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 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)

Emphasized Standards for Mathematical Practice: 2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning

of others

5. Use appropriate tools strategically.

6. Attend to precision.

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.

Rectangle

How many

squares do

estimate it will

take?

Size (square units)

A

B

C

D

E

F

G

H

I

J

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 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)

Emphasized Standards for Mathematical Practice: 2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning

of others

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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 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)

Emphasized Standards for Mathematical Practice: Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning

of others

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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 Dimensions:

Area Length Width

Example: 7 feet 4 feet 28 square feet

A

B

C

D

E

F

G

H

I

J

Day 4: Scaled Picture Graphs

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 the information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Emphasized Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 6. Attend to precision.

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. 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 the information presented in scaled bar graphs. For example, draw a bar graph in which each square 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.

Emphasized Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 6. Attend to precision.

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 one- and 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

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? _____

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Each represents 2 students

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.

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? ___________

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? _____