2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
2nd Grade Measurement and Data
Overview of the Unit
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Mesaurement
Scavenger hunt
Cubes vs Paper
Clips
Land of Inch
Measuring with Inch
Brick
A Bug’s Length
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
The King’s foot
The Nearest Foot
Moving to Metric
More Metric
Measurement
How much longer?
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
How much longer?
(Part 2)
What’s Your
Favorite
What’s Your Favorite
What’s the
difference? What’s
the total?
How Long are Our
Pencils
Lesson 16
Lesson 17
Measuring Our Feet
and Hands
Performance task
(2-3 days)
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
The lessons in this unit address the following Standards.
Measurement & Data
2.MD
Measure and estimate lengths in standard units.
1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements
relate to the size of the unit chosen.
3. Estimate lengths using units of inches, feet, centimeters, and meters.
4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
Relate addition and subtraction to length.
5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as
drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and
represent whole-number sums and differences within 100 on a number line diagram.
Work with time and money.
7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2
dimes and 3 pennies, how many cents do you have?
Represent and interpret data.
9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same
object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, takeapart, and compare problems1 using information presented in a bar graph.
Classroom Routines
This unit addresses the following Standards during Classroom Routines.
Lesson
Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson
10
Lesson
11
Lesson
12
Lesson
13
Lesson
Classroom Routine
What Time Is It?: What Time Will It Be?
Quick Images: Ten Frames
Quick Images: Strips and Singles
What Time Is It? What Time Will It Be?
Today’s Number: 42 Using Dimes and Pennies
Today’s Number: 12 with Missing Parts
Today’s Number: 44 Using Dimes and Pennies
What Time Is It?: What Time Will It Be?
Today’s Number: 49 Using Subtraction
Quick Images: Tens and Ones
Standard(s) Addressed
2.MD.7
2.NBT.3
2.NBT.3
2.MD.7
2.NBT.3, 2.MD.8
2.OA.2
2.NBT.3, 2.MD.8
2.MD.7
2.OA.1
2.NBT.3
Quick Images: Tens and Ones
2.NBT.3
Today’s Number: 26 Using Subtraction
2.OA.1
What Time Is It? : What Time Will It Be?
2.MD.7
Quick Images: Tens and Ones
2.NBT.3
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2nd Grade Unit- Measurement and Data
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Lesson
15
Lesson
16
Lesson
17
Charlotte Mecklenburg Schools
Today’s Number: 20 Using Subtraction
2.OA.1
What Time Is It? : What Time Will It Be?
2.MD.7
Quick Images: Tens and Ones
2.NBT.3
Lesson #1: Measurement Scavenger Hunt
Cluster: Measure and estimate lengths in standard units.
Standards:
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
Mathematical Goal:
Students will measure objects in their classroom using two
measuring tools: 5 connected cubes and 10 connected cubes.
Standards for Mathematical Practice
MP 3: Reason abstractly and quantitatively
MP 6: Attend to Precision
Materials:
Measuring tools- 5 connected cubes, 10 connected
cubes
Words you should hear students use in mathematical
conversations:
Longer, shorter, line up
Classroom Routine: What Time Is It?: What Time Will It Be? (2.MD.7)
Using the Clock (M43) students divide a clock in half by drawing a line between the 12 and 6. Students then count the
number of minutes on each half and on the clock as a whole. Show the transparency of The Clock (T36), and discuss that
30 minutes is exactly half of an hour.
Before:
Have two students to stand up in front of the class. Ask the class, “How can we find how tall each student is?” After a few
students have responded, have students clarify why they chose that approach by using the follow-up question, “What steps
do we need to complete when we measure the length of objects?” “
Students should talk about:
lining up the beginning of their tool with the beginning of the object that they are measuring,
placing the tool exactly next to the object and both should be facing the same direction (see picture below).
Correct:
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Incorrect:
During:
Distribute the 5-cube measuring tool to students. Students should find objects in the room that are close to the length of the
measuring tool. Students should record their list of objects in their math journal or on paper to refer to later.
After a few minutes, allow students to find a math partner. Partners will join their cubes to make a measuring tool that is 10
cubes long. Students will then find objects in the room that are close to the length of the measuring tool. Again, students
should record their list to refer to later.
As students are working, use questions to support students, such as:
How are you measuring the length of the object?
How do you know that your measurement is correct?
**Note- it may be difficult to have students find objects that are as long as 5 or 10 cubes long. Use teacher discretion to
modify the task by having students find and measure objects that are up to 5 cubes long in the first part, and objects that
are up to 10 cubes long in the second part. With this variation students would use the tool and record the object and how
many cubes long the object was. This builds off measurement work from Grade 1.
After:
Bring students back together to discuss what they found during their measurement scavenger hunt. Have students discuss
the processes that they used to measure, and demonstrate to their classmates how they measured objects.
Take an object that was discussed above. As a class measure the length with paper clips. Before you start ask students,
“When we measured the ______ with cubes it was _____ cubes long. When we measure it with paper clips how many
paper clips do you think we will need?” Ask students to share their answers and explain their reasoning.
If time permits, measure a few more objects with paper clips.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #2: Cubes vs. Paper Clips
Cluster: Measure and estimate lengths in standard units.
Standards for Mathematical Practice
MP 3: Reason abstractly and quantitatively
MP 6: Attend to Precision
Standards:
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
Mathematical Goal:
Materials:
Students will measure the same distance with both cubes and paper Measuring tools: connecting cubes, paper clips
clips and compare the measurement with each tool.
Words you should hear students use in mathematical
conversations:
Longer, shorter, line up
Classroom Routine: Quick Images: Ten Frames (2.NBT.3)
Using Ten-Frame Cards (T28-T29), show two ten-frames, one with 10 dots and one with 8 dots. Follow the basic Quick
Images activity. Once the class has established the total (28), have students write equations that represent the image.
Examples might include: 10 + 10 + 5 + 3 = 28 or 10 + 10 + 8 = 28.
Students should be able to explain how their equation represents the ten-frames.
Encourage students to look for groups of five and ten. If no one suggests 30 – 2, challenge students to write an equation
using subtraction.
Before:
Review Lesson 1 and ask students to explain how they measured the length of objects. Focus on the need to line up the
beginning of the tool with the beginning of the object that you are measuring.
Introduce paperclips as a measuring tool by having students measure the length of a book using paper clips as a class.
After measuring, ask students, “How are the paperclips arranged?” Emphasize the importance of having the paper clips in a
straight line, and not having gaps or overlaps in the paper clips.
During:
Ask students to measure the dimensions of each horse stall on the attached sheet. They should measure each side in both
paper clips and cubes. If a side length does not measure a whole number, have them approximate to the nearest whole
number of cubes or paper clips.
*As an alternative, you could use 1 inch grid paper and have students draw the stalls and then measure them with paper
clips.
As students work, observe them and ask them questions such as:
How are you measuring the length of this object?
What was the difference in the length of ___ when you measured with paper clips and cubes?
After:
After students have explored and measured objects bring them together to discuss what they found. Use the SMART Board
or white board to create a table showing the lengths of the various sides in both paper clips and cubes.
If time permits, have students draw lines on their paper that are a specific length, e.g. 4 cubes, 6 cubes, etc. Then have
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
students measure the length of those lines using paper clips.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Measuring the Horse Stall
You are designing a horse stall. For each of the 3 choices below, measure the length and width of the stall.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #3: Land of Inch (adapted from Investigations - Unit 9: Investigation 2.1)
Cluster: Measure and estimate length in standard units
Standards:
Standards:
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters,
and meters.
2.MD.4. Measure to determine how much longer one object is than
another, expressing the length difference in terms of a standard
length unit.
Standards for Mathematical Practice
Mathematical Goal:
Students will:
 Create and use a 12 inch measuring tool
 Identify strategies for accurate measurement
 Identify what to do with partial units of measurement
Materials:
SAB 19-20
M10- Inch Bricks- make copies on card stock. Give
each student one strip of 18 bricks
M11-Measuring Tool Template- make copies on
card stock. Each student gets one template
Demonstration measuring tool- glue 12 inch bricks
from M10 onto a measuring tool template. Number
the units 1-12
Chart paper- Label it with “Measuring Tips”
Words you should hear students use in mathematical
conversations:
Inch, measurement
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Classroom Routine: Quick Images: Strips and Singles
Using Stickers: Strips and Singles (T38-T39), display the number 14 with 1 strip and 4 singles.
Follow the basic Quick Images activity. Have pairs discuss how many squares they saw and how they determined the
amount.
Repeat with the numbers 24 and 34. As a class, find 14, 24, and 34 on the number line and 100 chart and discuss what is
the same and different about them. If time permits, repeat with the numbers 22, 32, and 42.
Before:
Prepare all materials before the lesson. (see list of materials)
Read the story “The Land of Inch” found in Investigation 2.1 of Unit 9 in Investigations. This is a story about the need for a
standard unit of measure. In the Land of Inch the miniature people wanted to have a contest to see which of the athletes
could jump the farthest. They realized that, without a common measuring unit, it was impossible to figure that out. This
activity introduces students to “inch-bricks” (units used in the imaginary Land of Inch). Students will be using these in the
next lesson.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
During:
After passing out the materials to each student, have them cut along the lines to make 18 separate inch bricks. Using SAB
p.19, students will begin to measure the lengths of the distances jumped. Teachers will need to clarify the terms length
and width of the notebook paper. Students will measure the length and width of a sheet of notebook paper and the lengths
of a glue stick and a craft stick. Have groups of students discuss their results and explain why some of the measurements
might be different (if gaps are left between inch bricks) Remember that writing the symbols for fractions such as 1/2 is not
part of the Common Core in second grade. Students can talk about between inch 8 and 9 being half, but should not be
required to actually write the symbol.
Finish the story on p 61 which explains why the people in the Land of Inch realized the need to make a tool to use for
measuring.
Students will now paste their inch bricks onto the Measuring Tool Template to create a 12 inch-brick measuring tool which
they will use in the next part of the lesson.
Students should revisit SAB p.19 and check their original measures with the new measuring tool to see how accurate they
were. Ask “how many whole units long is…” and then talk about what happens when the measure is a little over the whole
unit.
Finally, students should mount their inch-brick measuring tool on a piece of construction paper, card stock or sentence
strip and number each of the inch bricks at the END of the brick as shown below:
1
2
3
4
5
6
7
8
9
10
11
12
Have students check with a partner to see that their tools are numbered the same.
After:
Using chart paper, as a whole group create a “Measuring Tips” chart highlighting the following ideas:





Start measuring from the beginning or one end of the object
Line up your measuring tool or unit
Count every unit on the tool
If you are using more than one unit or tool, lay them end to end; do not leave gaps
Measure in a straight line
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #4: Measuring with the Inch Brick (adapted from Investigations - Unit 9: Investigation 2.2)
Cluster: Measure and estimate length in standard units
Standards:
Standards for Mathematical Practice
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and measuring
tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters, and
meters.
2.MD.4. Measure to determine how much longer one object is than
another, expressing the length difference in terms of a standard length
unit.
SMP.1 Make sense of problems and persevere in solving
them
Mathematical Goal: Students will identify strategies for accurate
measurement, iterate a 12-inch measuring tool and measure lengths
that are longer than 12 inches.
Materials:
SAB p.19 from previous lesson
SAB pp 21-28
Chart: “Measuring Tips”
Inch brick measuring tools from previous lesson
Connecting cubes, color tiles, craft sticks, markers
Words you should hear students use in mathematical
conversations:
“accurate” measurement, inch
SMP.4 Model with mathematics
SMP.6 Attend to precision
Classroom Routine: What Time Is It? What Time Will It Be?
Ask students to display 2:00 on their small clocks as you write 2:00 on the board. Ask the following question:
 In 2 hours what time will it be?
Students set the new time on their clocks and talk with their partner about what time it will be and how they know.
Then ask them how that time would look on a digital clock (4:00).
Do several of these, varying the start time (whole and half hours), and the time elapsed between 2 and 4 hours.
Each time discuss what the time would look like on a digital clock and how many times the minute hand traveled around
the clock.
Before:
Take down the chart of “Measuring Tips” from the previous lesson. Have students think about what the term “accurate
measurement” means and about some of the measuring tips they discussed previously.
Review some of the following measurement tips:
 Begin measuring at one end of the object
 Line up your measuring tool or unit
 Count every unit on the tool
 If you are using more than one unit or tool, lay them end to end, don’t leave gaps
 Measure in a straight line
During:
As a way of revisiting how to measure partial units, have students measure the width of a piece of standard paper which is 8
½ inches wide using their inch brick tool. Discuss the fact that it falls in the middle of the 9th inch brick. Ask students “how
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
many whole inch bricks does the paper measure? Is the width of the paper more than 9 inch-bricks or less?” (some
students may think of it as 8 ½ or even 9 ½) Allow them to discuss this.
Using SAB pp. 21-22 students will solve the problems using their inch brick tools, color tiles, craft sticks, pencils, and snap
cubes.
Teachers should make note of whether or not students are correctly aligning the end of the measuring tool with the end of
the object, and correctly measuring the length of an object when it is between two whole numbers.
Students will work in pairs to measure objects that are longer than their measuring tool. They will need to put their two
measuring tools together or iterate using one of the tools. Teachers need to make sure students are leaving no gaps
between tools when they are using two inch-brick tools, and leaving no gaps when they are iterating using the one tool.
They should also note how students calculate the total number of inch-bricks when the measurement is longer than one
inch-brick tool.
SAB 25 can be used to pose problems about comparing different lengths. Students can find the difference between two
lengths and use their tool to draw a line segment of specific length.
After:
Bring students back together in a whole group to discuss strategies used for measuring objects.
Ask the following questions:
 What did you have to remember when measuring objects using your inch-brick tool?
 How did you measure objects that fell between two inch bricks?
 How did you measure objects that were longer or wider than one inch-brick tool?
 What is important to remember when using two tools together to measure a larger object?
 How did you calculate the total number of inch-bricks used to measure a larger item?
Homework:
SAB p.27 Missing Numbers
SAB p.28 Measuring with Inch-Bricks at Home
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #5: A Bug’s Length
Cluster: Measure and estimate length in standard units
Standards:
Standards for Mathematical Practice
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and measuring
tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters, and
meters.
2.MD.4. Measure to determine how much longer one object is than
another, expressing the length difference in terms of a standard length
unit.
SMP.1 Make sense of problems and persevere in solving
them
Mathematical Goal:
Students will measure the lengths of various objects in inches and
compare their lengths using subtraction.
Materials:
Paper, pencil, activity sheet, inch bricks
*From Target or Wal Mart you can buy plastic
insects instead of the activity sheet.
SMP.4 Model with mathematics
SMP.6 Attend to precision
Words you should hear students use in mathematical
conversations:
Shorter than, longer than, length, measure
Classroom Routine: Today’s Number: 42 Using Dimes and Pennies
Students use pennies and dimes to make 42. Challenge them to find all possible combinations. Post the combinations and
discuss what students notice, paying particular attention to how the number of pennies decreases by 10 when a dime is
added. (4 dimes, 2 pennies; 3 dimes, 12 pennies; 2 dimes, 22 pennies, 1 dime, 32 pennies).
Before:
Give students an object from around the classroom and have them measure the object in inches using inch bricks. Ask
students to share how they are lining up their ruler and how they are determining the length of the object. Do this with 2 or 3
different lengths.
During:
Distribute the “A Bug’s Length” activity sheet to students. Ask students to share attributes or parts of the bug that could be
measured. Make a list for students to refer to later in the lesson.
Have students work in pairs to measure various attributes of each of the 4 bugs on the activity sheet in inches using inch
bricks. Lengths should be recorded on the activity sheet. If measurements are in between whole inches have students
estimate to the nearest whole or ½ inch. Use teacher judgment in these situations.
As students are working, observe them and ask them questions about how they are measuring the length of each attribute.
After:
Bring students together to discuss their lengths. Ask students, “how much longer is the grasshopper than the lady bug?”
Have students brainstorm ways to find the answer to this question, including measuring the lengths and then comparing the
lengths by subtracting the length of the lady bug from the length of the grasshopper. Solve this question as a class.
If time permits, pose 1 or 2 similar questions for students to explore.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
A Bug’s Length
For each bug, measure various parts of the bug in inches. List the part of the bug and its length.
Water Bug
Reduviidae
Lady Bug
Grasshopper
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #6: The King’s Foot
(Adapted from Investigations, Unit 9, Sessions 3.1 and 3.2)
Cluster: Measure and estimate length in standard units
Standards:
Standards for Mathematical Practice
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and measuring
tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters, and
meters.
2.MD.4. Measure to determine how much longer one object is than
another, expressing the length difference in terms of a standard length
unit.
SMP.1 Make sense of problems and persevere in solving
them
Mathematical Goal:
Students will measure the length of body parts using feet and
inches.
Words you should hear students use in mathematical
conversations:
Foot, feet, inches, measure, line up
Materials:
Paper, pencil, activity sheet, supplies to make an
inch-only ruler, copy of The King’s Foot story,
Investigation, Unit 9, p. 80-83
SMP.4 Model with mathematics
SMP.6 Attend to precision
Classroom Routine: Today’s Number: 12 with Missing Parts
Show Today’s Number: 12 with Missing Parts (T41), which presents several equations with one part missing. The class
works together to solve problems such as:
______ + 6 = 12
8 + ______ = 12
12 – 3 ______
12 = 10 + ______
Focus on one example at a time and ask a few students to explain how they figured out the answer.
Before:
Read “The King’s Foot” on page 80 of Unit 9 from Investigations. Instead of having students compose a letter (p. 81), have
students just discuss and talk mathematically about why the stall was too small, and explain what wrong in the story.
Read the rest of the story (p. 83).
During:
Students will enter Math Workshop using the activities described on p. 88-89. The activities are Body Benchmarks and
Measure and Compare. They will need the Student Activity Book pages (Unit 9, p. 33-35) for this.
After:
Review what students measured during Math Workshop and have them share both their measurements and how they found
their answer.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #7: The Nearest Foot (adapted from Investigations Unit 9: Session 3.3)
Cluster: Measure and estimate length in standard units
Standards:
Standards for Mathematical Practice
2.MD.1. Measure the length of an object by selecting and using appropriate tools
such as rulers, yardsticks, meter sticks, and measuring tapes.
2.MD.2. Measure the length of an object twice, using length units of different
lengths for the two measurements; describe how the two measurements relate to
the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters, and meters.
2.MD.4. Measure to determine how much longer one object is than another,
expressing the length difference in terms of a standard length unit.
SMP.1 Make sense of problems and persevere in solving
them
Mathematical Goal:
Students will measure objects to the nearest foot.
Materials:
Rulers, paper, pencil
SMP.4 Model with mathematics
SMP.6 Attend to precision
Words you should hear students use in mathematical
conversations:
Foot, feet, inch, line up
Classroom Routine: Today’s Number: 44 Using Dimes and Pennies
Students individually generate numerical expressions for the number 44, using all possible combinations of dimes and
pennies. Students then list at least 5 other expressions for 44 using addition and/or subtraction. They record these
expressions on blank paper, which they have labeled with the date and heading “Today’s Number: 44”.
Before:
Review by having students discuss and demonstrate how to measure the length of their desk using a 12” ruler. Make sure
to emphasize the need to hold the ruler straight and line it up as closely as possible to the object that is being measured.
Do this again with a different object.
During:
Students will participate in math workshop (p. 93) and complete the activities there. They will need Student Activity Book (p.
39) for these activities.
After:
Bring the class together and ask them to compare the lengths of two things that were measured during workshop. For
example, “how much longer is your hand than your thumb?”
Have students describe how they would solve this task by measuring the lengths of objects and then subtracting.
Do this with a few different lengths.
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2nd Grade Unit- Measurement and Data
Charlotte Mecklenburg Schools
Lesson #8: Moving to Metric (adapted from Investigations Unit 9: Session 3.4)
Cluster: Measure and estimate lengths in standard units.
Standards:
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters,
and meters.
Standards for Mathematical Practice
Mathematical Goal:
Students will be introduced to and become familiar with the terms
centimeters and meters as standard units of measure.
Students will use centimeters and meters to describe length
Materials:
M16
World map or globe (optional)
Centimeter cubes
Rulers and meter sticks
Meter strip
Scissors
Tape
SAB p. 43-46
Charts: “Things About 1 Centimeter Long in School”
“Things About 1 Meter Long in School”
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Words you should hear students use in mathematical
conversations:
metric system
centimeter
meter
Classroom Routine: What Time Is It?: What Time Will It Be?
Write 2:00 on the board and ask pairs to set their clocks to that time.
Then, introduce students to the quarter hour by asking:
 What would the clock look like if the minute hand only went 15 minutes past 2:00?
Write 2:15 on the board
 Does anyone know what time this is? This time is 2:15 or 15 minutes past 2:00.
On the demonstration clock, move the minute hand 15 minutes counting by ones as you go. Highlight that the hour
hand is slightly past the 2, indicating that it is not exactly 2:00, but some minutes past 2:00. Repeat with 1:00, 6:00 and
12:00. Students work in pairs setting their clocks to 15 minutes past the hour and writing the new time in digital
notation.
Before:
Remind students about the story “The King’s Foot” when the king and the carpenter had different ideas of how large the
horse stall should be. They had a problem because their feet were different sizes and they couldn’t agree whose foot to use
to measure.
Students should be introduced to the metric system of measurement which uses centimeters and meters instead of inches,
feet and yards. There is a great explanation about the metric system on page 158 of Unit Guide 9.
Show students what a centimeter is using centimeter cubes or centimeter grid paper.
Using the centimeter side of a ruler, students should practice measuring the centimeter with the cubes or centimeter grid
paper in order to gain an understanding of the size of a centimeter. They should practice measuring several objects that
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can easily be measured using centimeters and understand that the centimeter is used to measure small objects.
The teacher should construct a meter strip using 100 centimeters put together. (use 3 centimeters width instead of just 1 so
the strip does not tear too easily) Show students that a meter is a little longer than a yard by comparing the yardstick and
meter strip.
During:
Discuss as a group, what a meter is (100 centimeters) and ask students to discuss with their partner, how we could create
a meter strip using the centimeter grid paper. (they should realize that adding 5 strips of 20 cm together will make a meter
strip).
Using the centimeter grid paper, students should construct a meter strip by connecting 100 centimeters together. Instead of
making the strip one cm wide which will tear easily, use a width of 3 centimeters. Students will see that one meter is the
same as 100 centimeters. They can practice measuring with the meter strip by finding different objects in the classroom
that measure approximately 1 meter. If you have enough meter sticks, have students measure with those in the classroom
and have them save their meter strips to measure objects at home since they will tear easily.
Emphasize the need to estimate the length of an object before measuring it.
After:
Students should work on SAB pp. 43-45 and complete SAB p.46 for homework using their meter strips.
As a group discuss the different units of measure on a ruler (inches are larger than centimeters therefore there are more
centimeters on the ruler than inches)
Discuss how we know when to use centimeters and when to use meters to measure objects. (Use centimeters to measure
small objects and meters to measure larger objects)
Writing Task: Does it take more centimeters or meters to measure the length of the classroom? Explain how you know?
(this is the compensatory principle)
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Lesson #9: More Metric Measurement
Cluster: Measure and estimate lengths in standard units.
Standards:
2.MD.1. Measure the length of an object by selecting and using
appropriate tools such as rulers, yardsticks, meter sticks, and
measuring tapes.
2.MD.2. Measure the length of an object twice, using length units of
different lengths for the two measurements; describe how the two
measurements relate to the size of the unit chosen.
2.MD.3. Estimate lengths using units of inches, feet, centimeters,
and meters.
Standards for Mathematical Practice
Mathematical Goal:
Students will measure lengths using metric units.
Materials:
Paper, pencil, activity sheet
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Words you should hear students use in mathematical
conversations:
Meter, centimeter, difference, total
Classroom Routine: Today’s Number: 49 Using Subtraction – individually students should generate expressions for 49
using only subtraction and two numbers, for example 50 – 1 and 69 – 20. Collect a number of examples on the board and
discuss one or two patterns such as 59 – 10, 69 – 20, 79 – 30 or 50 – 1, 51 – 2, 52 – 3 as a whole class.
Before:
Review from yesterday by asking students to discuss, “how did we make a meter?” and “How do we know how many
centimeters are in a meter?”
During:
Give students meter strips from Lesson 8 and have them find objects in the classroom that are less than a meter in length.
Students should record the measurements of at least 5 different objects.
Bring the class together and ask them, “How could we determine how much longer one object is than other objects?”
Students have worked with idea in earlier lessons, but they may need help thinking about the idea that when we compare
lengths we are subtracting the lengths of two objects.
Students should choose 2 objects to compare. Have students use their math notebook (or paper) and write comparison
statements using the frame,
“____ is ___ centimeters longer/shorter than ____. I found this by ___________________.
As students are working on this, observe them and ask them questions about how they are
After:
Have students discuss and talk through their work in the During stage. Emphasize the use of the vocabulary words longer
and shorter as well as having students discuss their strategy for subtracting the lengths from each other.
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Time permitting, ask students to compare the lengths of two objects.
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Lesson #10: How Much Longer?
Cluster: Relate addition and subtraction to length.
Standards:
2.MD.5. Use addition and subtraction within 100 to solve word
problems involving lengths that are given in the same units, e.g., by
using drawings (such as drawings of rulers) and equations with a
symbol for the unknown number to represent the problem.
Standards for Mathematical Practice
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Mathematical Goal:
Students will compare the lengths of objects by using subtraction.
Materials:
Paper, pencil, “Catching Fish” activity sheet.
Words you should hear students use in mathematical
conversations:
Shorter, longer, centimeters, subtraction, difference
Classroom Routine: Quick Images: Tens and Ones - Show image A from Quick Images 1: Tens and Ones (T82).
Follow the basic Quick Images activity. Ask students to determine the total number of squares and share their strategies.
Record equations to represent the image, such as 10 + 10 + 10 + 5 = 35, or 40 – 5 = 35. Repeat for images B and C.
Before:
Give students two items that are different lengths. Ask them, “what is the difference in the length of these two objects?” Ask
students how they would answer this question. Have students measure the lengths in centimeters and then spend time
asking students to share how they would find the difference between the two lengths. If time permits, repeat this with
another set of objects.
During:
Give students the attached “Catching Fish” activity sheet or display it for students to see. Students will work on this activity
sheet. As students are working observe them to see what strategies they are using for each task. Ask students to explain
their strategies and if their answer makes sense.
If needed, you could have this part of the lesson as a Math Workshop, where you have small groups work on Catching Fish,
and also have students measuring body benchmarks or objects around the room.
After:
Bring the students back together and have them share their work on the Catching Fish activity sheet. The last question is
multi-step, and you should focus time on allowing students to describe and reason about how they solved the question.
If time permits, pose 1-2 more questions to the class that involve finding the difference between lengths of objects. You may
use objects in the classroom or lengths on the fish sheet.
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Catching Fish
During a recent fishing competition, Saul caught the following fish.
Fish
Trout
Length(s)
56 centimeters, 38 centimeters
Salmon
71 centimeters
Perch
19 centimeters, 27 centimeters
1) What is the difference in the length of the two perch that Saul caught?
2) What is the difference in the length of the two trout that Saul caught?
3) Which is longer: the salmon or the longest trout? What is the difference in length between the two
fish?
4) Which is longer: the shortest trout or the longest perch? What is the difference in length between
the two fish?
5) Saul’s father asked, “Which is greater: the total length of the trout or the length of the salmon?
What is the difference in length between the two fish?
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Lesson #11: How Much Longer? (Part 2 )
Cluster: Relate addition and subtraction to length.
Standards:
2.MD.5. Use addition and subtraction within 100 to solve word
problems involving lengths that are given in the same units, e.g., by
using drawings (such as drawings of rulers) and equations with a
symbol for the unknown number to represent the problem.
Mathematical Goal:
Students will compare the lengths of objects by using subtraction.
Standards for Mathematical Practice
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Materials:
Paper, pencil, tape measure or meter sticks
Words you should hear students use in mathematical
conversations:
Shorter, longer, centimeters, subtraction, difference
Classroom Routine: Quick Images: Tens and Ones
Show Image D, the 100 array, from Quick Images 2: Tens and Ones (T83).
Follow the basic Quick Images activity. Students determine the total number of squares and share their strategies.
Be sure to discuss the 10 x 10 structure of the array and the total number of squares (100).
Repeat with Image E.
Record equations to represent the image, such as 10 + 10 + 10 + 10 + 10 + 10 = 60.
If no one mentions 100 – 40 = 60, ask students how they could use subtraction to determine the number of filled-in squares.
Repeat with Image F.
Before:
Review work from the previous lesson by giving students two measurements and having students find the difference
between them. Focus your questions on the strategies that students use to subtract to find the difference. If time permits,
pose 2 questions.
During:
Put students into groups of 2 or 3 students. Give each group of students a meter stick or a meter strip. Students will
compete in three different activities and measure their distance.
Big Step: Students will measure the size of the biggest step that they take. Students will start with feet together and take a
step forward with both feet. Students measure in centimeters the distance from their toe when they start to the back of their
heel after their step.
Standing Two-footed Jump: Students stand on both feet and jump forward. Students measure in centimeters the distance
from their toe when they start to the back of their heel after their jump.
Standing One-footed Jump: Students stand on one foot and jump forward. Students measure in centimeters the distance
from their toe when they start to the back of their heel after their jump.
After students and their group members have measured their 3 distances they will write 3 subtraction equations to compare
the three distances that they measured. If they have time left, they can redo the three activities and recalculate the
differences.
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After:
Bring students back together to discuss the equations that they wrote and solved. Ask students to share their distances and
explain how they found the differences between their two differences.
If time permits, ask students to explore, “Sally jumped 53 centimeters from two feet and 28 centimeters from one foot. How
much longer did Sally jump from 2 feet than she jumped from one foot?
Lesson #12: What’s Your Favorite?
Cluster: 2.MD Measurement and Data
Standards: Represent and interpret data.
2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to
represent a data set with up to four categories. Solve simple put-together,
take-apart, and compare problems1 using information presented in a bar
graph.
Standards for Mathematical Practice
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Mathematical Goal:
Second grade students are expected to pose a question, determine
up to 4 categories of possible responses, collect data, represent
data on a picture graph or bar graph, and interpret the results.
Materials:
Paper, pencil
Words you should hear students use in mathematical
conversations:
Data, category, picture graph, bar graph, scale
Classroom Routine: Quick Images: Tens and Ones
Show Image M from Quick Images 5: Tens and Ones (T86)
Follow the basic Quick Images activity.
Students determine the total number of shaded squares and share their strategies.
Record equations to represent the image, such as 60 + 5 = 65.
If no one mentions 100 – 35 = 65, ask students how they could use subtraction to determine the number of shaded squares.
Repeat for Images N and O.
Before:
Review with your students the process of making a line plot by giving students a list of data about the number of books that
students have read in the last few weeks: 7, 6, 8, 8, 8, 9, 7, 7, 7, 6. As a class, have students make a picture graph to
represent that data. Ask students to state observations about their picture graph, including the most frequent, the least
frequent, the difference between the greatest and smallest value, and the shape of the data (clumped or spread out).
During:
Tell students that we will be collecting survey data about students’ favorite foods. Put students in groups of 2 or 3 students
and assign them one of the following- meats, vegetables, desserts, drinks, snacks, breakfast foods, etc. Once students get
their topic they need to brainstorm 4 possible answer choices and list them. Bring the class together and have a few groups
share their 4 answer choices.
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Allow students to conduct their survey to their classmates. Students should record their survey data using tallies or another
organized way on paper.
After students have had enough time to collect at least 10-12 data points, bring them together to discuss how to set up a bar
graph. Use questions to discuss the process of creating the bar graph, including totaling the data values for each category,
labeling the axis, and creating the bar graphs.
After:
Students will create a bar graph with the data that they collected. After they are done they should write 2 comparison
statements about the categories of data. You may support students by giving them the sentence frame, “There were ____
more votes for _____ than for _____ .” or “There were ____ fewer votes for _____ than for _____ .”
Lesson #13: What’s Your Favorite (part 2)
Cluster: 2.MD Measurement and Data
Standards: Represent and interpret data.
2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to
represent a data set with up to four categories. Solve simple put-together,
take-apart, and compare problems1 using information presented in a bar
graph.
Standards for Mathematical Practice
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Mathematical Goal:
Second grade students are expected to pose a question, determine
up to 4 categories of possible responses, collect data, represent
data on a picture graph or bar graph, and interpret the results.
Materials:
Paper, pencil, graphing template (optional)
Words you should hear students use in mathematical
conversations:
Data, category, picture graph, bar graph, scale
Classroom Routine: Today’s Number: 20 Using Subtraction
Individually students generate expressions for 20 using subtraction and several numbers (e.g., 30 – 5 – 5, or 46 – 10 – 10- 3
– 3).
For each expression they write a corresponding expression using only two numbers (e.g. 30 – 5 – 5 = 30, or 46 – 10 – 10 –
3 – 3 = 26).
Before:
Review with your students the process of making a bar graph by giving students a list of data about student’s favorite ice
cream: chocolate (11), mint chocolate chip (5), strawberry (8), and vanilla (2). Have students make a bar graph to represent
this data as a class. Ask students to state observations about their bar graph, including the most frequent, the least
frequent, the difference between the greatest and smallest value, and the shape of the data .
During:
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2nd Grade Unit- Measurement and Data
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Tell students that we will be collecting survey data about students’ favorite animal. Students need to brainstorm 4 possible
answer choices and list them. Bring the class together and have a few groups share their 4 answer choices.
Allow students to conduct their survey to their classmates. Students should record their survey data using tallies or another
organized way on paper.
After students have had enough time to collect at least 10-12 data points, bring them together to discuss how to set up a bar
graph. Use questions to discuss the process of creating the bar graph, including totaling the data values for each category,
labeling the axis, and creating the bar graphs.
After:
Students will create a bar graph with the data that they collected. After they are done they should write 2 comparison
statements (“How many more” or “How many less”) about the categories of data. You may support students by giving them
the sentence frame, “There were ____ more votes for _____ than for _____ .” or “There were ____ fewer votes for _____
than for _____ .”
Introduce to students the idea of a picture graph by showing them how a bar can be covered with multiple copies of an
object. For example, 5 votes for dogs could be represented by stacking 5 copies of a dog on top of each other. If needed,
use the picture graph template (attached) or the SMART Board to help.
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Graphing Template
Title: _______________________________________
11
10
9
8
7
6
5
4
3
2
1
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Lesson #14: What’s the difference? What’s the total?
Cluster: 2.MD Measurement and Data
Standards: Represent and interpret data.
2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to
represent a data set with up to four categories. Solve simple put-together,
take-apart, and compare problems1 using information presented in a bar
graph.
Standards for Mathematical Practice
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
SMP.6 Attend to precision
Mathematical Goal:
Materials:
Students will solve addition and subtraction problems and write
Paper, pencil, What’s the Difference Activity Sheet,
equations based on data in picture and bar graphs.
Graphing template from Lesson 15 (optional)
Words you should hear students use in mathematical
conversations:
Data, category, picture graph, bar graph, scale, total, difference
Classroom Routine: What Time Is It? : What Time Will It Be?
Write 1:45 on the board. Ask students to set their clocks to that time. Then ask:
 In one hour what time will it be?
Ask students to set the new time on their clocks and talk with their partner about what time it will be and how they know.
Ask them to describe what happens to the big hand and the small hand. Then ask them how that time would look on a
digital clock (2:45).
Repeat using hour intervals beginning on the three-quarter hour (6:45, 10:45).
Next, ask:
 If it is 11:45 now, in one half hour what time will it be?
Students set their clocks and record the new time (12:15). They describe the movement and position of the hands of
the clock. Repeat using two more half hour intervals.
Before:
Review with students how to plot data in a picture graph by giving students the following data set: When we surveyed
teachers what their favorite fruit was, this was the data: apples (10), oranges (8), banana (11), pineapple (5). As a class
make the picture graph from the data. Continue by asking students to think of “How many more?” questions that we can ask
based on the data. Spend a few minutes discussing and answering “How many more?” questions.
During:
Give students the “What’s the Difference?” activity sheet. As students work observe what strategies they use to solve each
problem and ask students to explain their reasoning and strategies.
After:
Discuss with the students their answers and strategies used for the tasks on the “What’s the Difference?” activity sheet.
Focus on the questions that students wrote and as a class talk about why questions are “What’s the difference?” or “What’s
the total?” questions.
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What’s the difference? What’s the total?
For each set of survey data below, create a bar graph and picture graph.
Then write and answer 2 What’s the difference? and 2 What’s the total? Questions.
Favorite Snacks
Chips (6)
Crackers (4)
Yogurt (9)
Fruit (7)
Bar Graph
Picture Graph
What’s the Difference Questions
What’s the Total Questions
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What’s the difference? What’s the total? (page 2)
Favorite Dessert
Ice Cream (4)
Brownies (5)
Cake (8)
Popsicle (2)
Bar Graph
Picture Graph
What’s the Difference Questions
What’s the Total Questions
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Lesson #15: How Long are Our Pencils?
Represent and interpret data.
Standards for Mathematical Practice
2.MD.9. Generate measurement data by measuring lengths of several objects to
the nearest whole unit, or by making repeated measurements of the same object.
Show the measurements by making a line plot, where the horizontal scale is
marked off in whole-number units.
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
Mathematical Goal:
Students will measure the length of objects and organize their data
in a line plot.
SMP.6 Attend to precision
Materials:
Pencils, paper, ruler (inches)
Words you should hear students use in mathematical
conversations:
inches, least, greatest, order, axis, line plot
Classroom Routine: Today’s Number: 26 Using Subtraction
Individually students generate expressions for 26 using only subtraction and 2 numbers. Remind them of the work you did
with patterns in the previous Today’s Number and ask them to generate 3 to 4 related expressions.
For example: 27 – 1, 28 – 2, 29 – 3, and 30 – 4, or 30 – 4, 40 – 14, and 50 – 24.
Collect a number of examples on the board and discuss one or two patterns as a whole class
Before:
Review students’ understanding of ordering numbers by giving them the following task, “Sally is 39 inches tall, Tom is 37
inches tall, and Nancy is 42 inches tall. Put them in order from shortest to tallest.
Give them 1 or 2 other problems. As you discuss tasks, ask students to explain how they know they have correctly ordered
the heights.
During:
Put students in groups of 2 or 3 students. Students will measure the lengths of pencils, pens and other writing tools that are
in their classroom. Students should measure to the nearest inch and record their lengths in an organized list on paper.
After students have had enough time to measure 10 to 12 writing tools bring them back together to discuss how to organize
the data in a line plot. Display your own list of data of 8 pencil lengths and have students help you make a line plot on the
Smart Board or white board. Use questions to have students help you complete the parts of the line plot, including, ordering
the data from least to greatest, labeling the axis, and then plotting the points. Remind students the importance of checking
their work afterwards to make sure they have accounted for all of the data points.
After:
Have students work through plotting their own data on paper. As students work, remind them that they should put their data
in order, and also establish a system of checking to make sure that they have not double counted or left out any data.
Students should write 2 statements about their data. These may be about which length was most common, least common,
or about the appearance of the line plot (data points being spread out or data points being clumped close together).
After students have had the opportunity to plot their data, bring them together to discuss their line plot. Have students share
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the process that they used to make their line plot and observations that they make about their data in their line plot.
Lesson #16: Measuring Our Feet and Hands
Represent and interpret data.
Standards for Mathematical Practice
2.MD.9. Generate measurement data by measuring lengths of several objects to
the nearest whole unit, or by making repeated measurements of the same object.
Show the measurements by making a line plot, where the horizontal scale is
marked off in whole-number units.
SMP.1 Make sense of problems and persevere in
solving them
SMP.4 Model with mathematics
Mathematical Goal:
Students will measure the length of objects and organize their data
in a line plot.
Words you should hear students use in mathematical
conversations:
centimeters, least, greatest, order, axis, line plot
SMP.6 Attend to precision
Materials:
Pencils, paper, ruler (centimeters)
Classroom Routine: What Time Is It? : What Time Will It Be?
Write 9:45 on the board.
Ask students to set their clocks to that time. Then ask: In one hour what time will it be? If it is 4:45 now, in one half hour
what time will it be?
Ask students to set the new time on their clocks and talk with their partner about what time it will be and how they know.
Ask them to describe what happens to the big hand and the small hand.
Then ask them how that time will look on a digital clock (10:45).
Repeat using hour intervals beginning on the three-quarter hour (1:45, 3:45). Students set their clocks and record the new
time (5:15). They describe the movement and position of the hands of the clock.
Repeat using two more half hour intervals.
Before:
Review students’ understanding of ordering numbers by giving them the following task, “Mike is 89 inches tall, Sarah is 78
inches tall, and Aaron is 87 inches tall. Put them in order from shortest to tallest.
Give them 1 or 2 other problems. As you discuss tasks, ask students to explain how they know they have correctly ordered
the heights.
During:
Put students in groups of 2 or 3 students. Students will measure the lengths of both the length of their foot and the width of
their hand (side of thumb to the side of pinky with fingers touching). Students should measure to the nearest centimeter and
record their lengths in an organized list on paper.
After students have had enough time to measure the lengths of the feet and hands for everyone in their group, bring them
back together to discuss how to organize the data in a line plot. Ask students questions about the processes involved with
creating a line plot, including ordering the numbers, labeling the axis, and plotting the points.
After:
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Have students work through plotting their own data on paper. As students work, remind them that they should put their data
in order, and also establish a system of checking to make sure that they have not double counted or left out any data.
Students should write 2 statements about their data. These may be about which length was most common, least common,
or about the appearance of the line plot (data points being spread out or data points being clumped close together).
After students have had the opportunity to plot their data, bring them together to discuss their line plot. Have students share
the process that they used to make their line plot and observations that they make about their data in their line plot.
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