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Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 4.0 International License
Unit 3.11: Volume and Weight
Big Idea: Volume and mass are attributes of objects that can be estimated and measured using standard units.
Teacher-facing pages are green
Student-facing pages are white
notes for teachers are in the speaker notes
Emphasized Standards in this unit:
In this unit, students apply their understanding of the additive nature of linear units (one can measure the length of an object by repeating or iterating the same unit, such as inches) as they use grams and kilograms to measure mass and liters to measure volume (i.e., one can measure the mass/weight of an object by repeating or iterating the same unit, such as grams; one can measure the volume of liquid by iterating the same unit, such as liters). Just as students developed references to support them in using linear units of measurement, students develop references to support them in using grams, kilograms, and liters.
Students apply their understanding of solving word problems using the four operations to interpret one-step word problems involving mass and volume. They use drawings, diagrams, and equations to represent and solve the problems.
Measurement and Data Solve problems involving measurement and estimation. 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. |
New Learning in this Unit:
Unit Objectives
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Important Notes |
Mass vs. Weight: The K–5 Progression on Measurement and Data states, “The Standards do not differentiate between weight and mass. Technically, mass is the amount of matter in an object. Weight is the force exerted on the body by gravity. On the earth’s surface, the distinction is not important (on the moon, an object would have the same mass, but would weigh less due to the lower gravity).” In this unit, the term “weight” is generally used, however it is suggested that you use both terms together so your students are familiar with both terms and their meanings. It is not necessary for students to make the distinction between the two terms. Capacity vs. Volume: According to John Van de Walle (mathematics educator, author, and long-time NCTM board member), “Volume typically refers to the amount of space that an object takes up [whereas] capacity is generally used to refer to the amount that a container will hold...Having made these distinctions [between volume and capacity], they are not ones to worry about. The term volume can also be used to refer to the capacity of a container.” Changes for distance learning:
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The Progression of Ideas of Weight and Volume
Prior Supporting Mathematics | Current Essential Mathematics | Future Mathematics |
In kindergarten, students worked informally with mass and volume as they used balance scales to determine which object is heavier or lighter, and counted and compared the number of objects that fit into a container. The focus was on objects having more or less of a particular measurable attribute. In Grades 1 and 2, students did not work directly with volume or mass, but developed concepts of measurement by measuring length, including the idea of iterated units and standard units. Grade 2 students also used addition and subtraction to solve word problems involving lengths. | In this unit, students apply their understanding of the additive nature of linear units (one can measure the length of an object by repeating or iterating the same unit, such as inches) as they use grams and kilograms to measure mass and liters to measure volume (i.e., one can measure the mass/weight of an object by repeating or iterating the same unit, such as grams; one can measure the volume of liquid by iterating the same unit, such as liters). Just as students developed references to support them in using linear units of measurement, students develop references to support them in using grams, kilograms, and liters. Students apply their understanding of solving word problems using the four operations to interpret one-step word problems involving mass and volume. They use drawings, diagrams, and equations to represent and solve the problems. | In Grades 4 and 5, students will solve problems involving measurement and conversion of measurement units. In 4th grade, they will convert from a larger unit to a smaller unit (e.g., kilograms to grams); in 5th grade, from a smaller unit to a larger unit (e.g., grams to kilograms). This will sometimes require them to use or find measurements in decimals. In Grade 5, students will build on their understanding of volume by using cubic units to pack a space, and expand their understanding of liquid volume having only one dimension (height of water in a beaker) to incorporate three dimensions (length, weight, and height of objects). In middle and high school, students will measure the volume of a variety of solid figures that can be composed and decomposed. |
Coordinating In-Person and Distance Learning
Many teachers are now using a combination of in-person and Distance Learning.
Here are some suggestions for managing this with this math unit:
In Person Suggestions | Distance Learning Suggestions |
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Continuing Daily Routines:
Extensions and Continuing Activities are listed in each lesson
Suggested Lesson Sequence
Week 1
Entry Task - “The Orange” - Introducing big ideas of weight and standard measurement.
Lesson 2 - How much is a gram? How much is a kilogram?
Unit Warm-up
The purpose of the warm-up is to kindle interest in the topics of the unit and to bring forth what students already know about weight and volume.
Students re-engage with what they learned in Kindergarten about weight and volume by discussing the relative weight and volume of familiar objects.
Students then learn about Dr. Charles Drew, a pioneering African-American scientist who is known as the “father” of the blood bank.
Measuring Weight and Volume
Volume is a measure of how much something holds.
In the last unit we measured length.
Length is a measure of how long something.
In this unit we’ll measure weight and volume.
Weight is a measure of how heavy something is.
lighter
heavier
holds more
holds less
What do you notice? What do you wonder?
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Weight
12
Let’s put these items in order from the lightest to the heaviest
lightest → heaviest
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Volume
13
Let’s put these items in order from the one that holds the least to the one that holds the most
holds the least → holds the most
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Dr. Charles Drew
14
Pioneer of blood storage and “father” of the blood bank
Dr. Charles R. Drew discovered a method of separating red blood cells from plasma and then storing the two components separately. This new process allowed blood to be stored for more than a week, which was the maximum at that time.
The ability to store blood (or, as Dr. Drew called it, banking the blood) for longer periods of time meant that more people could receive transfusions.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Dr. Charles Drew
15
Dr. Drew supervised blood preservation and delivery in World War II. Then he was appointed director of the first American Red Cross Blood Bank, a blood bank for the U.S. Army and Navy that served as the model for blood banks today.
Dr. Drew resigned because the armed forces insisted on separating blood by race and providing white soldiers with blood donated from white people. He knew that race made no difference in blood composition, and he felt that this unnecessary segregation would cost too many lives.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
More about Dr. Charles Drew
16
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Donating Blood
17
Dr. Drew developed the idea of separating the components of blood. This new process allowed blood to be stored for more than a week, which was the maximum at that time.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Donating Blood
18
How much blood does a person donate during one donation?
O +
Bag of donated blood
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Lesson 1 (Entry Task)
Core Math |
CCSS-M Standard(s) |
Measurement and Data
Solve problems involving measurement and estimation.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
The Entry Task answers the question: What do you already know?
Lesson 1 (Entry Task)
Whole Class or Groups:
Independent or Group work:
Whole Class or Groups:
Core Math to Emphasize
Strengths to highlight
See the following slide for options for in-person vs. distance learning and what can be done if students have access to a pan balance.
Options for this Task for In-Person and/or Distance Learning | |
Launch | |
| |
Explore | |
In-Person | Distance Learning |
Group work
or Teacher Demonstration
|
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Summarize | |
Math Norms
22
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
The Orange
LAUNCH |
1 |
We are going to watch a short video about an orange.
What did you notice?
What do you wonder?
The Orange
LAUNCH |
1 |
I notice...
I wonder...
We notice:
LAUNCH |
1 |
We wonder:
LAUNCH |
1 |
Today we will answer 2 questions:
LAUNCH |
1 |
How many cubes will balance the orange? and,
How much does the orange weigh?
I estimate:
First, let’s estimate:
About how many cubes will balance the orange?
Way too low:
Way too high:
The Orange
EXPLORE |
2 |
Look at your estimates:
How many cubes do you think we will need?
Can we balance the pan?
How many cubes did we use?
What if we try a different material?
Balancing Weights
EXPLORE |
2 |
Find something at home that you have a lot of. For example, pens, paper clips, pennies, legos (of the same size).
Put a bunch of the objects in one hand. Find something else at home that weighs ABOUT the same amount.
Example:
This glove weighs ABOUT the same as 4 big paper clips
SUMMARIZE |
3 |
EXPLORE |
2 |
Options for student work:
Options for monitoring and sharing work:
Measuring Weight
SUMMARIZE |
3 |
I used my hands to measure weight.
I found that a fork weighs about the same as 15 paper clips.
What do you notice?
What do you wonder?
Measuring Weight
SUMMARIZE |
3 |
I used my hands to measure weight.
I found that a pen weighs about the same as 3 pennies.
What do you notice?
What do you wonder?
Measuring Weight
SUMMARIZE |
3 |
I used a pan balance to measure weight.
I found that an orange weighs the same as 48 cubes.
Who got a different result? Why?
Measuring Weight
SUMMARIZE |
3 |
I found that an orange weighs the same as 30 cubes.
Why did this orange balance with fewer cubes?
The Orange
Let’s see what happens in the video of the orange!
How close were our estimates?
SUMMARIZE |
3 |
How many cubes will balance the orange?
How much does the orange weigh?
SUMMARIZE |
3 |
The orange weighs 55 cubes. If the cubes were heavier, would it take more or fewer cubes? How can we compare the weight of this orange to another one?
Each cube weighs 3 grams!
How many grams does the orange weigh?
We can’t compare weights unless we use a STANDARD UNIT. This image shows the weight of each cube.
SUMMARIZE |
3 |
Our class of mathematicians knows that we can get better at estimating by looking back on our estimate after we find a solution.
How would you and a friend estimate the weight of a grapefruit or an apple?
I think that measuring weight is easy/hard because...
Math Norms
39
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Options for continuing activities
This interactive simulated pan balance gives students some practice in balancing weight while it builds up to algebraic thinking.
This engaging logic puzzle has two rocks with known weights—2 and 6 kg—and a rock with an unknown weight between 1 and 9 kg sitting on the left pan of a balance. Students determine whether they can find the weight by using the pan and the rocks.
Lesson 2 (Modified from Lesson Series 1)
Core Math |
CCSS-M Standard(s) |
Measurement and Data
Solve problems involving measurement and estimation.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
Lesson 2 update
Whole Class or Groups:
Independent or Group work:
Whole Class or Groups:
Core Math to Emphasize
Strengths to highlight
Math Norms
43
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Standard Measures
LAUNCH |
1 |
Why is it important to use standard measures?
This apple weighs 15 large cubes
This orange weighs 37 small cubes
Can you tell which fruit is heavier? Why or why not?
Standard Measures: a Gram
45
A large paper clip weighs about a gram!
One standard unit of weight is called the GRAM
How much is a gram?
A raisin weighs about 1 gram!
A dollar bill weighs about a gram!
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Standard Measures: a Kilogram
46
Another standard unit of weight is called the KILOGRAM
How much is a kilogram?
A small to medium melon weighs about a kilogram!
A medium bottle of juice weighs about a kilogram!
A small pair of adult shoes weighs about 1 kilogram
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Sort the objects by weight
LAUNCH |
1 |
about a gram
about a kilogram
I think the ___ weighs about a gram/kilogram because ...
Finding Objects
EXPLORE |
2 |
Today you will finding as many objects as you can that weigh
about a gram and about a kilogram
about a gram
about a kilogram
SUMMARIZE |
3 |
EXPLORE |
2 |
Options for student work:
Options for monitoring and sharing work:
What weighs about a gram?
SUMMARIZE |
3 |
I found a potato chip. I think it weighs about a gram because it's like a leaf.
I found a small block. I think it weighs about a gram because it’s like the cubes in the movie.
I found a small piece of paper. I think its weight is about the same as a paper clip.
What weighs about a kilogram?
SUMMARIZE |
3 |
I found a bunch of bananas. I think they weigh about the same amount as a melon.
I found a toaster. I think it weighs about a kilogram because it is like a pair of shoes.
I found some milk. I think it weighs 1 kilo because it is similar to a small bottle of juice.
SUMMARIZE |
3 |
Our class of mathematicians knows that we have to justify our answers with because.
What is a way that a friend explained their answer that helped you understand how much a gram or kilogram is?
What do you think is heavier? 10 oranges or a melon? Explain your thinking.
Grams and Kilograms
54
A gram is about the weight of a large paper clip.
A kilogram is about the weight of a medium melon
“Kilo” means 1,000!
There are 1,000 grams in a kilogram!
How many paper clips weigh the same as a medium melon?
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Math Norms
55
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Options for continuing activities
Students can do a scavenger hunt to find labels with the words “gram” (g) and/or “kilogram” (kg) in their homes. Food labels are a good source.
These 3 pages from unit 3.11 are a source of more problems related to weight measurement:
Core Math |
CCSS-M Standard(s) |
Measurement and Data
Solve problems involving measurement and estimation.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
Lesson 3 (Modified from LS 2 Day 2)
Whole Class or Groups:
Independent or Group work:
Whole Class or Groups:
Core Math to Emphasize
Strengths to highlight
Math Norms
59
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Measuring Volume
Volume or Capacity is a measure of how much something holds.
holds more
holds less
Let’s look at these items again.
How much liquid do they hold?
Show the amount with your hands
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Standard Measures
LAUNCH |
1 |
Why is it important to use standard measures?
This bowl holds 24 small cups of water
This bowl holds 15 large cups of water
Can you tell which bowl holds more water? Why or why not?
24
15
Standard Measures: a Liter
62
One standard unit of volume is called the LITER
How much is a liter?
A large water bottle holds about a liter!
A medium carton of milk or juice holds about 1 liter!
You might find a bottle at home that says “1L” - this is short for 1 Liter!
1 L
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Sort the objects by volume
LAUNCH |
1 |
less than a liter
about a liter
more than a liter
I think the ___ is less than / about/ more than a liter because ...
Finding Objects
EXPLORE |
2 |
Today you will find a few objects around your house that hold
less than a liter, about a liter, and more than a liter
less than a liter
about a liter
more than a liter
SUMMARIZE |
3 |
EXPLORE |
2 |
Options for student work:
Options for monitoring and sharing work:
What holds less than a liter?
SUMMARIZE |
3 |
I found a small jar. I think it holds less than a liter because it's about the same size as a cup.
I think each cup in the pan is less than a liter. Maybe altogether they hold 1 liter.
I found a small cup. I think it holds less than a liter because you can fill it from a milk container lots of times.
What holds about a liter?
SUMMARIZE |
3 |
I found some milk. I think it is a liter because it’s as big as an orange juice container.
I think my fish bowl holds about a liter because I think the milk would fill it up.
I think 2 jars of pickles hold about 1 liter. One is not enough.
What holds more than a liter?
SUMMARIZE |
3 |
I think our recycling bin holds more than 1 liter. I can put a lot of containers in it.
This juice bottle said “2 Liters” on it so I know it is more than 1 Liter.
Liters
69
We can estimate how much a container holds by comparing it to another container.
A liter is the amount of liquid that a medium bottle of water or juice or milk holds.
1 liter of liquid weighs about 1 Kilogram!
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Donating Blood
70
Let’s watch the video again and find out how much blood people donate.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Donating Blood
71
O +
Bag of donated blood
Remember that 1 liter of water weighs about 1 kilogram!
When a person donates blood, they donate 1 pint. 2 pints make a liter.
How much does a pint of blood weigh?
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
SUMMARIZE |
3 |
Our class of mathematicians knows that we can compare containers to estimate how much they hold.
What is a container that a friend found that helped you understand about how much a liter is?
Something I learned about volume is ...
Math Norms
74
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Lesson 4 (LS3 Day 1)
Core Math |
CCSS-M Standard(s) |
Measurement and Data
Solve problems involving measurement and estimation.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
Lesson 4 (LS3 Day 1)
Whole Class or Groups:
Independent or Group work:
Whole Class or Groups:
Core Math to Emphasize
Strengths to highlight
Note: in this lesson we have left out the problems involving millliliters to adjust for the reduced time available this year. The standards and the Milestone do not require students to work with milliliters.
Math Norms
77
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Solving Problems with Weight and Volume
LAUNCH |
1 |
When do you need to figure out the weight or volume of something?
Today we’ll solve a problem about the volume of 2 containers.
Seaside Elementary School is having a car wash fundraiser.
The Car Wash
LAUNCH |
1 |
The soap for the car wash is shown in these containers.
6L –––
5L –––
4L –––
3L –––
2L –––
1L –––
6L –––
5L –––
4L –––
3L –––
2L –––
1L –––
What is this story about?
What are the quantities in the story?
What mathematical questions could you ask about this story?
Container A Container B
The Car Wash
LAUNCH |
1 |
Let’s all solve this problem together:
6L –––
5L –––
4L –––
3L –––
2L –––
1L –––
6L –––
5L –––
4L –––
3L –––
2L –––
1L –––
How much more soap is in container B than in container A?
Container A Container B
Here are two ways to solve this problem
LAUNCH |
1 |
6 liters is 4 more than 2 liters
How much more soap is in container B than in container A?
2 Liters in Container A | ------ ? more ------- |
| |
6 Liters in Container B | |
Container A Container B
2 + ? = 6
or
6 – 2 = ?
EXPLORE |
2 |
1) Eight liters of soap need to be shared equally among 4 teams of students washing cars. How many liters of soap will each team get?
2) A grocer splits a 40 kg tub of oranges into five smaller containers. Each container holds the same amount. How many kilograms of oranges are in each container?
3) There are 6 liters of water in one container. How many liters are there in 5 containers?
4) I had some flour in a bowl. I added another 325 g to give me a total of 550 g of flour. How much flour did I have to begin with?
5) An adult tiger weighs 310 kg. A rhinoceros weighs 680 kg. How much heavier is the rhinoceros than the tiger?
More Problems with Weight or Volume
SUMMARIZE |
3 |
EXPLORE |
2 |
Depending on what you are seeing in class, decide where you want to focus. You may:
Students can work on
Options for monitoring and sharing work:
1) Eight liters of soap need to be shared equally among 4 teams of students washing cars. How many liters of soap will each team get?
SUMMARIZE |
3 |
----------------- 8 Liters of soap ------------------ | |||
? liters per team | | | |
4 teams | |||
8 L ÷ 4 = ? L
or
4 x ? L = 8 L
What do you notice?
What do you wonder?
Each team gets 2 liters of soap.
2) A grocer splits a 40 kg tub of oranges into five smaller containers. Each container holds the same amount. How many kilograms of oranges are in each container?
SUMMARIZE |
3 |
----------------- 40 kg of oranges ------------------ | ||||
? kg per container | | | | |
5 containers | ||||
40 kg ÷ 5 = ? kg
or
5 x ? kg = 40 kg
What do you notice?
What do you wonder?
There are 8 kg of oranges in each container.
3) There are 6 liters of water in one container. How many liters are there in 5 containers?
SUMMARIZE |
3 |
----------------- ? liters altogether ------------------ | ||||
6 liters of water | | | | |
5 containers | ||||
5 x 6 L = ? L
What do you notice?
What do you wonder?
There are 30 liters of water in 6 containers.
4) I had some flour in a bowl. I added another 325 g to give me a total of 550 g of flour. How much flour did I have to begin with?
SUMMARIZE |
3 |
? g + 325 g = 550 g
What do you notice?
What do you wonder?
I had 225 grams of flour to begin with.
? grams of flour | ---- 325 more g ----- |
| |
550 g of flour | |
or
550 g – 325 g = ? g
5) An adult tiger weighs 310 kg. A rhinoceros weighs 680 kg. How much heavier is the rhinoceros than the tiger?
SUMMARIZE |
3 |
310 kg + ? kg = 680 kg
What do you notice?
What do you wonder?
A rhino is 370 kg heavier than a tiger.
Tiger 310 kg | ---- ? more g ----- |
| |
Rhino 680 kg | |
or
680 kg – 310 kg = ? kg
SUMMARIZE |
3 |
Our class of mathematicians knows that we can use tape diagrams and equations to represent problems and help us solve them.
What is a way that a friend thought of a situation that helped you understand it ?
How can a tape diagram help you solve problems involving weight or volume?
Math Norms
91
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Options for continuing activities
More problems from the Weight and Volume Cards include:
Bird Bath
Jody removed 350 mL of water from her bird bath. If she left 125 mL of water in the bird bath, how much water was there in the beginning?
Leopard and Horse
A leopard weighs 53 kg. A horse weighs 477 kg. What is the combined weight of the two animals?
Potatoes
A farmer loads two sacks of potatoes into a box. The total weight of the box is 137 kg. One sack weighs 80 kg. What is the weight of the other sack?
Lesson 5 Milestone Task
Core Math |
CCSS-M Standard(s) |
Measurement and Data
Solve problems involving measurement and estimation.
3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same unit, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
The Milestone answers the question: Did you learn what was expected of you from this unit?
Lesson 5 Milestone Task
Whole Class or Groups:
Independent or Group work:
Whole Class or Groups:
Core Math to Emphasize
Strengths to highlight
Math Norms
95
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT
Packing for a Trip
LAUNCH |
1 |
Have you ever gone on a trip for a few days?
What did you do to prepare for the trip?
What did you pack?
Packing for a Trip
LAUNCH |
1 |
The Milestone Task is about someone packing for a trip.
Packing for a Trip
LAUNCH |
1 |
What unit did Jason use: grams or kilograms?
Explain your reason.
Part 1
Jason is going on a trip. He packed a backpack and a suitcase.
He weighed each item, but forgot to write down the units of measure.
Backpack weight: 7 ? Suitcase weight: 21 ?
Packing for a Trip
LAUNCH |
1 |
How much heavier is his suitcase than his backpack?
Part 1
Backpack weight: 7 ? Suitcase weight: 21 ?
How many of Jason’s backpacks weigh the same as his suitcase?
Packing for a Trip
LAUNCH |
1 |
How many liters of water did those 3 cases contain?
Part 2
Jason’s family had 3 full cases of water bottles in their house.
case of 6 1 liter water bottles
After Jason’s family took some water bottles for their trip, there were 13 liters of water left in the house.
How many liters of water did Jason’s family take?
How much do you think all the water bottles that his family took weigh together?
Should they be weighed in grams or kilograms? Why?
Packing for a Trip
EXPLORE |
2 |
What unit did Jason use: grams or kilograms? Explain your reason.
How much heavier is his suitcase than his backpack?
How many of Jason’s backpacks weigh the same as his suitcase?
Part 1
Jason is going on a trip. He packed a backpack and a suitcase.
He weighed each item, but forgot to write down the units of measure.
Backpack weight: 7 ? Suitcase weight: 21 ?
How many liters of water did those 3 cases contain?
After Jason’s family took some water bottles for their trip, there were 13 liters of water left in the house.
How many liters of water did Jason’s family take?
How much do you think all the water bottles that his family took weigh together?
Should they be weighed in grams or kilograms? Why?
Part 2
Jason’s family had 3 full cases of water bottles in their house.
case of 6 1 liter water bottles
SUMMARIZE |
3 |
EXPLORE |
2 |
Options for student work:
Options for monitoring and sharing work:
Packing for a Trip
What unit did Jason use: grams or kilograms?
Part 1: Jason is going on a trip. He packed a backpack and a suitcase.
He weighed each item, but forgot to write down the units of measure.
Suitcase weight: 21 ?
Backpack weight: 7 ?
SUMMARIZE |
3 |
Who had a different reason?
I think that Jason used kilogram because 7 grams is about 7 paper clips, which is a lot less than the weight of a backpack.
A water bottle weighs about a kilogram, and I see a water bottle in the backpack. The backpack must weigh more than 1 kilogram, so it couldn’t weigh 7 grams.
Packing for a Trip
How much heavier is his suitcase than his backpack?
Suitcase weight: 21 k
Backpack weight: 7 k
SUMMARIZE |
3 |
The suitcase is 14 kilograms heavier than the backpack!
7 kilograms | ---- ? more kg ----- |
| |
21 kilograms | |
7 kg + ? kg = 21 kg
or
21 kg – 7 kg = ? kg
Packing for a Trip
How many of Jason’s backpacks weigh the same as his suitcase?
Suitcase weight: 21 k
Backpack weight: 7 k
SUMMARIZE |
3 |
The suitcase is 3 times as heavy as the backpack!
----------------- 21 kg = weight of suitcase ------------------ | ||
7 kg = weight of backpack | | |
How many backpacks? | ||
7 kg x ? = 21 kg
or
21 kg ÷ ? = 7 kg
Packing for a Trip
How many liters of water did those 3 cases contain?
Part 2: Jason’s family had 3 full cases of water bottles in their house.
case of 6 1 liter water bottles
SUMMARIZE |
3 |
----------------- ? liters altogether ------------------ | ||
6 liters of water | | |
3 cases | ||
3 x 6 L = ? L
3 cases contain 18 Liters of water!
Packing for a Trip
After Jason’s family took some water bottles for their trip, there were 13 liters of water left in the house.
How many liters of water did Jason’s family take?
Part 2 Jason’s family had 3 full cases of water bottles in their house.
case of 6 1 liter water bottles
SUMMARIZE |
3 |
They took 5 Liters.
13 Liters left | ---- ? Liters taken ----- |
| |
18 Liters at first | |
18 L – ? = 13 L
or
13 L + ? = 18 L
Packing for a Trip
How much do you think all the water bottles that his family took weigh together?
Should they be weighed in grams or kilograms? Why?
Part 2: Jason’s family had 3 full cases of water bottles in their house.
SUMMARIZE |
3 |
I think the water weighs 5 liters because 1 liter weighs about 1 kilogram, so all their water would weigh 5 kilograms
The water should be weighed in kilograms because you would have to use a lot of grams to weigh all that water (more than a thousand!)
Remember that 1 liter of water weighs about 1 kilogram!
SUMMARIZE |
3 |
Our class of mathematicians knows that we have to have an idea about how much a measure is to solve problems about measurement.
What is a way that a friend helped you understand something about weight or volume in this unit?
One thing I learned about weight was…
One thing I learned about volume was...
Math Norms
111
Errors are gifts that promote discussion.
Answers are important, but they are not the math.
Talk about each other’s thinking.
Ask questions until ideas make sense.
Use multiple strategies and multiple representations.
SAN FRANCISCO UNIFIED SCHOOL DISTRICT