
kilograms (kg)
Process
Output
Number of
newtons (N)
Use Transparency 5/Handout 2 (page 10-28)
to create an input/output table with a process
column in between. Record an input of 1 kg
f
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
and output of 10 N; 2 kg, 20 N; 4 kg, 40 N;
etc….
After determining the process or rule for
finding the outputs, ask: If you have a mass
of 60 kg, your weight on Earth would be
about _____?
(600 N)
20.
21.
Tarleton State University
Notes
Participants should determine that
the process or rule for finding the
outputs is “input times 10.”
Ask: What does 1 kg weigh?
(Participants may say about 10 N.)
State that although mass is constant and
does not change with location, weight
does!! Your weight on the moon would be
approximately one sixth of your Earth weight,
because the gravitational pull on the moon is
1/6 that of the Earth.
The purpose of these examples is
to emphasize that weight, or the
force of gravity, changes with
location. This concept applies to
any measure of weight, SI (metric)
or customary.
If your Earth weight is about 600 N, what
would your weight be on the moon?
(about 100 N)
And, if 1 kg on Earth weighs about 10 N,
what would 1 kg weigh on the moon?
(about 1.64 N)
Note: Participants can calculate
their weight (customary) on other
celestial bodies at the internet
sites listed in the Resources
section at the end of this activity.
Have one person at each table hold each
Responses may vary, but they
gelatin box in his/her outstretched hand. Ask may say the full box feels heavier.
them to describe what they feel.
State that they are experiencing the
downward force due to the pull of gravity on
the two boxes.
22.
(PowerPoint – show slide 23)
E xp
x p lo re
ƒ W ill th e fu ll b o x (w ith m o re m a s s )
w e ig h m o re ?
ƒ U s e th e s p rin g s c a le to w e ig h
e a c h b o x.
x.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Say: We have already determined that the
full gelatin box has more mass. Will it weigh
more, too?
Tarleton State University
Notes
Have participants put each gelatin box in a
sandwich bag. Thread the hook on the spring
scale through the corner of the sandwich
bag.
Verify their prediction using a spring scale
(< 5 N).
23.
(PowerPoint – show slide 24)
Explain
ƒ Mass and weight are proportional.
24.
Explain that weight and mass are
proportional. The greater an object’s mass,
the more it weighs. An object that has twice
the mass of another object will weigh twice
as much in the same location. So, weight
depends on mass and gravitational pull.
W=mg (Weight = mass × gravity)
Remind participants that they
experienced this proportionality
earlier when they were weighing
the kilogram masses. One kg
weighed about 10 N, two kg
weighed about 20 N, etc….
Optional Activity or Extension (whole
group)
Remember that weight is the
measure of the gravitational force
exerted on an object, while mass
refers to the amount of matter in
an object. An object on the moon
would weigh less than the same
object would weigh on the Earth
because the force of gravity is less
on the moon. However, that
This part of the lesson is designed to be
done as a demonstration.
Attach a rubber band around the neck of an
unopened baby food jar. Hook a large
paperclip to the rubber band. Using a spring
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Procedures
scale, weigh the baby food jar. Record its
weight in newtons to the nearest tenth.
Notes
object would have the same mass
on the moon as it would on the
Earth.
Tell the group that you know that they will not
be able to read the spring scale from their
seats, so you have scanned in a picture of
the experiment with the weight of the baby
food jar stated on the slide.
Since we cannot go to the moon
to illustrate that weight can
change with location due to the
change in gravitational force, this
optional activity or extension can
be used to demonstrate to
participants that the reading on
the spring scale can be affected
when we change the forces acting
on the object. Granted, we are
not able to change the force of
gravity acting on the object while
we are here on planet Earth, but
this activity can help show that
mass remains constant no matter
what forces are present. When
the baby food jar is submerged in
water, the buoyant force is
pushing up on the object, i.e., the
water itself is supporting some of
the weight. However, a
gravitational field pulls down on
the object uniformly. So, in water
the body still experiences the
force of gravity, and its weight
does not change; however, the
reading on the spring scale
changes due to the object
experiencing the counterforce due
to buoyancy.
Show slide 25 from the PowerPoint.
Elaborate
ƒ Weighing the Baby
Food Jar – Out of
Water
ƒ Record the weight
in newtons to the
nearest tenth
An interesting connection to this
activity or extension is that
astronauts sometimes simulate
weightlessness in an underwater
environment during their training.
See the website listed below for
more information on this topic.
(http://starchild.gsfc.nasa.gov/doc
s/StarChild/space_level2/hubble_
practice.html)
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
25.
Tarleton State University
Procedures
While still attached to the spring scale, lower
the baby food jar into a clear container of
water until it sits just below the water level.
Record its weight in newtons to the nearest
tenth.
Notes
Once again, tell the participants that you
have scanned in a picture and the weight of
the baby food jar when submerged in water
so that they might be able to see better.
Participants will find that the
reading on the spring scale for the
submerged baby food jar is less in
water due to the buoyant force of
the water that is acting on the jar.
Show slide 26 from the PowerPoint.
Elaborate
ƒ Weighing the Baby
Food Jar – Under
Water
ƒ Record the weight
in newtons to the
nearest tenth
26.
Now let’s consider the mass of the baby food
jar both in and out of water.
Tell the participants that since this part of the Participants will find that the jar
experiment can get messy, you have done
has the same mass, whether in
the experiment ahead of time and scanned in the water or out of the water.
pictures with the masses labeled on the
slide. Remind them to use a waterproof
balance and masses if they decide to “try this
at home.”
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Show slide 27 from the PowerPoint.
Tarleton State University
Notes
Elaborate
Determining the Mass of the Baby Food Jar
Out of Water
27.
Under Water
(PowerPoint – show slide 28)
KWL Chart – Weight
Reflection & Closure
At your table, discuss…
discuss…
ƒ What you’
you’ve learned about weight.
ƒ Any misconceptions regarding weight.
ƒ What questions you still have about
weight.
ƒ Be ready to share.
Return to the Weight KWL chart or use
Transparency 2.
Have participants reflect on their initial
responses regarding WEIGHT. Elicit
statements about what they have Learned
about WEIGHT and record these on that
chart.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
28.
Procedures
Closure (whole group)
Tarleton State University
Notes
(PowerPoint – show slide 29)
Closure
ƒ Mass is a fundamental property of matter
and is not dependent upon location.
ƒ Weight is a measure of gravitational force
and therefore varies with location.
ƒ Both the SI (metric) and customary
systems have units of mass and weight.
Say: This lesson has focused on weight and
mass in the SI (metric) system.
In the SI (metric) system, the gram and
kilogram typically are used to measure mass
while the newton is used to measure weight.
Units of mass exist in the customary system
(one such unit is the slug), but we don’t
usually go there because the customary
units of mass are cumbersome. The units
exist…but are not used very often. Ounces
and pounds are common units for weight in
the customary system.
Because we have dealt only with metric units
of mass and customary units of weight in
elementary mathematics, educators often
assume (incorrectly) that mass is only
measured in metric units, and weight in
customary units.
The reality is that both the SI (metric) and
customary systems have units for weight and
mass. We just haven’t expected our students
to deal with newtons in the metric system or
units of mass in the customary system.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
29.
Procedures
(PowerPoint – show slide 30)
Check for Understanding
ƒ
ƒ
ƒ
ƒ
Tarleton State University
Notes
The answers are provided in the
Assessment Section below.
Have participants determine whether the statements
below exhibit a concern about weight or mass:
mass:
The weatherman has predicted flooding, and you have
gone to buy bags of sand to stem the flow of water.
You have to lift the bags of sand into the back of your
truck.
The roads are very wet. The bags of sand in the back
help to keep the truck from hydroplaning.
However, you are going too fast and your truck runs off
the road into a muddy ditch. Now you are going to have
to get help to push or pull the truck out of the ditch.
(PowerPoint – show slide 31
Materials Management
ƒ Organize and return the materials from
this activity.
ƒ Straighten your tables.
ƒ Throw away trash.
Assessment:
1. Have participants determine whether the statements below exhibit a
concern about weight or mass:
• The weatherman has predicted flooding, and you have gone to
buy bags of sand to stem the flow of water. (mass)
• You have to lift the bags of sand into the back of your truck.
(weight)
• The roads are very wet. The bags of sand in the back help to
keep the truck from hydroplaning. (weight)
• However, you are going too fast and your truck runs off the road
into a muddy ditch. Now you are going to have to get help to
push or pull the truck out of the ditch. (mass)
2. Use appropriate quiz questions with participants, perhaps in the
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
form of a game like Jeopardy.
Extensions:
1.
Below are some extensions which elaborate on the differences
between weight and mass.
Procedures
Show NASA Video: Liftoff to Learning:
Newton in Space
http://quest.nasa.gov/content/rafiles/space/n
ewton.rm
Notes
This excellent resource reinforces
the concepts of weight and mass
via video clips in the space shuttle
and cartoon animation. You will
need RealPlayer (free download)
to view the video.
2.
Create a microgravity environment through
Adapted from Suited for
the act of free-fall. You will need a heavy
Spacewalking Teacher’s Guide,
book, a bathroom scale and a mattress or
NASA publication EG 101
soft landing surface. Put the book on the
scale and observe its weight. Then drop the
book and scale together onto the soft surface
positioned about a meter below them.
Watch what happens to the book’s weight.
(The book’s weight drops to zero as it falls.)
3.
Show the cartoon version of an elevator free- You will need RealPlayer (free
fall as described in the video resource guide download) to view the video.
for NASA Video: Liftoff to Learning:
Microgravity
http://quest.arc.nasa.gov/space/teachers/mic
rogravity/
4.
Ask participants to think of other instances
where they might experience free-fall and
perceived “weightlessness.”
They may talk about experiences
on a rollercoaster, in a car, on a
skateboard, snowboard, or skis,
etc….
5.
Create or show a handmade spring scale
calibrated with nonstandard or standard
units. Examine how it models scales found
in grocery stores, bathroom scales, etc.
A model of this can be found in
Van de Walle’s book, Elementary
and Middle School Mathematics
(see bibliography) or in the AIMS
activity entitled, “Hooked on
Algebra.” See the preview for this
activity on AIMS E-Activities list at
www.aimsedu.org.
6.
Share appropriate grade level literature or
trade books.
Some suggestions are given
below.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Resources:
Internet sites:
This link provides a concise definition of weight and mass.
http://www.beyondbooks.com/psc91/4e.asp?pf=on
Correct SI-metric usage:
http://lamar.colostate.edu/~hillger/correct.htm
Select “Encyclopaedia of the base units” in the sidebar (scroll down to “kilogram” to see
history of, definition of, and difference between weight and mass).
http://www.metre.info/
PowerPoint clarifying Newton’s 2nd Law:
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Newton2/N2_in_a_nutshell.htm
Everything you ever wanted to know about the metric system (try the link “For Teachers”
on left sidebar).
http://lamar.colostate.edu/~hillger/
NIST Educational Resources and Kid’s Page:
http://ts.nist.gov/WeightsAndMeasures/Metric/mpo_edulinks.cfm
http://www.nist.gov/public_affairs/kids/metric.htm
NASA Video Series: Liftoff to Learning
http://quest.nasa.gov/space/photos/videos/
Internet sites for measuring weight on other solar bodies:
http://www.exploratorium.edu/ronh/weight/
http://www.nasa.gov/audience/forkids/games/weight.html
Simple explanations of mass, weight, and gravity by author and science educator,
Vicki Cobb:
http://www.educationworld.com/a_lesson/showbiz_science/showbiz_science019.shtml
http://www.vickicobb.com/pointofview.htm (Scroll down to I Fall Down)
Children’s Literature and Trade Book Bibliography
A nonfiction book with grade 4-5 appropriate investigations related to gravity and weight.
Ardley, N. (1992). The science book of gravity. San Diego: Harcourt Brace Jovanovich.
A book of primary activities for discovering the science of gravity and weight. See internet
site above for the scientific explanation related to each page of this book.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Cobb, V. (2004). I fall down. New York: HarperCollins.
A grade 3-5 book that answers nine questions about motion, Newton’s laws, etc., in a
scientifically accurate, but entertaining format.
Cobb, V. (1988). Why doesn't the earth fall up?: And other not such dumb questions
about motion. New York: E. P. Dutton Books.
Peasants grow an enormous turnip and collectively try to apply enough force to overcome
the turnip’s inertia.
Morgan, P. (1990). The turnip: An old Russian folktale. New York: Philomel Books.
An introductory book (grades 1-2) on measurement and standard units.
Patilla, P. (2000). Measuring. Des Plaines, IL: Heinemann Library.
David M. Schwartz introduces the reader to the world of metrics.
Schwartz, D. M. (2003). Millions to measure. New York: HarperCollins.
Colorful photographs taken inside the Space Shuttle illustrate the effects of microgravity.
Skurzynski, G. (1994). Zero gravity. New York: Bradbury Press.
The Whiz Kids investigate weight. This book includes things to make and do (grades 1-2).
Willis, S. (1999). Tell me how much it weighs. Danbury, CT: Franklin Watts.
A young boy figures out a clever way to weigh his elephant.
Ye Ting-xing. (1998). Weighing the elephant. Ontario: Annick Press Ltd.
Other References
Texas Education Agency (TEA) and Texas Science Center. (2003). Bridging II TAKS:
Module 2: Using tools to explore matter. Houston, TX: Region IV Education Service
Center.
Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching
developmentally. Boston: Pearson Education, Inc.
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
KWL Chart
Mass
What I
KNOW
What I WANT
to know
What I
LEARNED
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
Transparency 1
10-24
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
KWL Chart
Weight
What I
KNOW
What I WANT
to know
What I
LEARNED
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
Transparency 2
10-25
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Jogging the Gelatin Boxes
Key Question: How far will the golf ball move
each of the gelatin boxes?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Empty Gelatin Box
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
Full Gelatin Box
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
a. What patterns and relationships do you see in the data?
b. What generalized statement(s) can you make regarding
the results of these tests?
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
Transparency 3
10-26
Tarleton State University
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
Transparency 4/Handout 1
10-27
The amount of acceleration is inversely proportional to the object’s mass.
The box with (more, less) mass moves (more, less).
The amount of force needed to accelerate an object
is directly proportional to the object’s mass.
(More, Less) force is needed to move the box with (more, less) mass.
The more mass something has, the harder it is to accelerate or move. The full
box with more _____ is harder to _____.
An object’s mass is a measure of its inertia or “unwillingness to move.” The full
box of gelatin has more ____ or ____ than the empty box.
A force (________) causes the object (________) to accelerate (________).
Mathematics TEKS Refinement 2006 – K-2
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
“How Much Does a Kilogram Weigh?”
Input
Process
Output
Number of
kilograms (kg)
Number of
newtons (N)
kg
N
a.
How much does 1 kilogram weigh in newtons?
2 kg? 4 kg? 10 kg?
b.
Use the second column to show the process.
c.
Write a sentence and a rule describing how the
number of newtons relates to mass (kg).
d.
If you have a mass of 60 kg, your weight on Earth
would be about _____?
Transparency 5/Handout 2
Does It Matter? A Mathematical Investigation of Weight and Mass (PowerPoint Version)
10-28
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Activity:
Does It Matter? A Mathematical Investigation of Weight and Mass
(without PowerPoint slides embedded in trainer notes)
TEKS:
See Appendix for Student Version of this Activity with correlated TEKS.
Overview:
This lesson will give teachers the opportunity to further develop the
concepts of weight and mass and to reflect on methods of introducing
each of these concepts to students in grades K-5 based on the newly
adopted elementary mathematics TEKS. (NOTE: This lesson is written for
participants as a review of the concepts of weight and mass as clarified by
TEA. However, most of the activities are easily adaptable to 4th grade,
and the appendix lesson reflects those modifications. Since the lesson is
designed around the SI (metric) system, it is suggested that teachers of
mathematics and science collaborate on the introduction of these
concepts. This lesson would be a prerequisite to many of the 4th grade
science TEKS.)
This activity should be included in all trainings for grades K-5 teachers.
Materials:
Introductory Activity - for demonstration with large group
Balance
Container of water placed in an overflow tray
Waterproof object such as an unopened baby food jar
Transparency 1-Mass KWL Chart (page 10-45)
Transparency 2-Weight KWL Chart (page 10-46)
Markers
Exploration of Mass - for each group
Two gelatin boxes (one full and one empty)
Empty Paper towel roll (cut in half longwise)
Masking tape
Golf ball
Meter tape or stick
Books or plastic shoeboxes
Pan balance
Centimeter/gram cubes
Gram stackers
Mass sets
Calculators
Exploration of Mass - for the trainer
Transparency 3-Jogging the Gelatin Boxes (page 10-47)
Transparency 4/Handout 1-Newton’s 2nd Law of Motion, teacher
training only (page 10-48)
Transparency 1-Mass KWL Chart (page 10-45)
Markers
Exploration of Weight - for each group
Sturdy plastic grocery or shoe bag
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
10-29
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Materials
(cont.):
Large bag or bucket of sand, rice, or small gravel with scoop
Gallon freezer bag
1 kg mass or other item that approximates 1 kg
Spring scale ≤ 5 newtons
Spring scale > 40 newtons
Pan balance or triple beam balance with mass sets
Gelatin boxes from mass activities
2-4 sandwich bags
Calculators
Exploration of Weight - for the trainer
Transparency 5/Handout 2-How Much Does a Kilogram Weigh? (page
10-49)
Transparency 2-Weight KWL Chart (page 10-46)
Markers
Optional Activity or Extension - for demonstration with large group
Unopened baby food jar
Large rubber band
Large paperclip
Spring scale ≤ 5 newtons
Clear container of water placed in an overflow tray
Other materials
Does It Matter? A Mathematical Investigation of Weight and Mass
PowerPoint, optional
Grouping:
Introductory Activity – whole group
Exploration of Mass – groups of four
Exploration of Weight – groups of four
Optional Activity or Extension – whole group
Time:
1 hour
Lesson:
The Does It Matter? A Mathematical Investigation of Weight and Mass
PowerPoint is optional but may be used as a guide during the lesson. If
you choose to use the PowerPoint, please be aware that the participants
are asked to Explore the concepts before the Explanations are given, so
be careful not to “give away” too much by advancing the slides too quickly.
A version of the trainer notes correlated with screen captures of the
PowerPoint slides is available on pages 10-1 – 10-28. Even though the
use of this PowerPoint is optional, all trainers that choose to present the
extension activity should use slides 25, 26, and 27 either as a PowerPoint
or as color transparencies.
1.
Procedures
Introductory Activity (whole group)
Set up the balance and the container of
Notes
The introductory activity serves as
a formative assessment by
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
10-30
Mathematics TEKS Refinement 2006 – K-2
Procedures
water so that all participants can see the
demonstration. Introduce the object that will
be the focus of this observation.
Tarleton State University
Notes
activating prior knowledge about
matter and the concepts of weight
and mass.
Demonstrate what happens when the object
is placed on the balance and in the waterfilled container.
a) Have participants predict what will happen
when you place the object on one side of a
zeroed balance. Confirm their prediction and
ask what they can tell you about the object
based on what they just observed.
b) Now predict what will happen when the
object is placed in the container filled with
water. Confirm their prediction and ask what
else they can tell you about the object from
their observations.
a) They will probably say it has
mass, but they may say it is
heavy or has weight.
b) They will probably say it takes
up space, i.e. volume. They may
say it displaces an amount of
water equal to its volume.
Remind participants that they have just
described two properties of matter (mass
and volume). They may remember the
definition: “All matter has mass and takes up
space.” In this unit, we will be focusing on
the property of mass and how it relates to
weight.
2.
On KWL charts (or use Transparencies 1
and 2, pages 10-45 – 10-46), record
participants’ knowledge statements and
questions about each concept - weight and
mass. Ask participants to tell you what they
already Know or think they Know about each
concept. Record their comments on each
chart under “What I Know.” Then, ask them
what questions they might have, or what they
expect to learn about each concept and
record those responses under “Want to
Know.” Post charts on the wall to refer to
later.
3.
Exploration of Mass (table groups of four)
Direct participants’ attention to some
If participants don’t provide
responses about when or why
weight and mass are important in
our everyday world, pose that
question.
You can choose any heavy and
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
10-31
Mathematics TEKS Refinement 2006 – K-2
Procedures
identified heavy object (table) and some light
object (pencil) in the room.
Tarleton State University
Notes
light object on which to focus the
questions (example: table and
pencil).
Ask: What can we do to make this table
move? (push it or pull it).
Would it be easier to move the table or this
pencil? Why?
(pencil, the table is heavier)
Continue questioning: Which would require
more force to make it move, the table or the
pencil?
(table)
Tell the participants to keep these ideas in
mind as we do the next activity.
4.
Provide each group with the golf ball, empty
paper towel roll, gelatin boxes, meter tape,
masking tape, and stack of books or plastic
shoeboxes.
Have the participants work at their tables to
design and to conduct a fair test to answer
this key question: How far will the golf ball
move each of the gelatin boxes?
Emphasize that the system should
be set up the same for each test -the only difference (variable) being
the full or empty gelatin box
Groups should conduct 3 trials with each
box, recording the results of each trial to the
nearest cm. Then, the group should find the
mean for the results for each box.
Some possible questions to clarify
the task might include:
• What do you notice about
the gelatin boxes?
• What is the role of the golf
ball?
• What function might the
empty paper towel roll
perform? The notebooks?
The meter tape?
5.
Chart each group’s results on Transparency
3 (page 10-47). Have participants examine
the data and discuss any patterns and
relationships they observe.
They should conclude that the
full/heavier box moved the fewest
cm; the empty/lighter box moved
the greatest number of cm.
6.
Introduce the word, “mass,” and write it on a
chart. Explain that all matter, whether solid,
liquid, or gas, has mass. Mass is the amount
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Procedures
of stuff in an object. The full gelatin box has
more mass, so it is harder for the golf ball to
push it. The empty box has less mass, so it
is easier for the golf ball to push it.
Notes
7.
Have participants think back to the table and
pencil scenario. Using the word, “mass,”
have them explain why it would be harder to
move the table.
Responses may vary, but they
should explain that the table has
more mass than the pencil, so it is
harder to move.
8.
Introduce the pan balance. Ask participants
to predict what will happen when the two
gelatin boxes are placed on each side of the
balance. Demonstrate or have them verify
their predictions at their tables. (The pan with
the full box will go down.)
9.
Explain that a balance is a tool/instrument
used to measure mass. An object’s mass is
determined by balancing it with objects of
known mass.
In the (SI) metric system, mass is most
commonly measured in kilograms (kg),
grams (g), and milligrams (mg).
Examine gram stackers, brass mass sets,
and centimeter/gram cubes as “known
masses.”
If available, show different kinds of
balances, i.e., bucket, pan, triple
beam, homemade, etc…. Be sure
that participants know how to zero
a balance before using the
tool/instrument to determine the
mass of objects.
If needed, talk about the rules for
symbols (abbreviations) in the
metric system and conversion
between units. (For more
information, see internet sites in
Resources at the end of this
activity, (page 10-43.)
Note: Not all centimeter cubes are
gram cubes, such as the base 10
unit cubes.
10.
Have participants predict and then determine
the mass of each of their gelatin boxes using
a pan balance and at least two of the types
of mass sets.
The results obtained when using
each of the types of mass sets
may vary by a gram or two.
Emphasize that measurement is
never exact.
Discuss the results.
11.
Provide Transparency 4/Handout 1 of
This handout is designed to be
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
Newton’s Second Law (page 10-48).
Tarleton State University
Notes
used with trainers and teachers.
Have participants relate the objects and
events from the gelatin box investigation with
the concepts of force, acceleration, mass
or measure of inertia or “unwillingness to
move.”
Sample Responses:
• The force, (the push from the golf ball),
causes an object (the gelatin box) to
accelerate (move some distance from its
state of rest).
• The object’s mass is a measure of the
amount of matter in an object or its
inertia or “unwillingness to move.”(The
full box has more mass/inertia than the
empty box.)
• The more mass something has, the
harder it is to accelerate. (The full box
with more mass was harder to move than
the empty box).
• The amount of force needed to
accelerate an object is directly
proportional to the object’s mass. (More
force is needed to move the box with
more mass.)
• The amount of acceleration is inversely
proportional to the object’s mass. (The
box with more mass moves less.)
• F=ma, a=F/m
12.
Reiterate that mass is a measurement of the
amount of matter in an object. Mass is
constant and does not change when the
object’s location changes. Your mass is the
same on Earth as it is on the moon. So, if
your mass is 60 kilograms on Earth, your
mass would be 60 kilograms on the moon.
One of commonly used units of mass in the
metric (SI) system is the kilogram which is
equal to 1000 grams.
13.
Return to Transparency 1-Mass KWL chart.
Have participants reflect on their initial
Remember that friction (another
force) acts on the object opposite
to the direction of motion, hence
the box decelerates and
eventually comes to a stop
(Newton’s First Law – The Law of
Inertia).
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
Procedures
responses regarding MASS. Elicit
statements about what they have Learned
about MASS and record these on that chart.
14.
Tarleton State University
Notes
Exploration of Weight (table groups of four)
Provide each group with a sturdy plastic
grocery bag or shoe bag, a kilogram mass or
other object that approximates 1 kg, and a
pan balance.
15.
Using their referent for 1 kg, have
participants fill their bag with sand, rice, or
gravel until they think they have a mass of
approximately 1 kg.
Hint: A liter of water has a mass of
1 kilogram. A nickel has a mass
of about 5 grams, etc.
16.
Using a pan or triple beam balance, allow
groups to check their estimates, and then to
adjust the contents of their bag to create a
more accurate mass of 1 kg.
A pan balance is sufficient if you
are using a kilogram mass or
other small objects.
17.
Next, introduce a spring scale (> 40 N) and
have participants hang their bags
approximating 1 kilogram on the spring
scale.
Tape over the kilogram/gram side
of the spring scale if it has one.
Ask them to read the results to the nearest
N.
1 kg on the spring scale is equal
to about 10 (9.8) N.
Explain that a spring scale measures weight
or the pull/force of gravity acting on the
object (in this case, the group’s kg mass).
The SI (metric) unit for weight is newton (N).
Names of units in the SI (metric)
system are written in lower case. If
the unit is named after a person,
such as Isaac Newton, the first
letter of the symbol is written in
upper case.
18.
Say: You now know that a 1 kg mass creates When they add the kg mass to
a force of about 10 N. If you add the kilogram their bags, they will have about 2
mass to your bag, what do you predict the
kg to hang on the spring scale.
readout will be?
(about 20 N)
What might the readout be if we combine two If they combine their table’s bag
tables’ bags? (about 40 N)
with another table’s bag, they will
have about 4 kg.
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
19.
20.
Procedures
Use Transparency 5/Handout 2 (page 10-49)
to create an input/output table with a process
column in between. Record an input of 1 kg
and output of 10 N; 2 kg, 20 N; 4 kg, 40 N;
etc….
Notes
After determining the process or rule for
finding the outputs, ask: If you have a mass
of 60 kg, your weight on Earth would be
about _____?
(600 N)
Participants should determine that
the process or rule for finding the
outputs is “input times 10.”
Ask: What does 1 kg weigh?
(Participants may say about 10 N.)
State that although mass is constant and
does not change with location, weight
does!! Your weight on the moon would be
approximately one sixth of your Earth weight,
because the gravitational pull on the moon is
1/6 that of the Earth.
The purpose of these examples is
to emphasize that weight, or the
force of gravity, changes with
location. This concept applies to
any measure of weight, SI (metric)
or customary.
If your Earth weight is about 600 N, what
would your weight be on the moon?
(about 100 N)
Note: Participants can calculate
their weight (customary) on other
celestial bodies at the internet
sites listed in the Resources
section at the end of this activity.
And, if 1 kg on Earth weighs about 10 N,
what would 1 kg weigh on the moon?
(about 1.64 N)
21.
Tarleton State University
Responses may vary, but they
Have one person at each table hold each
gelatin box in his/her outstretched hand. Ask may say the full box feels heavier.
them to describe what they feel.
State that they are experiencing the
downward force due to the pull of gravity on
the two boxes.
22.
Say: We have already determined that the
full gelatin box has more mass. Will it weigh
more, too?
Verify their prediction using a spring scale
(< 5 N). Have participants put each gelatin
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Procedures
box in a sandwich bag. Thread the hook on
the spring scale through the corner of the
sandwich bag.
Tarleton State University
Notes
23.
Explain that weight and mass are
proportional. The greater an object’s mass,
the more it weighs. An object that has twice
the mass of another object will weigh twice
as much in the same location. So, weight
depends on mass and gravitational pull.
W=mg (Weight = mass × gravity)
Remind participants that they
experienced this proportionality
earlier when they were weighing
the kilogram masses. One kg
weighed about 10 N, two kg
weighed about 20 N, etc….
24.
Optional Activity or Extension (whole
group)
Remember that weight is the
measure of the gravitational force
exerted on an object, while mass
refers to the amount of matter in
an object. An object on the moon
would weigh less than the same
object would weigh on the Earth
because the force of gravity is less
on the moon. However, that
object would have the same mass
on the moon as it would on the
Earth.
This part of the lesson is designed to be
done as a demonstration.
Attach a rubber band around the neck of an
unopened baby food jar. Hook a large
paperclip to the rubber band. Using a spring
scale, weigh the baby food jar. Record its
weight in newtons to the nearest tenth.
Tell the group that you know that they will not
be able to read the spring scale from their
seats, so you have scanned in a picture of
the experiment with the weight of the baby
food jar stated on the slide.
Show slide 25 from the PowerPoint.
Elaborate
ƒ Weighing the Baby
Food Jar – Out of
Water
ƒ Record the weight
in newtons to the
nearest tenth
Since we cannot go to the moon
to illustrate that weight can
change with location due to the
change in gravitational force, this
optional activity or extension can
be used to demonstrate to
participants that the reading on
the spring scale can be affected
when we change the forces acting
on the object. Granted, we are
not able to change the force of
gravity acting on the object while
we are here on planet Earth, but
this activity can help show that
mass remains constant no matter
what forces are present. When
the baby food jar is submerged in
water, the buoyant force is
pushing up on the object, i.e., the
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Notes
water itself is supporting some of
the weight. However, a
gravitational field pulls down on
the object uniformly. So, in water
the body still experiences the
force of gravity, and its weight
does not change; however, the
reading on the spring scale
changes due to the object
experiencing the counterforce due
to buoyancy.
An interesting connection to this
activity or extension is that
astronauts sometimes simulate
weightlessness in an underwater
environment during their training.
See the website listed below for
more information on this topic.
(http://starchild.gsfc.nasa.gov/doc
s/StarChild/space_level2/hubble_
practice.html)
25.
While still attached to the spring scale, lower
the baby food jar into a clear container of
water until it sits just below the water level.
Record its weight in newtons to the nearest
tenth.
Once again, tell the participants that you
have scanned in a picture and the weight of
the baby food jar when submerged in water
so that they might be able to see better.
Participants will find that the
reading on the spring scale for the
submerged baby food jar is less in
water due to the buoyant force of
the water that is acting on the jar.
Show slide 26 from the PowerPoint.
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Tarleton State University
Notes
Elaborate
ƒ Weighing the Baby
Food Jar – Under
Water
ƒ Record the weight
in newtons to the
nearest tenth
26.
Now let’s consider the mass of the baby food
jar both in and out of water.
Tell the participants that since this part of the Participants will find that the jar
experiment can get messy, you have done
has the same mass, whether in
the experiment ahead of time and scanned in the water or out of the water.
pictures with the masses labeled on the
slide. Remind them to use a waterproof
balance and masses if they decide to “try this
at home.”
Show slide 27 from the PowerPoint.
Elaborate
Determining the Mass of the Baby Food Jar
Out of Water
27.
Under Water
Return to the Weight KWL chart or use
Transparency 2.
Have participants reflect on their initial
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responses regarding WEIGHT. Elicit
statements about what they have Learned
about WEIGHT and record these on that
chart.
28.
Tarleton State University
Notes
Closure (whole group)
Say: This lesson has focused on weight and
mass in the SI (metric) system.
Mass is a fundamental property of matter
and is not dependent upon location;
however, weight is a measure of gravitational
force and therefore varies with location.
In the SI (metric) system, the gram and
kilogram typically are used to measure mass
while the newton is used to measure weight.
Units of mass exist in the customary system
(one such unit is the slug), but we don’t
usually go there because the customary
units of mass are cumbersome. The units
exist…but are not used very often. Ounces
and pounds are common units for weight in
the customary system.
Because we have dealt only with metric units
of mass and customary units of weight in
elementary mathematics, educators often
assume (incorrectly) that mass is only
measured in metric units, and weight in
customary units.
The reality is that both the SI (metric) and
customary systems have units for weight and
mass. We just haven’t expected our students
to deal with newtons in the metric system or
units of mass in the customary system.
29.
Use the scenario presented in the
assessment section below to check for
understanding.
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Mathematics TEKS Refinement 2006 – K-2
Assessment:
Tarleton State University
1. Have participants determine whether the statements below exhibit a
concern about weight or mass:
• The weatherman has predicted flooding, and you have gone to
buy bags of sand to stem the flow of water. (mass)
• You have to lift the bags of sand into the back of your truck.
(weight)
• The roads are very wet. The bags of sand in the back help to
keep the truck from hydroplaning. (weight)
• However, you are going too fast and your truck runs off the road
into a muddy ditch. Now you are going to have to get help to
push or pull the truck out of the ditch. (mass)
2. Use appropriate quiz questions with participants, perhaps in the
form of a game like Jeopardy.
Extensions:
1.
Below are some extensions which elaborate on the differences
between weight and mass.
Procedures
Show NASA Video: Liftoff to Learning:
Newton in Space
http://quest.nasa.gov/content/rafiles/space/n
ewton.rm
Notes
This excellent resource reinforces
the concepts of weight and mass
via video clips in the space shuttle
and cartoon animation. You will
need RealPlayer (free download)
to view the video.
2.
Create a microgravity environment through
Adapted from Suited for
the act of free-fall. You will need a heavy
Spacewalking Teacher’s Guide,
book, a bathroom scale and a mattress or
NASA publication EG 101
soft landing surface. Put the book on the
scale and observe its weight. Then drop the
book and scale together onto the soft surface
positioned about a meter below them.
Watch what happens to the book’s weight.
(The book’s weight drops to zero as it falls.)
3.
Show the cartoon version of an elevator free- You will need RealPlayer (free
fall as described in the video resource guide download) to view the video.
for NASA Video: Liftoff to Learning:
Microgravity
http://quest.arc.nasa.gov/space/teachers/mic
rogravity/
4.
Ask participants to think of other instances
where they might experience free-fall and
perceived “weightlessness.”
They may talk about experiences
on a rollercoaster, in a car, on a
skateboard, snowboard, or skis,
etc….
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
5.
6.
Tarleton State University
Procedures
Create or show a handmade spring scale
calibrated with nonstandard or standard
units. Examine how it models scales found
in grocery stores, bathroom scales, etc.
Notes
A model of this can be found in
Van de Walle’s book, Elementary
and Middle School Mathematics
(see bibliography) or in the AIMS
activity entitled, “Hooked on
Algebra.” See the preview for this
activity on AIMS E-Activities list at
www.aimsedu.org.
Share appropriate grade level literature or
trade books.
Some suggestions are given
below.
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Resources:
Internet sites:
This link provides a concise definition of weight and mass.
http://www.beyondbooks.com/psc91/4e.asp?pf=on
Correct SI-metric usage:
http://lamar.colostate.edu/~hillger/correct.htm
Select “Encyclopaedia of the base units” in the sidebar (scroll down to “kilogram” to see
history of, definition of, and difference between weight and mass).
http://www.metre.info/
PowerPoint clarifying Newton’s 2nd Law:
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Newton2/N2_in_a_nutshell.htm
Everything you ever wanted to know about the metric system (try the link “For Teachers”
on left sidebar).
http://lamar.colostate.edu/~hillger/
NIST Educational Resources and Kid’s Page:
http://ts.nist.gov/WeightsAndMeasures/Metric/mpo_edulinks.cfm
http://www.nist.gov/public_affairs/kids/metric.htm
NASA Video Series: Liftoff to Learning
http://quest.nasa.gov/space/photos/videos/
Internet sites for measuring weight on other solar bodies:
http://www.exploratorium.edu/ronh/weight/
http://www.nasa.gov/audience/forkids/games/weight.html
Simple explanations of mass, weight, and gravity by author and science educator,
Vicki Cobb:
http://www.educationworld.com/a_lesson/showbiz_science/showbiz_science019.shtml
http://www.vickicobb.com/pointofview.htm (Scroll down to I Fall Down)
Children’s Literature and Trade Book Bibliography
A nonfiction book with grade 4-5 appropriate investigations related to gravity and weight.
Ardley, N. (1992). The science book of gravity. San Diego: Harcourt Brace Jovanovich.
A book of primary activities for discovering the science of gravity and weight. See internet
site above for the scientific explanation related to each page of this book.
Cobb, V. (2004). I fall down. New York: HarperCollins.
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
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A grade 3-5 book that answers nine questions about motion, Newton’s laws, etc., in a
scientifically accurate, but entertaining format.
Cobb, V. (1988). Why doesn't the earth fall up?: And other not such dumb questions
about motion. New York: E. P. Dutton Books.
Peasants grow an enormous turnip and collectively try to apply enough force to overcome
the turnip’s inertia.
Morgan, P. (1990). The turnip: An old Russian folktale. New York: Philomel Books.
An introductory book (grades 1-2) on measurement and standard units.
Patilla, P. (2000). Measuring. Des Plaines, IL: Heinemann Library.
David M. Schwartz introduces the reader to the world of metrics.
Schwartz, D. M. (2003). Millions to measure. New York: HarperCollins.
Colorful photographs taken inside the Space Shuttle illustrate the effects of microgravity.
Skurzynski, G. (1994). Zero gravity. New York: Bradbury Press.
The Whiz Kids investigate weight. This book includes things to make and do (grades 1-2).
Willis, S. (1999). Tell me how much it weighs. Danbury, CT: Franklin Watts.
A young boy figures out a clever way to weigh his elephant.
Ye Ting-xing. (1998). Weighing the elephant. Ontario: Annick Press Ltd.
Other References
Texas Education Agency (TEA) and Texas Science Center. (2003). Bridging II TAKS:
Module 2: Using tools to explore matter. Houston, TX: Region IV Education Service
Center.
Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching
developmentally. Boston: Pearson Education, Inc.
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KWL Chart
Mass
What I
KNOW
What I WANT
to know
What I
LEARNED
Transparency 1
Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
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Mathematics TEKS Refinement 2006 – K-2
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KWL Chart
Weight
What I
KNOW
What I WANT
to know
What I
LEARNED
Transparency 2
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Mathematics TEKS Refinement 2006 – K-2
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Jogging the Gelatin Boxes
Key Question: How far will the golf ball move
each of the gelatin boxes?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Empty Gelatin Box
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
Full Gelatin Box
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
c. What patterns and relationships do you see in the data?
d. What generalized statement(s) can you make regarding
the results of these tests?
Transparency 3
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10-47
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Does It Matter? A Mathematical Investigation of Weight and Mass (non-PowerPoint Version)
Transparency 4/Handout 1
10-48
The amount of acceleration is inversely proportional to the object’s mass.
The box with (more, less) mass moves (more, less).
The amount of force needed to accelerate an object
is directly proportional to the object’s mass.
(More, Less) force is needed to move the box with (more, less) mass.
The more mass something has, the harder it is to accelerate or move. The full
box with more _____ is harder to _____.
An object’s mass is a measure of its inertia or “unwillingness to move.” The full
box of gelatin has more ____ or ____ than the empty box.
A force (________) causes the object (________) to accelerate (________).
Mathematics TEKS Refinement 2006 – K-2
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
“How Much Does a Kilogram Weigh?”
Input
Process
Output
Number of
kilograms (kg)
Number of
newtons (N)
kg
N
a.
How much does 1 kilogram weigh in newtons?
2 kg? 4 kg? 10 kg?
b.
Use the second column to show the process.
c.
Write a sentence and a rule describing how the
number of newtons relates to mass (kg).
d.
If you have a mass of 60 kg, your weight on Earth
would be about _____?
Transparency 5/Handout 2
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Mathematics TEKS Refinement 2006 – K-2
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Activity:
Foundations for Weight and Mass
TEKS:
This lesson is designed for teachers. Please refer to the appendix for
grade-level appropriate lessons to use with students.
Overview:
This lesson gives teachers the opportunity to refresh and to clarify their
knowledge of grade level expectations in the TEKS for Kindergarten
through 5th grade regarding weight/mass concepts. It is important that
teachers in K-2 know where the students are headed so that the
appropriate foundation can be laid. Furthermore, it is important that
teachers in grades 3-5 appreciate the power of the early conceptual
development for weight and mass concepts and the lasting benefits that a
strong foundation can have on student success.
Trainers should include this activity in trainings for all grades K-5 teachers.
Materials:
Grades K-5 Mathematics TEKS, 1 copy per group
Handout 1-Grade Level Expectations for Development of Attributes of
Weight and Mass (page 10-61)
Handout 2-Sample Completed Chart for Grade Level Expectations for
Development of Attributes of Weight and Mass (page 10-62)
Transparencies 1 & 2/Handout 3-Clarifications from TEA Concerning
Weight and Mass (page 10-63 – 10-64)
Grouping:
Groups of 4
Time:
30 minutes
Lesson:
Trainers need to be aware that there is a discrepancy between the
science TEKS and the mathematics TEKS for units and tools of mass.
The MTR materials are developed using the mathematics TEKS. In the
first grade science modules, students compare and order more than two
objects, but they also use nonstandard units to measure and record the
mass of those objects. In the second grade science modules, students
are introduced to the standard units of mass and gram, and they begin to
develop benchmarks for items greater than, equal to, and less than one
gram, 10 grams, etc. They determine the mass of objects and record the
number of grams. Trainers will need to make a decision of how to
address this discrepancy with teachers.
1.
Procedures
Review some of the key points that came
from the lesson Does It Matter? A
Mathematical Investigation of Weight and
Mass. (pages 10-1 – 10-49)
Foundations for Weight and Mass
Notes
This review can be very brief (and
possibly omitted) if this lesson is
done immediately following Does
It Matter? A Mathematical
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Mathematics TEKS Refinement 2006 – K-2
Procedures
UNITS
In the metric system, what standard units
typically are used to measure mass?
grams and kilograms
Tarleton State University
Notes
Investigation of Weight and Mass.
In the metric system, what standard units
typically are used to measure weight?
newtons
In the customary system, what standard
units typically are used to measure mass?
One such unit is the slug, but we don’t
usually go there because the customary
units of mass are cumbersome. The units
exist…but are not used very often.
In the customary system, what standard
units typically are used to measure weight?
ounces and pounds
TOOLS
What attribute are you measuring when
using a pan balance?
mass of an object
What attribute are you measuring when
using a spring scale?
weight
DISTINCTION BETWEEN MASS AND
WEIGHT
What is the distinction between mass and
weight?
Mass is the amount of matter in an object.
Mass remains constant, regardless of
location.
Weight is a measure of the gravitational
force exerted on an object. Weight depends
upon location. For example, an object will
have less weight on the moon than it will
have on Earth since gravity is less on the
moon.
Even though weight and mass are distinct
Foundations for Weight and Mass
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Mathematics TEKS Refinement 2006 – K-2
2.
Tarleton State University
Procedures
attributes, they are proportional. An object
having twice the mass of another object will
weigh twice as much, too (as long as both
objects are in the same location).
Notes
Refer participants to their copies of the
mathematics TEKS for Kindergarten through
5th grade. (See the materials list for link.)
The actual knowledge and skills
statement and student expectation
is stated as follows:
Ask: When will our students be expected to
know the difference between weight and
mass?
The difference between weight and mass is
specified in the TEKS for 4th grade. See
4.11(E).
(4.11) Measurement. The
student applies measurement
concepts. The student is
expected to estimate and measure
to solve problems involving length
(including perimeter) and area.
The student uses measurement
tools to measure capacity/volume
and weight/mass.
Note that the terms weight and mass are
referred to in the TEKS prior to 4th grade as
weight/mass.
The student is expected to:
(E) explain the difference
Up until 4th grade, we are not making a
between weight and mass.
distinction between weight and mass since
our all of our measurements are being taken
in the same location – on the Earth. Even
though we as teachers know that weight and
mass are distinct attributes, the attributes are
bundled together as weight/mass in the
TEKS for Kindergarten through 3rd grade.
3.
Have participants find Handout 1-Grade
Level Expectations for Development of
Attributes of Weight and Mass (page 1061).
Let’s look at TEKS concerning weight/mass
in grades K-3 to understand the foundation
that must be built during the early grades in
order for students to be successful in
understanding the distinction between these
two attributes in 4th grade. As we discuss
each grade level, you may record a summary
of our discussion on Handout 1.
Foundations for Weight and Mass
Handout 2 (page 10-62) provides
a sample completed chart for
Handout 1-Grade Level
Expectations for Development of
Attributes of Weight and Mass.
If participants have done the
activity Of Course We Have
Standards (and Nonstandards)!
(pages 8-18 – 8-27), they will have
already looked at the weight/mass
TEKS for Kindergarten through 5th
grade, along with the TEKS
dealing with the attributes of
length, area, and capacity/volume.
In that activity, the participants
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Mathematics TEKS Refinement 2006 – K-2
Procedures
4.
Refer participants to the Kindergarten
mathematics TEKS.
What is expected and appropriate with
regards to weight/mass at the Kindergarten
level?
At the Kindergarten level, the students are
making direct comparisons between two
objects for weight/mass. See K.10(D).
As teachers, we should ask questions that
will elicit the comparative language as
mentioned in part (D) of the TEKS. Which
object feels heavier? Which object feels
lighter?
5.
Let’s move to the 1st grade TEKS.
What is expected and appropriate with
regards to weight/mass at the 1st grade
level?
At the 1st grade level, the students still are
making direct comparisons for
weight/mass. The number of objects is now
“two or more” instead of just two objects at
a time as in Kindergarten, and the students
put the objects in order according to
weight/mass. See 1.7 (F).
Tarleton State University
Notes
were focusing solely on the use of
nonstandard units and standard
units. This lesson provides a
more in-depth look at what is
expected and appropriate for
weight/mass activities at each
grade level.
The knowledge and skills
statement and student expectation
for weight/mass is stated as
follows:
(K.10) Measurement. The
student directly compares the
attributes of length, area,
weight/mass, capacity, and/or
relative temperature. The student
uses comparative language to
solve problems and answer
questions.
The student is expected to:
(D) compare two objects
according to weight/mass (heavier
than, lighter than or equal to).
The knowledge and skills
statement and student expectation
for weight/mass is stated as
follows:
(1.7) Measurement. The student
directly compares the attributes of
length, area, weight/mass,
capacity, and temperature. The
student uses comparative
language to solve problems and
answer questions. The student
selects and uses nonstandard
units to describe length.
The student is expected to:
(F) compare and order two or
more objects according to
Foundations for Weight and Mass
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Mathematics TEKS Refinement 2006 – K-2
Procedures
6.
Tarleton State University
Notes
weight/mass (from heaviest to
lightest).
Ask each group to consider the following
questions for a few minutes and to be
prepared to share some of the key points
that come up in their small group discussion:
What should direct comparison of
weight/mass look like in the Kindergarten
and 1st grade classrooms?
What should direct comparison of
weight/mass NOT look like in the
Kindergarten and 1st grade classrooms?
Give the groups about 5 minutes to
brainstorm ideas.
7.
Lead the large group in a debriefing
discussion.
Here are some key ideas that should come
out of this discussion dealing with direct
comparisons of weight/mass for
Kindergarten and 1st grade.
What should direct comparison of
weight/mass look like in the Kindergarten
and 1st grade classrooms?
•
Students should place the items in their
hands first (one item in each hand) and
make a prediction concerning which
object feels heavier, lighter, or if the items
feel about the same (about equal to each
other in weight/mass). This experience
leads nicely into using a pan balance.
•
After making a prediction, students can
use a pan balance to directly compare
the weight/mass of the items. The pan
that “goes down” holds the heavier
object. Make sure that your students
understand how to zero the balance
Foundations for Weight and Mass
Remind teachers that when using
a pan balance, they should not
use the term “weight.” Pan
balances measure mass, and
spring scales measure weight.
Even though we are not
differentiating between weight and
mass until 4th grade, we do not
want to use incorrect vocabulary
that could lead to confusion for the
students later on.
A participant might bring up this
question…
Even though we are not
distinguishing between weight and
mass at this level, we as teachers
know that “heavier” and “lighter”
are descriptions of weight. If a
pan balance measures mass, then
how can we use that tool to
determine which object is heavier
than, lighter than, or equal to
another object in weight/mass?
A sample response to this
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Mathematics TEKS Refinement 2006 – K-2
Procedures
before comparing the objects.
•
Students may believe that as an object’s
size increases, its weight/mass will
increase. Sometimes this relationship is
true, but not always! It depends on the
object’s density. (For more information on
density, see “How Dense Are You?” from
TexTEAMS Rethinking Elementary
Mathematics Part II.) Certainly, some of
the comparisons that students perform
should have this relationship. However,
when giving students items to compare,
be sure to provide the following types of
comparisons as well.
⇒ Objects that are similar in size, but
have different weights. For example,
provide two jars that are the same
size but fill one jar with Cheerios and
the other jar with sand. Another
example might be to have two small
flowerpots that are about the same
size, but one is made of plastic and
the other is made of clay.
⇒ Objects that are similar in weight, but
have different sizes. For example,
you might provide a small stuffed
animal filled with beans and a larger
stuffed animal filled with polyfill that
weighs the same as the smaller
stuffed animal. Even though the
stuffed animals differ in size, they will
balance on the pan balance.
⇒ Objects that differ in weight and size.
For example, be sure to have a large
item that does not weigh much and a
small item that is heavier than the
large item. For example, a large
piece of Styrofoam and a relatively
small rock would work well.
Tarleton State University
Notes
question might look like the
following:
When we use a pan balance to
compare two objects, we are
comparing the masses of the two
objects. When students compare
objects and describe them in
terms of heavier or lighter, they
are describing the weight, but the
weight is directly related to the
mass of the object. As we saw in
Does It Matter? A Mathematical
Investigation of Weight and Mass,
weight and mass are proportional.
For example, an object with twice
the mass of another object will
weigh twice as much (in the same
location). So, our students can
say that the object that “goes
down” on the pan balance is
heavier than the object to which it
is being directly compared
because of the proportional
relationship between weight and
mass.
What should direct comparison of
weight/mass NOT look like in the
Kindergarten and 1st grade classrooms?
Foundations for Weight and Mass
10-55
Mathematics TEKS Refinement 2006 – K-2
•
8.
Procedures
At the direct comparison level for
Kindergarten and 1st grade, the students
are not quantifying the weight/mass with
any kind of unit.
Ask the participants to look at the TEKS
dealing with weight/mass for 2nd grade.
Ask: What is the same as it was in
Kindergarten and 1st grade? What is
different than it was in Kindergarten and 1st
grade?
In 2nd grade, the direct comparison of objects
with regard to weight/mass remains. The
comparative language remains as well. The
difference is that in 2nd grade, the students
are now expected to extend their work with
weight/mass by selecting and using a
nonstandard unit to determine the
weight/mass of a given object. Students
should also begin to recognize and use
models that approximate standard units for
weight/mass. See 2.9 (D).
Tarleton State University
Notes
The knowledge and skills
statement and student expectation
for weight/mass is stated as
follows:
(2.9) Measurement. The student
directly compares the attributes of
length, area, weight/mass, and
capacity, and uses comparative
language to solve problems and
answer questions. The student
selects and uses nonstandard
units to describe length, area,
capacity, and weight/mass. The
student recognizes and uses
models that approximate standard
units (from both SI, also known as
metric, and customary systems) of
length, weight/mass, capacity, and
What might weight/mass activities look like in time.
the 2nd grade classroom?
The student is expected to:
As an example, you might have your
(D) select a non-standard unit of
students use a pan balance to determine
measure such as beans or
how many beans it takes to balance an
object. The students are basically finding the marbles to determine the
weight/mass of a given object.
amount of beans that have the equivalent
weight/mass as the given object. Students
need practice measuring the weight/mass of
objects and reporting how many units as
they quantify the weight/mass of the object.
In addition, the knowledge and skills
statement mentions that the students should
recognize and use models that approximate
standard units. For example, you might say
to your students that a centimeter cube has a
mass of about 1 gram. Then you could ask
the students how many centimeter cubes it
would take to balance the object in question.
Foundations for Weight and Mass
10-56
Mathematics TEKS Refinement 2006 – K-2
9.
Procedures
Ask the participants what objects they are
familiar with that could be used to
approximate standard units for weight/mass.
Tarleton State University
Notes
Sample responses might include the
following:
Centimeter cubes (about 1 gram)
Nickel (about 5 grams)
Marbles (about 5 grams, but not consistent)
Large paperclip (about 1 gram)
Milk lid (about 2 grams)
Beans (about 1 gram, but not consistent)
Bags of sugar, flour, etc… (available in 1
pound, 4 pounds, 5 pounds, etc…)
Fishing equipment like sinkers (various
ounces – check the label)
Cheese (available in 1 pound blocks)
Small jars of cooking spices (various ounces
– check the label)
10.
Ask participants to look for the 3rd grade
TEKS that deal with weight/mass.
What is the same as in prior grades? What
is different when compared to prior grades?
Direct comparisons and comparative
language remain in the TEKS through 3rd
grade. The difference now is that students
are using standard units for weight/mass,
with an emphasis still on concrete models.
See 3.11 (D).
What might activities for weight/mass look
like in the 3rd grade classroom?
The students might use a pan balance and
gram stackers or pieces from a gram mass
set to determine the mass of the object. It is
also important for the students to continue to
build and develop mental benchmarks for
standard units of weight/mass. The
benchmarks will be more effective for the
students if they include everyday objects with
which the students are familiar. The
students could collect items from home or
from around the school to bring to class as
Foundations for Weight and Mass
The knowledge and skills
statement and student expectation
for weight/mass is stated as
follows:
(3.11) Measurement. The
student directly compares the
attributes of length, area,
weight/mass, and capacity, and
uses comparative language to
solve problems and answer
questions. The student selects
and uses standard units to
describe length, area,
capacity/volume, and
weight/mass.
The student is expected to:
(D) identify concrete models that
approximate standard units of
weight/mass and use them to
measure weight/mass.
10-57
Mathematics TEKS Refinement 2006 – K-2
Procedures
benchmarks are developed. Activities such
as these will help students to identify
concrete models that approximate standard
units of weight/mass.
11.
We have already discussed the fact that 4th
grade is the time when the difference
between weight and mass is acknowledged.
Let’s take another look at the 4th grade TEKS
to see what else is going on with weight and
mass at this level.
Tarleton State University
Notes
The knowledge and skills
statement and student expectation
for weight/mass is stated as
follows:
(4.11) Measurement. The
student applies measurement
Ask the participants to revisit the 4th grade
concepts. The student is
expected to estimate and measure
TEKS and to compare to what has been
to solve problems involving length
done in Kindergarten through 3rd grade.
(including perimeter) and area.
The TEKS do not mention direct
comparisons for weight/mass at the 4th grade The student uses measurement
tools to measure capacity/volume
level. The omission of the direct
and weight/mass.
comparisons implies that mastery of this
rd
concept is expected by the end of 3 grade.
The student is expected to:
In addition, 4th grade students will be
expected to estimate and use measurement (A) estimate and use
tools for weight/mass using standard units in measurement tools to determine
the metric and customary systems. Students length (including perimeter), area,
capacity and weight/mass using
most likely will be familiar with the pan
standard units SI (metric) and
balance (tool used to measure mass).
Students can use a spring scale to measure customary;
(B) perform simple conversions
weight. Simple conversions between
different units of weight within the customary between different units of length,
between different units of
measurement system are addressed in 4th
capacity, and between different
grade. Finally, as mentioned before,
units of weight within the
students are expected to explain the
customary measurement system;
difference between weight and mass. See
(E) explain the difference
4.11 (A) (B) (E).
between weight and mass.
What might weight and mass activities look
like in the 4th grade classroom?
Students should have many opportunities to
reinforce their mental benchmarks for
standard units for weight and mass that they
have been developing since 3rd grade as
they estimate the weight or the mass of an
object. The students may want to use direct
comparisons here (even though direct
comparisons are not specifically mentioned
Foundations for Weight and Mass
10-58
Mathematics TEKS Refinement 2006 – K-2
Procedures
in the TEKS). Holding a referent for a
standard unit in one hand and holding the
object to be measured in the other hand can
assist the students in making a good
estimate for weight or mass. After making
the estimate, the students will need handson practice using pan balances and spring
scales to confirm their predictions.
Remember that pan balances measure
mass, while spring scales measure weight.
For the conversions in the TEKS, the
students need practice reporting weights
using different units. For example, after
measuring the weight of an object in pounds,
have the students report the weight in
ounces as well. Remind participants that a
student version of Does It Matter? A
Mathematical Investigation of Weight and
Mass is included in the appendix as a grade
appropriate lesson to address 4.11 (E).
Tarleton State University
Notes
Encourage participants to develop strong
lines of communication between the
mathematics teachers and the science
teachers in the school.
12.
We have now seen what needs to be in
place in Kindergarten through 3rd grade so
that students can be successful with the
weight and mass concepts outlined in the 4th
grade TEKS. Let’s round out our discussion
of the weight and mass concepts for K-5 by
looking at the 5th grade TEKS for weight and
mass.
13.
Ask participants to investigate the 5th grade
TEKS that deal with weight or mass. What is
expected and appropriate at the 5th grade
level for weight/mass concepts?
The knowledge and skills
statement and student expectation
for weight/mass is stated as
follows:
Weight/mass is mentioned in the knowledge
and skills statement, but not specifically
mentioned in the student expectations.
However, student expectation (A) states that
students perform simple conversions within
(5.10) Measurement. The
student applies measurement
concepts involving length
(including perimeter), area,
capacity/volume, and weight/mass
Foundations for Weight and Mass
10-59
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Procedures
the same system, implying that students
continue to reinforce their knowledge of
simple conversions for weight/mass that
began in 4th grade. See 5.10 (A).
Notes
to solve problems.
The student is expected to:
(A) perform simple conversions
within the same measurement
system (SI (metric) or customary).
14.
Have participants finalize their summaries of
each grade level’s development of weight
and mass concepts on Handout 1 if they
have not finished.
Handout 2 is a sample completed
chart.
15.
As participants reflect on the lesson, remind
them how important each teacher is in the
cycle of progressive development of these
concepts of weight and mass. It is important
that teachers in K-2 know where the students
are headed so that the appropriate
foundation can be laid. Furthermore, it is
important that teachers in grades 3-5
appreciate the power of the early conceptual
development for weight and mass concepts
and the lasting benefits that a strong
foundation can have on student success.
16.
As a final reflection, have the participants
review their completed Handout 1-Grade
Level Expectations for Development of
Attributes of Weight and Mass as you share
with them the information contained on
Transparencies 1 & 2/Handout 3Clarifications from TEA Concerning
Weight and Mass (pages 10-63 – 10-64).
You might wish to use this
document as a handout, or you
might wish to make a
transparency to project as you
share the information with the
participants.
Assessment:
Assessment is done throughout the lesson, as groups discuss, share,
and refine their understanding of the concepts.
Resources:
Murphy, S.J. (2004). Mighty maddie. New York: HarperTrophy.
Foundations for Weight and Mass
10-60
Kindergarten
Foundations for Weight and Mass
Weight/Mass
Attribute
1st Grade
2nd Grade
3rd Grade
4th Grade
As you investigate the TEKS dealing with weight/mass for each grade, summarize your findings below.
Handout 1
10-61
5th Grade
Tarleton State University
Grade Level Expectations for Development of Attributes of Weight and Mass
Kindergarten – Fifth Grade
Mathematics TEKS Refinement 2006 – K-2
•
•
•
Perform direct •
comparisons
– two objects
Use
comparative
language
Kindergarten
Foundations for Weight and Mass
Weight/Mass
Attribute
Perform direct
comparisons
– two or more
objects (put in
order
according to
weight/mass)
Use
comparative
language
1st Grade
•
•
•
•
Perform direct
comparisons
Use
comparative
language
Select and
use
nonstandard
units
Recognize
and use
models that
approximate
standard units
(SI and
customary)
2nd Grade
•
•
•
•
4th Grade
Estimate and
use tools to
determine
weight/mass
(SI and
customary)
Perform
simple
conversions
between
different units
of weight
(customary)
Explain the
difference
between
weight and
mass
3rd Grade
Perform direct •
comparisons
Use
comparative
language
Select and
use standard •
units (SI and
customary)
Identify
concrete
models that
approximate
standard units •
(SI and
customary)
and use them
to measure
weight/mass
As you investigate the TEKS dealing with weight/mass for each grade, summarize your findings below.
•
Handout 2
10-62
Perform
simple
conversions
within the
same system
(metric and
customary)
5th Grade
Tarleton State University
Grade Level Expectations for Development of Attributes of Weight and Mass
Kindergarten – Fifth Grade
Sample Completed Chart
Mathematics TEKS Refinement 2006 – K-2
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
Clarifications from TEA Concerning Weight and Mass
The following information was received via email from TEA to clarify some questions
from the MTR writing team concerning the weight and mass TEKS.
Definitions
The mass of an object is a fundamental property of the object; a numerical measure of
its inertia; a fundamental measure of the amount of matter in the object.
The weight of an object is the force of gravity on the object and may be defined as the
mass times the acceleration of gravity, w=mg.
Gravity is the force; weight is a result of the force acting on the mass.
The mass of an object is constant regardless of the location of the object. For example,
an object with a mass of 1 kg on Earth has a mass of 1 kg on the moon.
The weight of an object can vary depending on its location. For example, a man who
weighs 180 lbs on Earth would weigh just 30 lbs on the moon.
Weight is a measure of the gravitational force between two objects.
The reason that the person weighs less on the moon is because the moon has
considerably less mass than the Earth.
The 180 lb man will weigh less the farther he is away from the center of the Earth. This
is because there is an inverse relationship between the distance the objects are apart
and the force of attraction. This distance is measured from the center of the objects.
In kindergarten and first grade, children are asked to compare the weight/mass of
different objects. They are asked to describe them in terms of heavier and lighter.
These are descriptions of weight. The descriptions are directly related to the mass of
the object. If the objects are in the same location then a heavier object has a greater
mass than the lighter object. If the objects are in different locations then this is not
necessarily true.
In second grade, children determine the weight/mass of a given object using a
nonstandard unit. Technically we are not determining the mass or weight of the object
in beans (for example). We are determining the amount of beans that have the
equivalent weight or mass as the given object.
In third grade, children identify concrete models that approximate standard units for
weight/mass. A balance is used to determine mass. SI (metric) units are easier to work
with for mass (grams for example). There are English units for mass but these can be
problematic because they are the same units that describe weight (ton for example –
Foundations for Weight and Mass
Transparency 1/Handout 3-1
10-63
Mathematics TEKS Refinement 2006 – K-2
Tarleton State University
confusing!). Remember, weight is a measure of a force. Its SI unit is the Newton or
kg*m/s^2 or w=m*g. An example of this might be to use a balance and gram stackers
to determine the mass of the object. This is problematic for weight. A tool or device
such as a scale is used to determine the weight not a comparative measure.
In 4th grade the difference between mass and weight is acknowledged. 4.11(E) explains
the difference between weight and mass.
See the explanations above.
At 5th grade there is a discrepancy between the knowledge statement and the student
expectations. We say weight/mass in the knowledge statement but do not use the
terms weight or mass in the student expectations. Perhaps the intention is to just work
with conversions within the same system.
At 6th grade weight is mentioned but mass is not. Since there is a direct relationship
between mass and weight then the assumption is that when working with weight then
one must be able to convert units of mass within the same system. Since this was
introduced at earlier grade levels the assumption is that it is addressed at the
application level in 6th grade.
From 7th grade forwards the measurement TEKS are much more geometrical in nature.
Foundations for Weight and Mass
Transparency 2/Handout 3-2
10-64