Measurement and Data (2.MD)
Measure and estimate lengths in standard units.
2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks,
and measuring tapes.
The intent of this standard is…
Learning Targets
Notes for teacher
Samples
Common misconceptions
Students recognize
tools that are used for
measuring the length of
objects.
Students in second grade will build upon
what they learned in first grade from
measuring length with non-standard units
to the new skill of measuring length in
metric (centimeters and meters) and U.S.
Customary ( inches and feet) with standard
units of measure. They should have many
experiences measuring the length of
objects with rulers, yardsticks, meter
sticks, and tape measures. They will need
to be taught how to actually use a ruler
appropriately to measure the length of an
object especially as to where to begin the
measuring. Do you start at the end of the
ruler or at the zero? What if your ruler is
broken and the first number you see is 2?
Have students measure the same length with
different-sized units then discuss what they
noticed. Ask questions to guide the discussion so
students will see the relationship between the size
of the units and measurement.
When some students see
standard rulers with numbers
on the markings, they believe
that the numbers are counting
marks instead of the units or
spaces between the marks.
Have students use informal or
standard length units to make
their own rulers by marking
each whole unit with a number
in the middle. They will see
that the ruler is a
representation of a row of
units and focus on the spaces.
Students choose the
appropriate tools to
measure the length of
an object.
Students correctly line
up the measuring tool
with the end of the
object I am measuring.
Students use
appropriate tools to
accurately measure the
length of an object.
After students have performed many tasks
of “real” measurements, the following
foundational understandings of
measurements are developed:
* Understand that larger units (e.g., yard)
can be subdivided into equivalent units
(e.g., inches) (partition)
* Understand that the same object or
many objects of the same size such as
paper clips can be repeatedly used to
determine the length of an object
(iteration).
* Understand the relationship between the
size of a unit and the number of units
needed (compensatory principal). Thus,
the smaller the unit, the more units it will
take to measure the selected attribute.
By providing students with many opportunities to
create and use a variety of rulers they can
connect their understanding of non-standard unit
from first grade to standard units in second grade.
Example:
By helping students progress from a “ruler” that is
blocked off into colored units (no numbers)…
…to a “ruler” that has numbers along with the
colored units…
1
2
3
4
5
6
7
8
…to a “ruler” that has inches (centimeters) with
and without numbers. Students develop the
understanding that the numbers on a ruler do not
count the individual marks but indicate the space
(distance) between the marks. This is a critical
understanding that students need when using
Some students might think
that they can only measure
lengths with a ruler starting at
the left edge. Provide
situations where the ruler does
not start at zero. For example,
a ruler is broken and the first
inch number that can be seen
is 2. If a pencil is measured
and it is 9 inches on this ruler,
the students must subtract 2
inches from the 9 inches to
adjust for where the
measurement started.
By the end of second grade, students will
have also learned specific measurements
as it relates to feet, yards, and meters:
* There are 12 inches in a foot.
* There are 3 feet in a yard.
* There are 100 centimeters in a meter.
such tools as ruler, yardsticks, meter sticks, and
measuring tapes.
‘Broken rulers' are a great way to assess if
students really understand how to correctly use a
ruler. Copy the first page (the one with the rulers)
on cardstock and cut the rulers apart. You might
want to laminate them for repeated use in your
classroom. Each student, or pair of students, will
only need one of the rulers. The second page has
several line segments they can measure with the
rulers. After practicing with the broken rulers using
the line segments, you could always have the kids
do a scavenger hunt in the room (find three things
that are about 2 inches long, etc.).
Vocabulary
Use:
measure
about
a little less than
a little more than
longer
shorter
standard units
inch
foot
metric units
centimeter
meter
tools
Don’t Use:
One of the big misconceptions
when kiddos measure with a
ruler is what is called tick
counting. What that means is
that instead of counting the
units between the ticks on the
ruler, kids count the tick marks
instead. It's important that
kids have LOTS of practice
measuring with nonstandard
units to prevent the tick
counting error. When they
measure using, for example,
paper clips, there are no tick
marks, so they realize the unit
is the length of the paper
clip. A line segment is 5 paper
clips long. Inch color tiles are
a good transition from
nonstandard units to a ruler
because kids can use both the
color tiles and a ruler to
measure the length of
objects. The measurements
should match!”
Mathematical Practices
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.7: Look for and make use of structure.
ruler
yardstick
meter stick
measuring tape
estimate
Resources
Measurement and Data (2.MD)
Measure and estimate lengths in standard units.
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.
The intent of this standard is…students measure an object using two units of different lengths.
Learning Targets
Explain how two
different measurements
can describe the same
object.
Accurately measure the
length of an object
twice using two different
units of measurement.
Notes for teacher
Students need many opportunities to
measure using different units of measure.
They should not be limited to measuring
within the same standard unit. Students
should have access to tools, both U.S.
Customary and metric. The more students
work with a specific unit of measure, the
better they become at choosing the
appropriate tool when measuring.
Samples
Example: A student measured the length of a
table in both feet and inches. She found that
the table was 4 feet long. She also found out
that it was 48 inches long.
Teacher: Why do you think you have two
different measurements for the same table?
Student: It only took 4 feet because the feet are
so big. It took 48 inches because an inch is a
whole lot smaller than a foot.
Vocabulary
Use:
Measure
Longer
Shorter
Standard units
Non-standard
Inch
Foot
Metric units
Centimeter
Meter
Tools
Ruler
Yardstick
Don’t Use:
Common misconceptions
Some students see standard
rulers with numbers on the
marking, they believe that the
numbers are counting the
marks instead of the units or
spaces between the marks.
Have students use informal or
standard length units to make
their own rulers by marking
each whole unit with a number
in the middle. They will see
that the ruler is a
representation of a row of
units and focus on the spaces.
Mathematical Practices
MP.2: Reason abstractly and quantitatively.
MP.3: Construct viable arguments and critique the reasoning of others.
MP.5: Use appropriate tools strategically.
MP.6: Attend to Precision
MP.7: Look for and make use of structure.
Meter stick
Measuring tape
Resources
Measurement and Data (2.MD)
Measure and estimate lengths in standard units.
2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.
The intent of this standard is…for students to be able to make good estimates using all four units of measure, recognizing an
object that is equal to about one of the units, as well as making a good estimate of the total length of an object that would be
measured with one of the units.
Learning Targets
Notes for teacher
Samples
Common misconceptions
Identify the approximate
size of an inch.
Identify an object that is
approximately one inch.
Identify the
approximate size of a
foot.
Identify an object that is
approximately one foot.
Identify the approximate
size of a centimeter.
Identify an object that is
approximately one
centimeter.
Identify the approximate
size of a meter.
Identify an object that is
approximately one
meter.
Look at any object and
make an estimate of the
total length when the
unit is determined.
Estimate the difference
We cannot expect students to make good
estimates until they have had plenty of
good experiences using the various units
and seeing what the size looks like up
against many different objects
After students have had plenty of practice
measuring with each unit, they should be
prepared to learn about estimation and
begin using it.
Estimation should be viewed as a problem
to be solved rather than a task to
complete. Using estimation before each
measuring task will allow students that
opportunity to think first and reason.
When students make an estimate, it is
important to ALWAYS follow up with the
opportunity to actually measure the objects
so students are able to see how close their
estimate was to the actual measurement.
Students can use 1 object of the unit size
to view and hold next to the object in order
to see how one of that unit compares to
the whole length of the object being
measured.
Good objects to use:
- centimeter cube
- inch tile
- yard stick
- meter stick
Students are given a pink eraser to measure.
They lay a centimeter cube next to the eraser to
see what space is covered by one centimeter.
They make an estimate of the total length based
on what they see. *Students use a centimeter
ruler to measure the eraser.
When looking at two books, students are able to
estimate the difference in their size. For example,
they might say the math book is about 3 inches
longer than my library book.
This standard DOES NOT
refer to measuring to the
“nearest inch” or nearest of
any given unit. If you are
asking students to measure to
the nearest unit (for objects
that aren’t exact), have
students use the word “about”
to name their measurement,
instead of estimate.
Making an estimate happens
“before” the measurement is
recorded with any type of
standard measuring tool.
While measuring to the
nearest unit is sometimes
helpful in second grade (since
students do not measure to
the half inch yet),
in the length of two
different objects.
After students estimate, determine the
actual measurement:
Have students discuss their procedure for
finding the measurement and challenge
them to find the differences between their
estimates and actual measurements.
Vocabulary
Use:
estimate
about
approximate
unit
centimeter
inch
yard
meter
Don’t Use:
Mathematical Practices
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
Resources
Measurement and Data (2.MD)
Measure and estimate lengths in standard units.
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.
The intent of this standard is… for students to estimate and measure lengths in standard units and describe the differences
between the two objects.
Learning Targets
Notes for teacher
Samples
Common misconceptions
Compare the length of
two objects using
standard units.
Describe the length of
two objects using
standard units.
Insist that students always estimate
lengths before they measure. Estimation
helps them focus on the attribute to be
measured, the length units, and the
process. After they find measurements,
have students discuss the estimates, their
procedures for finding the measurements
and the differences between their
estimates and the measurements.
Second graders should be familiar enough
with inches, feet, yards, centimeters, and
meters to be able to compare the
differences in lengths of two objects. They
can make direct comparisons by
measuring the difference in length between
two objects by laying them side by side
and selecting an appropriate standard
length unit of measure.
Addition and subtraction of lengths is part
of the transition from whole number
addition and subtraction to fraction addition
and subtraction and to bar graphs.
Students determine the difference in length
between two objects by using the same tool and
unit to measure both objects. Students choose
two objects to measure, identify an appropriate
tool and unit, measure both objects, and then
determine the differences in lengths.
Example:
Teacher: Choose two pieces of string to measure.
How many inches do you think each string is?
Student: I think String A is about 8 inches long. I
think string B is only about 4 inches long. It’s
really short.
Teacher: Measure to see how long each string is.
Student measures. What did you notice?
Student: String A is definitely the longest one. It
is 10 inches long. String B was only 5 inches long.
I was close!
Teacher: How many more inches does your short
string need to be so that it is the same length as
your long string?
Student: String B is 5 inches. It would need 5
more inches to be 10 inches. 5 and 5 is 10.
Students often begin
measuring an object in the
middle rather than at the end.
They need to know that
measuring must start at the
point of zero on the ruler and
at the edge of the object.
Vocabulary
Use:
measure
about
a little less than
a little more than
longer
shorter
standard units
inch(es)
foot
metric units
centimeter
meter
tools
ruler
yardstick
meter stick
measuring tape
estimate
sums
differences
length
Don’t Use:
Mathematical Practices
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
Resources
Measurement and Data (2.MD)
Relate addition and subtraction to length.
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.
The intent of this standard is…
Learning Targets
Notes for teacher
Add lengths of two or
more given objects.
Students should use the same unit of
measurement in these problems.
Solve addition and/or
subtraction involving
lengths with the same
unit of measurement.
Written equations may vary depending on
students’ viewpoint of how to solve the
problem.
Example:
Jon is 58 inches tall and his brother is 47
inches tall. How much taller is Jon?
One students may write the equation
58-47= ___, while another may choose to
express their thinking as 47+___=58
Solve word problems
involving lengths. t
Solve equations that
involve a symbol for the
unknown number.
Make connections of the whole-number
units on rulers, yardsticks, meter sticks and
measuring tapes to whole number units on
number lines. Use these measuring tools
to model different representations for
whole-number sums and differences less
than or equal to 100 using the numbers 0100.
Provide students with one and two step
word problems that include different length
measurements using the same unit
(inches, feet, centimeters, and meters).
Students add and subtract within 100 on a
number line.
Samples
Example: In P.E. class Kate jumped 14 inches.
Mary jumped 23 inches. How much farther did
Mary jump than Kate? Write an equation and
then solve the problem.
Student A
My equation is 14 + __ = 23 since I thought, “14
and what makes 23?”. I used Unifix cubes. I
made a train of 14. Then I made a train of 23.
When I put them side by side, I saw that Kate
would need 9 more cubes to be the same as
Mary. So, Mary jumped 9 more inches than Kate.
14 + 9 = 23.
Student B
My equation is 23 - 14 = __ since I thought about
what the difference was between Kate and Mary.
I broke up 14 into 10 and 4. I know that 23 minus
10 is 13. Then, I broke up the 4 into 3 and 1. 13
minus 3 is 10. Then, I took one more away. That
left me with 9. So, Mary jumped 9 more inches
than Kate. That seems to make sense since 23 is
almost 10 more than 14. 23 – 14 = 9.
23 – 10 = 13
13 – 3 = 10
10 – 1 = 9
Common misconceptions
Vocabulary
Use:
unit
Length
Inches
Foot
Centimeter
Meter
Standard units
Sums
Difference
measure
Don’t Use:
Mathematical Practices
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.8: Look for and express regularity in repeated
Resources
Measurement and Data (2.MD)
Relate addition and subtraction to length.
2.MD.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.
The intent of this standard is… to connect measurement to the critical area of building fluency with addition and subtraction within
100 by creating number line diagrams with equally spaced points.
Learning Targets
Notes for teacher
Samples
Common misconceptions
Represent whole
numbers as equally
spaced points from 0 on
a number line.
Represent whole
number sums and
differences within 100
on a number line.
By building on students experiences with
open number lines, students create
number lines with evenly spaced points
corresponding to the numbers to solve
addition and subtraction problems to 100;
therefore they can recognize the
similarities between a number line and a
ruler.
Example: There were 27 students on the bus.
19 got off the bus. How many students are on
the bus?
Student A: I used a number line. I started at 27.
I broke up 19 into 10 and 9. That way, I could
take a jump of 10. I landed on 17. Then I broke
the 9 up into 7 and 2. I took a jump of 7. That got
me to 10. Then I took a jump of 2. That’s 8. So,
there are 8 students now on the bus.
It is important that students
transition to connecting the
proportionality of their “jumps”
on the number line to the
quantity of the number. This
demonstrates a deeper
conceptual understanding.
Some students will not make
this connection at first when
creating open number lines,
but should begin to develop
this understanding with a
proportional number line.
Connect the whole-number units on rulers,
yardsticks, meter sticks and measuring tapes to
number lines showing whole-number units starting
at 0. Use these measuring tools to model different
representations for whole-number sums and
differences less than or equal to 100 using the
numbers 0 to 100.
Vocabulary
Use:
unit
Length
Inches
Foot
Centimeter
Meter
Standard units
Sums
Don’t Use:
Mathematical Practices
MP.2: Reason abstractly and quantitatively
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
Difference
measure
Resources
Measurement and Data (2.MD)
Work with time and money.
2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
The intent of this standard is…
Learning Targets
Determine which are
the hour and minute
hands on an analog
clock.
Recognize that each
tick on a clock
represents one minute.
Understand that there
are five minutes
between numbers on a
clock.
Explain when a.m.
hours occur during a
day.
Explain when p.m.
hours occur during a
day.
I can tell time to the
nearest five minutes.
Notes for teacher
Samples
Common misconceptions
In first grade, students learned to tell time
to the nearest hour and half-hour. Students
build on this understanding in second
grade by skip-counting by 5 to recognize 5minute intervals on the clock. They need
exposure to both digital and analog clocks.
It is important that they can recognize time
in both formats and communicate their
understanding of time using both numbers
and language.
Learning to tell time is challenging for children. In
order to read an analog clock, they must be able
to read a dial-type instrument. Furthermore, they
must realize that the hour hand indicates broad,
approximate time while the minute hand indicates
the minutes within each hour. As students focus
on the hour hand, they begin to realize that when
the time is two o’clock, two-fifteen, or two fortyfive, the hour hand looks different – but is still
considered “two”. Discussing time as “about 2
o’clock”, “ a little past 2 o’clock”, and “almost 3
o’clock”, helps build vocabulary to use when
introducing time to the nearest 5 minutes.
Some students might confuse
the hour and minutes hands.
For the time of 3:45, they say
the time is 9:15. Also, some
students name the numeral
closest to the hands,
regardless of whether this is
appropriate. For instances, for
the time of 3:45 they say the
time is 3:09 or 9:03. Assess
students’ understanding of the
roles of the minute hand and
hour hands and the
relationship between them.
Have them focus on the
movement and features of the
hands.
In third grade, students will solve elapsed
time problems using a linear model. It will
be beneficial if students are exposed to the
linear model when introducing telling time
to five minutes.
The model below is great for showing how
the hour hand moves between hours as
the minute hand moves around the full
circle of the clock. So, when a students
points their minute hand to 45 minutes,
their hour hand will be ¾ past the 2:00.
Ex:
All of these clocks indicate the hour of “two”,
although they look slightly different. This is an
important idea for students as they learn to tell
time.
3:00
2:00
0
15
30
45
60
Students must understand that there are
two cycles of 12 hours a day- a.m. and
p.m. Recording their daily actions in a
journal would be helpful for making realworld connections and understanding the
difference between these two cycles.
A helpful way to teach the difference
between the hour hand the minutes hand
is this:
Hour is the short word; hour is the short
hand.
Minute is the long word; minute is the
long hand.
Vocabulary
Use:
clocks
hand
hour hand
minute hand
hour minute
a.m.
p.m.
o’clock
multiples of 5 (5, 10, 15, etc.)
analog clock
digital clock
quarter “till
quarter after
half past
quarter hour
Don’t Use:
Mathematical Practices
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
half hour
thirty minutes before
30 minutes after
30 minutes past
30 minutes till
30 minutes before
Resources
Measurement and Data (2.MD)
Work with time and money.
2.MD.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?
The intent of this standard is…for students to demonstrate their understanding of coin values and groups of coins through solving
addition and subtraction word problems.
Learning Targets
Notes for teacher
Samples
Common misconceptions
Identify penny, nickel,
dime, quarter, and
dollars (1, 5, 10, 20, 50,
100).
Identify the value of
penny, nickel, dime,
quarter, and dollars (1,
5, 10, 20, 50, 100).
Use the correct
symbols to write money
amounts ($ and ¢).
Count groups of mixed
coins containing (some
or all) pennies, nickels,
dimes, quarters.
Solve addition word
problems using
pennies, nickels, dimes,
quarters, and dollars (1,
5, 10, 20, 50, 100).
Solve subtraction word
problems tasks
pennies, nickels, dimes,
quarters, and dollars (1,
5, 10, 20, 50, 100).
*See last note
concerning solving
addition and subtraction
word problems.
It is important to note that students are
using coins for the first time based on their
value (as it is stated in the standards).
It is important to note that students should
be able to identify coins and their individual
values before they are given addition and
subtraction tasks.
We need to ensure that students are able
to count similar groups of coins before
moving on to mixed groups of coins.
Counting similar groups should be
facilitated with basic skip counting practice
by 5, 10, and 25. Use play money to
collect coins in similar groups as students
practice skip counting.
Provide opportunities for students to make
connections to place value by linking the
value of a dollar bill as 100 cents.
Additionally, students should communicate
that 38 has a value of 3 tens, 8 ones or
that it can be represented with 3 dimes, 8
pennies.
With word problems, students will use the
context of money to find sums and
differences less than or equal to 100 using
the numbers 0 to 100 when counting coin
values or dollar values but never
combining the two where decimals would
be involved.
How many different ways can you make 37¢ using
pennies, nickels, dimes, and quarters?
How many different ways can you make 12 dollars
using $1, $5, and $10 bills?
Sarah went to the store and received $ 0.76 in
change. What are three different sets of coins
she could have received?
You can use 5 frames, tens frames and a 5x5
array to help students make connections between
pennies and the larger coin values of a nickel,
dime, or quarter.
a) place a nickel next to a five-frame filled with
pennies
b) place a dime next to a ten-frame filled with
pennies
c) place a quarter next to a 5x5 array filled with
pennies
Do not assume that students
have had several experiences
with seeing coins, identifying
the names, or counting their
values. They may have been
exposed to the coins but not
directly taught what is
expected by the end of this
grade level.
Students may count each coin
as a value of 1 or may relate
the value of a coin to the size
of it.
Students need to see and
have regular practice with both
notations for cents:
a) 56 ¢
b) $ 0.56
Vocabulary
Use:
penny
nickel
dime
quarter
dollar
cents
value
total
sum
difference
spent
made
Don’t Use:
Mathematical Practices
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.8: Look for and express regularity in repeated reasoning.
Resources
Measurement and Data (2.MD)
Represent and interpret data.
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.
The intent of this standard is…emphasizing representing data using a line plot. Students will use the measurement skills learned in earlier standards to
measure objects. Line plots are first introduced in this grade level. A line plot can be thought of as plotting data on a number line. An interactive
whiteboard may be used to create and/or model line plots.
Learning Targets
Notes for teacher
Samples
Common misconceptions
Represent multiple
measurements on a line
plot.
Second graders use measurement data as
they move through the statistical process
of posing a question, collecting data,
analyzing data, creating representations,
and interpreting the results.
Example: Measure 8 objects in the basket to
the nearest inch. Then, display your data on a
line plot.
The attributes for the same
kind of object can vary. This
will cause equal values in an
object graph to appear
unequal. For example, when
making an object graph using
shoes for boys and girls, five
adjacent boy shoes would
likely appear longer than five
adjacent girl shoes. To
standardize the objects, place
the objects on the same sized
construction paper, then make
the object graph.
Measure multiple
objects to the nearest
whole unit.
Measure the same
object to the nearest
inch and centimeter or
foot and meter.
In second grade, students represent the
length of several objects by making a line
plot. Students should round their lengths to
the nearest whole unit.
Teacher: What do you notice about your data?
Student: Most of the objects I measured were 9
inches. Only 2 objects were smaller than 4
inches. I was surprised that none of my objects
measured more than 9 inches!
Teacher: Do you think that if you chose all new
objects from the basket that your data would look
the same? Different? Why do you think so?
Vocabulary
Use:
Collect
Organize
Display
Show
Sort
Data
Attribute
Line plot
Picture graph
Bar graph
Chart
Table
Most
Least
More than
About same
Different
Measure
Inch
Foot
Yard
Centimeter
Meter
Length
Don’t Use:
Mathematical Practices
MP.4: Model with mathematics
MP.5: Use appropriate tools strategically.
MP. 6: Attend to precision.
MP. 8: Look for and express regularity I repeated reasoning.
Resources
Measurement and Data (2.MD)
Represent and interpret data.
2.MD.10 Draw a picture graph and bar graph (with single-unit scale) to represent a data set with up to four categories.
Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
The intent of this standard is…
Learning Targets
Notes for teacher
Samples
Common misconceptions
Interpret data from
graphs to solve
addition, subtraction, or
comparison problems.
In Second grade, students 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. This is an extension
from first grade when students organized,
represented, and interpreted data with up
to three categories. They are able to use
the graph selected to note particular
aspects of the data collected, including the
total number of responses, which category
had the most/least responses, and
interesting differences/similarities between
the four categories. They then solve simple
one-step problems using the information
from the graph.
Example:
The Second graders were responsible for
purchasing ice cream for an open house event at
school. They decided to collect data to determine
which flavors to buy for the event. As a group, the
students decided on the question, “What is your
favorite flavor of ice cream?” and 4 likely
responses, “chocolate”, “vanilla”, “strawberry”, and
“cherry”.
The students then divided into teams and
collected data from different classes in the school.
Each team decided how to keep track of the data.
Most teams used tally marks to keep up with the
responses. A few teams used a table and check
marks.
The attributes for the same
kinds of object can vary. This
will cause equal values in an
object graph to appear
unequal. For example, when
making an object graph using
shoes for boys and girls, five
adjacent boy shoes would
likely appear longer than five
adjacent girl shoes. To
standardize the objects, place
the objects on the same-sized
construction paper then make
the object graph.
Create a picture graph
to illustrate a set of data
that has up to four
categories.
Create a bar graph to
illustrate a set of data
that has up to four
categories.
Note: Graphing of these
types should be
incorporated regularly
throughout the school
year in various
situations and with all
content areas.
At first, students should create real object
and picture graphs so each row or bar
consists of countable parts. These graphs
show items in a category and do not have
a numerical scale. For example, a real
object graph could show the students’
shoes (one shoe per student) lined end to
end in horizontal or vertical rows by their
color. Students would simply count to find
how many shoes are in each row or bar.
The graphs should be limited to 2 to 4 rows
or bars.
Students would then move to making
horizontal or vertical bar graphs with 2 to 4
categories and a single-unit scale. Use the
information in the graphs to pose and solve
When back in the classroom, each team
organized their data by totaling each category in a
chart or table. Team A’s data was as follows:
Flavor
Chocolate
Vanilla
Strawberry
Cherry
Number of people
12
5
6
9
Each team selected either a picture graph or a bar
graph to display their data and created it using
either paper or the computer.
Graphs are shown below:
Team A: Bar Graph
simple put together, take-apart, and
compare problems.
Students should draw both picture and bar
graphs representing data that can be
sorted up to four categories using single
unit scales (e.g. scales should count by
ones). The data should be used to solve
put together, take-apart, and compare
problems.
In second grade, picture graphs
(pictographs) include symbols that
represent single units. Pictographs should
include a title, categories, category label,
key, and data.
Team B’s data was as follows:
Flavor
Number of People
Chocolate
6
Vanilla
10
Strawberry
5
Cherry
3
Team B: Picture Graph
Second graders should draw both
horizontal and vertical bar graphs. Bar
graphs include a title, scale, scale label,
categories, category label, and data.
Once the data was represented on a graph, the
teams then analyzed and recorded observations
made from the data. Statements such as,
“Chocolate had the most votes” and “Vanilla had
more votes than strawberry and cherry votes
combined” were recorded.
The teacher then facilitates a discussion around
the combination of the data collected to determine
the overall data of the school. Simple problems
are posed:
 The total number of chocolate votes for Team
A was 12 and the total number of chocolate
votes for Team B was 6. How many chocolate
votes are there altogether?

Right now, Cherry has a total of 12 votes.
What if 8 people came and wanted to change
their vote from Cherry to another choice. How
many votes would Cherry have?
After a careful study of the data, students
determined that Chocolate was the preferred
flavor. Vanilla was the second most popular. The
class decided that more chocolate should be
purchased than vanilla, but both should be
purchased. The teacher then asked the class, “If
each gallon of ice cream served 20 children, how
many gallons of ice cream would we need to buy
for 460 students? How many of those total gallons
should be chocolate? How many should be
vanilla? Why?”
Vocabulary
Use:
picture graph (pictograph)
bar graph
data
categories
compare
title
category label
key
scale
scale label
Don’t Use:
Mathematical Practices
MP.1: Make sense of problems and persevere in solving them.
MP.2: Reason abstractly and quantitatively.
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.
MP.6: Attend to precision.
MP.8: Look for and express regularity in repeated reasoning.
Resources