Grade 3 Area & Scaled Pictographs and Bar Graphs Unit Overview
Geometric measurement: Understand concepts of area and relate area to multiplication and to addition.
3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. (a) A square
with a side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
(b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square
units.
3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units)
Day 1: Area: How Many Squares to Cover this Shape?
This 3-day area unit is designed to introduce students to area only. Students were introduced to perimeter during the
geometry unit at the beginning of the year (3.MD.8). Perimeter is not addressed at this time to allow students to make a
clear distinction between perimeter and area. The relationship between area and perimeter will be explored in the week
long unit between Units 7 and 8.
Day 1 focuses on the concept of covering with squares to measure the area of a shape. Students should understand that
same-size squares can be used to measure an attribute of a shape called area and that the unit we are using to measure
is called square units since we are counting the number of squares to cover the shape.
Day 2: What’s the Area? (Using Multiplication to Find the Area of Rectangles)
Day 2 is Unit 5, Session 3.1A. This lesson focuses on the relationship between multiplication and the area of rectangles.
Day 3: Using Standard Units to Measure Area
Day 3 introduces standard units of measure for area. Students see and measure with a variety of standard units.
Students are also challenged to consider which unit is most appropriate for which area (ie square inches for smaller areas
like a pieces of paper, square feet for somewhat larger areas like tables or dry erase boards, and square yards or square
meters for things like hallways or room floors.)
Represent and interpret data.
3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and
two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example,
draw a bar graph in which each square in the bar graph might represent 5 pets.
Day 4: Introducing Picture Graphs
Third Grade students should come to third grade with some familiarity with picture graphs and bar graphs.
CCSS.Math.Content.2.MD.10 Draw a picture graph and a bar graph (with a 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 is the second grade standard. Third graders extend this content using their new understanding of multiplication to
create scaled graphs to represent data and interpret data by solving one- and two-step questions about the graphs. Day 4
focuses on using scaled picture graphs to represent favorite spots to read. You will need to collect survey information from
several classes prior to the start of this lesson. Simply ask students to write and record their favorite place to read. Part of
the challenge of graphing is organizing the responses into categories to graph. Surveying several classes is important
because students need to understand why we sometimes need to make the symbol represent more than one thing.
Day 5: Introducing Scaled Bar Graphs
Day 5 focuses on introducing scaled bar graphs. As mentioned above, students have already created bar graphs with
single unit scales in second grade. This lesson is designed to expose students to scaled bar graphs. This lesson also
gives students additional experiences with shape recognition.
Additional Ten Minute Math
This is a brief introduction to graphing and students will need to continue practicing interpreting scaled bar and picture
graphs through the remainder of the year. This section contains examples of graphs you may want to use as an add-on
piece for ten minute math or as additional homework once students have demonstrated a solid understanding of scaled
graphs. Also consider collecting grade level data (so scaled graphs are needed because of the amount of data) to graph
on topics relevant to third graders.
Day 1: Area: How Many Squares to Cover This Shape?
Geometric measurement: Understand concepts of area
Emphasized Standards for Mathematical Practice:
and relate area to multiplication and to addition.
3.MD.C.5 Recognize area as an attribute of plane figures and 2. Reason abstractly and quantitatively.
understand concepts of area measurement. (a) A square with 3. Construct viable arguments and critique the reasoning
a side length 1 unit, called “a unit square,” is said to have “one
of others
square unit” of area, and can be used to measure area. (b) A
5. Use appropriate tools strategically.
plane figure which can be covered without gaps or overlaps
6. Attend to precision.
by n unit squares is said to have an area of n square units.
3.MD.C.6 Measure areas by counting unit squares (square
cm, square m, square in, square ft, and improvised units)
Materials:
Shape Set A-J
Square Tiles
Recording Sheet
Exit Ticket-Area Day 1
Words that you should hear students using in
mathematical conversations:
scale Area
Square units
Cover
Measure
Ten Minute Math: Today’s Number: Students make expressions that equal 79. They must use one 3-digit number and
subtraction only in each expression they create.
Before:
Say: If we want to know the size of a shape, we can cover it with squares to see how many squares it takes to cover the
shape. When we use squares to measure a shape, we call the squares “square units” because we are using them to
measure size like we use the units inches and centimeters to measure length and pounds to measure weight. The
number of squares it takes to cover a shape is called the area.
Today, we are going to find the area of some shapes to see which shape is the biggest. Each shape is labeled with a
letter. Begin by estimating the size and order of the shapes. Then measure to see the actual size. Record the letter of
your shape and how many square units it takes to cover the shape.
During:
Students use square tiles to measure the square units of shapes A-J. Student use the area to order the shapes by size.
After:
Say: Since we are measuring these shapes to see what size they are…the area, these squares are units of measure.
Just like we use units such as inches to measure how long something is, we use square units to see what size a flat shape
is…to find its area. So, today when we talk about our shapes, let’s describe them in square units. The area of shape (A)
is (22) square units.
Ask students for the size of some of the shapes they measured (making sure that students describe the size in square
units). Eventually determined the shape with the greatest area.
Evaluation:
What is the Area? Exit ticket
Name:______________
Which Shape is the Biggest?
Work with your group to estimate the size order of the shape set.
___ ___
___ ___
___
___
___
___
___
(smallest)
___
(largest)
Next, measure the area of each shape. Record the size of each shape
in the chart.
How many
Rectangle
squares do
estimate it will
take?
A
B
C
D
E
F
G
H
I
J
Size (square units)
Now that you have measured each shape, put them in order from least
to greatest. Record the letter of the shapes on the lines below.
_____
(smallest)
_____
_____
_____
_____
_____
_____
(largest)
Were the shapes in the order that you thought before you measured
them? _______________________________________________
How did measuring the area help you to know for sure? __________
____________________________________________________
Shape A
Shape B
Shape C
Shape D
Shape E
Shape F
Shape G
Shape H
Shape I
Shape J
Exit Ticket: Area - Day 1
Name: ____________________
What is the area of these shapes?
1.
2.
___________________
Exit Ticket: Area - Day 1
____________________
Name: ____________________
What is the area of these shapes?
1.
___________________
2.
____________________
Day 2: What’s the Area?
Geometric measurement: Understand concepts of area
Emphasized Standards for Mathematical Practice:
and relate area to multiplication and to addition.
3.MD.C.5 Recognize area as an attribute of plane figures and 2. Reason abstractly and quantitatively.
understand concepts of area measurement. (a) A square with 3. Construct viable arguments and critique the reasoning
a side length 1 unit, called “a unit square,” is said to have “one
of others
square unit” of area, and can be used to measure area. (b) A
5. Use appropriate tools strategically.
plane figure which can be covered without gaps or overlaps
6. Attend to precision.
by n unit squares is said to have an area of n square units.
7. Look for and make use of structure.
3.MD.C.6 Measure areas by counting unit squares (square
8. Look for and express regularity in repeated reasoning.
cm, square m, square in, square ft, and improvised units)
Materials:
Investigations Unit 5: Session 3.1A
Rectangle that is 5 inches by 7 inches (teacher)
Square Tiles
Student Activity Book Pages 26B-F (C22-26)
Words that you should hear students using in
mathematical conversations:
Area
Square units
Square inches
Cover
Measure
Dimensions
Ten Minute Math: Today’s Number: Students use at least three numbers to make expressions that equal 150. They
must use both addition and subtraction for each expression they create.
Before:
(Lesson Plan for Investigations Unit 5, Session 3.1 A, The beginning dialogue needs to be adjusted because students will
not have complete the Unit 4 lesson combining area and perimeter yet)
Say: Yesterday, we found the area of some funny shapes. Who can remind us what it means to find the area of a shape?
(Discussion should include that area is covering a shape with squares, called square units, to figure out how big the shape
is.)
Today, we are going to find the area of some rectangles. (Show student the 5-inch by 7-inch rectangle. Discuss
strategies for finding the area of the rectangle and how you might describe the rectangle. Introduce the word dimensions
and describing a rectangle using dimensions, ie 5 by 7 rectangle. Model recording dimensions and area of the rectangle)
Introduce Student Activity Book Pages 26B-F.
During:
 Students use tiles to find the area of rectangles on first 2 pages, recording dimensions and area.
 Students build 4 rectangles using square tiles on third page, recording dimensions and area.
 Students record dimensions and area for all 8 rectangles on the fourth page.
 Encourage students use the fourth page to look for and describe patterns in the dimensions and area as they
complete the activity.
After:
We have been thinking a lot about multiplication over the past few weeks. Yesterday, we started thinking about area. Do
you see any connections between multiplication and area?
Evaluation:
What’s the Area? (SAB 26F) Consider including a #3 in which students describe the relationship between area and
multiplication.
Rectangle
Day 3, Title: Using Standard Units to Measure Area
Geometric measurement: Understand concepts of area
Emphasized Standards for Mathematical Practice:
and relate area to multiplication and to addition.
Reason abstractly and quantitatively.
3.MD.C.5 Recognize area as an attribute of plane figures and 3. Construct viable arguments and critique the reasoning
understand concepts of area measurement. (a) A square with
of others
a side length 1 unit, called “a unit square,” is said to have “one
5. Use appropriate tools strategically.
square unit” of area, and can be used to measure area. (b) A
6. Attend to precision.
plane figure which can be covered without gaps or overlaps
7. Look for and make use of structure.
by n unit squares is said to have an area of n square units.
8. Look for and express regularity in repeated reasoning.
3.MD.C.6 Measure areas by counting unit squares (square
cm, square m, square in, square ft, and improvised units)
Materials:
4 rulers marked with centimeters (or cm cubes)
4 rulers marked with inches (or square tiles)
4-8 12 inch rulers
4-8 yard sticks
4-8 meter sticks
Tape or chalk shapes that can be measured in square
centimeters, square inches, square feet, square yards, or
square meters.
5 sheets of chart paper
Recording Sheet
How Big Is a Foot? By Rolf Myller (optional)
Words that you should hear students using in
mathematical conversations:
Area
Square units
Square inches
Square centimeters
Square feet
Square yards
Square meters
Cover
Measure
Dimensions
Ten Minute Math: Today’s Number: Students create expressions that equal 86. They must use multiples of 10 in each
expression they create.
Before:
(Prior to this lesson, you might consider reading aloud the book How Big Is a Foot? By Rolf Myller. This book emphasizes
the need for standard units).
We’ve been measuring area for two days using square tiles. Yesterday, we said that we could name the area in square
inches since each tile is 1 inch on each side. So, when we found the area of the rectangle that was 2 inches by 4 inches,
we said it was 8 square inches. Mathematicians use different sized squares to measure area. We name the unit by how
long one side is. What is a square inch? What is a square foot? What is a square yard? (Tape together 4 rulers to make
a square foot, 4 yard sticks to make a square yard, and 4 meter sticks to make a square meter) What would you measure
with a square inch? Foot? Yard?
Today, we are going to do a two-part activity. We are going to create a list of things we can measure using a square
centimeter, inch, foot, yard, and meter. We have 5 posters around the room that we are going to use as a graffiti wall. We
are going to rotate around the room and record things that we might measure using each of these units. Then, we will
measure some shapes/rectangles using these square units. (Some shapes will be very large and you may need to
consider ways to arrange you classroom to accommodate or use a hallway space with planned adult supervision or use
side walk chalk on a safe, supervised outdoor black top area used for student play).
During:
 Students create lists of things that might be measured with square units of different sizes.
 Students measure rectangles using square units of different sizes.
After:
Why would you use one unit to measure one size shape, but another unit to measure a different size shape? How do you
decide which unit to use? Why is it important to know the length of the side of the square unit you are using to measure?
Evaluation:
Would you measure the size of your school hallway in square inches or square yards? Explain why.
Name:______________________
Measuring Area with Standard Units Recording Sheet
Shape
Example:
A
B
C
D
E
F
G
H
I
J
Dimensions:
Length
7 feet
Width
4 feet
Area
28 square feet
Day 4: Scaled Picture Graphs
Represent and interpret data.
Emphasized Standards for Mathematical Practice:
3.MD.3 Draw a scaled picture graph and a scaled bar graph
to represent a data set with several categories. Solve one1. Make sense of problems and persevere in solving
and two-step “how many more” and “how many less”
them.
problems using the information presented in scaled bar
graphs. For example, draw a bar graph in which each square 6. Attend to precision.
in the bar graph might represent 5 pets.
Materials:
- Where is Your Favorite Place to Read? Survey Completed
- Paper
Words that you should hear students using in
mathematical conversations:
scale
scaled picture graph
category/categories
key
symbol
title
data
Ten Minute Math: Count around the class by 10’s. Tell students that we use numbers to represent a quantity. Ask
students what data we might be collecting about our room when we count 10 for each person. Students should suggest
some ideas such as fingers and/or toes. Extend by asking students what we might be counting if we counted by 2’s or 5’s.
Before:
Present students with the completed surveys “Where is Your Favorite Place to Read?” Ask students, “How could we
organize the data so that we can easily see how students in our grade level like to read best?” Develop a class plan for
how to organize the data, and use the plan to do so. Because you have data from several classes, the number of
students selecting various spots should be large. Once the data is organized so that you know how many chose each
place to read, tell students that mathematicians often display data in graphs because graphs make data easier to see and
to think about. Remind students that they learned to make picture graphs in second grade. Show students an example of
a picture graph with a scale of one. Remind students of the parts of a picture graph including the title, the symbol, the key,
and the labels for the categories. Tell students that today they will make a picture graph for the data that you have
collected. Acknowledge the fact that we have some large numbers and it will take us a long, long time to draw all of those
symbols. Ask students, “Is there a way that we could show this data without drawing so many symbols?” If no one
suggests it, bring up the idea of having one symbol represent more than student. Tell students that they will work with a
partner today to represent the data that we have collected using a picture graph. Students need to think of a symbol and
how many students they want their symbol to represent.
During:
Students work with a partner or small group to create picture graphs with a symbol that represents more than one student.
Students should include a title, a key with the value of the symbol, and labels for each of their categories. When a group
realizes that a number is not a multiple of 10 and they need to graph it. Include a mid-workshop discussion to talk about
the problem with the whole class. Ask students for ideas. If no one mentions it, be sure to tell students that
mathematicians often use half or partial symbols to represent a number in between.
After:
Have a couple groups share their picture graph and discuss how their graphs represent the data. As groups share ask
one- and two-step questions about the data in the graph. The following are some examples:
How many more students prefer to read on their (beds) than on the (couch)?
If you combined the number of students who prefer to read at their (desk) and at the (table), would that be more or less
than the number of students who like to read in the (car)? How many more? How many less?
Evaluation:
Picture Graph Exit Ticket
Name: __________________________
Scaled Picture Graphs Exit Ticket
How Students Travel Home at the End of the Day:
Bus
Van Rider
Car Rider
After school
Each
equals 5 students
How many students are represented in this graph? ______
How many students are car riders? _____
How many more students ride the bus than ride in a van? _____
If bus riders are dismissed at 2:45 and car riders and van riders are dismissed at 2:55, then how
many more students are dismissed at 2:45 than at 2:55? _____
Name: ___________________________
Scaled Picture Graphs Exit Ticket
How Students Travel Home at the End of the Day:
Bus
Van Rider
Car Rider
After school
Each
equals 5 students
How many students are represented in this graph? ______
How many students are car riders? _____
How many more students ride the bus than ride in a van? _____
If bus riders are dismissed at 2:45 and car riders and van riders are dismissed at 2:55, then how
many more students are dismissed at 2:45 than at 2:55? _____
Day 5: Scaled Bar Graphs
Represent and interpret data.
Emphasized Standards for Mathematical Practice:
3.MD.3 Draw a scaled picture graph and a scaled bar graph
to represent a data set with several categories. Solve one1. Make sense of problems and persevere in solving
and two-step “how many more” and “how many less”
them.
problems using the information presented in scaled bar
graphs. For example, draw a bar graph in which each square 6. Attend to precision.
in the bar graph might represent 5 pets.
Reason with shapes and their attributes
3.G.1 Understand that shapes in different categories (e.g.
rhombuses, rectangles, and others) may share attributes (e.g.
having 4 sides) and that they shared attributes can define a
larger category (e.g. quadrilaterals). Recognize rhombuses,
rectangles, and squares as examples of quadrilaterals,, and
draw examples of quadrilaterals that do not belong to any of
these subcategories.
Materials:
- Paper
- Anchor Charts
Words that you should hear students using in
mathematical conversations:
scale
scaled bar graph
data
title
category/categories
Ten Minute Math: Have students do a 3 minute visual hunt for shapes in the classroom. Tell students to record the
shapes they see and where they see it. Afterwards have students share what they found. Look for examples in which one
student says “quadrilateral” and another says, “trapezoid” for the same shape. Ask, “How can both students be right?”
Before:
Tell students that we are complete a quick activity to practice identifying 2-D shapes/polygons that we learned about
earlier this year. If you have anchor charts used early in the year, you may want to post those to remind students of
definitions of triangles, quadrilaterals, pentagons, and hexagons.
Directions for creating shapes sheets (see example pictures on next page):
1-Give each student a blank sheet of paper. Have them close their eyes and make 5 folds in the paper without looking or
trying to line up edges. Unfold the paper.
2-Label the shapes on the page as triangles quadrilaterals, pentagons, and hexagons.
3-Collect class data on the number of each type of shape created.
Tell students that today, we are going to use a bar graph to record our data. Review the parts of a bar graph using a
graph with a scale of 1 (Title, labels for categories, labels for counting how many). Discuss with students the fact that it
would take a long time to write numbers up to (142) for (quadrilaterals) on the side of the graph, so sometimes
mathematicians use a scale that skip counts so that they can get all of the information on the graph. They might count by
2’s, 3’s, 4’s, 5’s, 10’s or some other number. Tell students that they will use the data that was collected to build a scaled
bar graph with a partner.
During:
Students work with a partner or small group to create scaled bar graphs. Students should include a title and labels on the
horizontal and vertical axis. As students are working discuss with them how to decide where to mark the number of
shapes when it comes in between numbers on the scale.
After:
Have a couple groups share their bar graph and discuss how their graphs represent the data. As groups share, ask oneand two-step questions about the data in the graph. The following questions are examples:
How many more (quadrilaterals) than (triangles) did we create?
How many shapes less is the (hexagons) than the (pentagons)?
Were there more shapes with an even number of sides or an odd number of sides? How many more?
Evaluation: Bar Graph Exit Ticket
Geometry Folding Activity Pictures
Additional Ten Minute Math
The following pages contain additional graphing practice that can be included throughout the
remainder of the year as ten minute math or an extra workshop activity.
Horizontal Bar Graph 1
Name:______________
Scaled Picture Graphs 1
Name:_______________
The principal at Panther’s Elementary School decided to keep track of the numbers of
absences each grade level in her school. She made a scaled picture graph to show the results
for February.
Panthers Elementary School Absences in February
Kindergarten
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Each
represents 2 students
1. How many kindergarten students were absent in February? _____
2. How many fourth grade students were absent in February? _____
3. The principal noticed that many K-2 students were absent. How many K-2 students
were absent in February? ______
4. How many less 3-5 students were absent than K-2 students? ______
5. How many more second grade students were absent than third grade students? _____
6. What was the total number of absences for February? _____
Vertical Bar Graphs 1
Name: ________________
Scaled Picture Graphs 2
Name: ________________
A group of third graders were surveyed to find their favorite way to spend their free time.
They put all of the results into six categories: Playing Sports, Reading, Crafts and Drawing,
Playing Games, Building (ie forts, Legos), and Watching Television. They created a scaled
picture graph to show the results.
Favorite Way to Spend Free Time for Third Graders
Sports
Reading
Crafts/Drawing
Games
Building
Television
= 5 students
1. Students who enjoy strategizing usually chose sports or games. How many
students chose sports or games? _____
2. Students who enjoy creating usually chose Crafts/Drawings or Building. How
many students chose Crafts/Drawings or Building? _____
3. How many less students chose television than reading? _____
4. How many more students chose building than games? _____
5. How many students were surveyed? ____
Horizontal Bar Graph 2
Name:____________
Lydia is practicing for a bicycle race. She is practicing riding every day. She created
a graph to show how many miles she practices each week.
1. How many miles did Lydia practice for during Week 4? ____
2. How many less miles did Lydia practice Week 3 than Week 2? ____
3. Did Lydia practice more miles during Weeks 1 & 2 or during Weeks 3 & 4?
___________ How many more miles? ______
4. If Lydia wants to practice for 100 miles during Week 5, how many more miles
will she need to ride than on Week 4? _________
5. If Lydia rides 100 miles during Week 5, how many miles will she have
practiced for so far? __________
Vertical Bar Graphs 2
Name: ________________
Ms. Ouellette’s third grade class is trying to read 1,000 books by the end of the
school year. They collect the data and record the number of books read on a bar
graph each month.
1. How many books did
Ms. Ouellette’s class read
in October? _____
2. How many fewer books
did Ms. Ouellette’s class
read in September than
in October? ______
3. How many more books
did Ms. Ouellette’s class
read in December than in
November? _____
4. Did Ms. Ouellette’s class read more in September and October combined or in
November and December combined? _____
5. How many more books does Ms. Ouellette’s class need to read to make their
end of year goal? ___________