General Information
Subject(s): Mathematics
Grade Level(s): 3
Suggested Technology:
Document Camera, Computer for Presenter, Computers for Students, Internet Connection, LCD Projector, Overhead Projector, Adobe Flash Player, Adobe Acrobat Reader, Microsoft Office, Java Plugin
Instructional Time:
1 Hour(s)
Resource supports reading in content area:Yes
Freely Available: Yes
Keywords: area, perimeter, square unit
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Lesson Content

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
By the end of this lesson, students will be able to find all the possible rectangles with a given perimeter and calculate the area of each one.

Prior Knowledge: What prior knowledge should students have for this lesson?
Prior to the lesson, students should have had experiences with solving problems involving both perimeter and area. They should know that they are both are attributes of twodimensional figures.They should know that perimeter is a linear measure of the distance around a figure and that area is a measurement of the number of the square units needed to cover a flat surface. They should have prior knowledge of the following measurement units: inch, foot, centimeter, square inch, square foot, and square centimeter. Knowing the terms length (or base), width (or height), and perpendicular would be helpful, but not necessary, as they will be reviewed.

Guiding Questions: What are the guiding questions for this lesson?
 What is perimeter a measure of?
 What unit of measure do we use for perimeter?
 How do you find the perimeter of a shape?
 What is area a measure of?
 What unit of measure do we use for area? Why?
 How do you find the area of a shape?
 Which 2 numbers do you multiply to find area?
 Why did the perimeter stay the same for each rectangle (we created) but the area changed?
 Which rectangle had the greatest area and why? Is this always true?

Teaching Phase: How will the teacher present the concept or skill to students?
 The teacher will show students the PBS Kids Cyberchase video The Dumas Diamond. If you click on the video screen, a button with arrows will appear to expand to full screen mode. This 3:26 minute video will get students thinking about figures that have the same perimeter but different areas.
 The teacher will review perimeter and area by asking students questions about the similarities and differences between perimeter and area. This could be recorded on a large anchor chart using a Venn Diagram or Tchart for students to refer to during and after this lesson.
 The teacher will project the Inch Grid Paper using a document camera and LCD projector or an overhead projector.
 The teacher will show the students a piece of string measuring 1inch. Use a ruler to show that the string is 1inch long.
 The teacher will place the 1inch piece of string along 1 side of a square on the grid paper and another piece of 1inch string along a perpendicular side. This will show that this square has a length of 1inch and a width of 1inch.
 The teacher will discuss the terms length (the side with the longer length) and width (the side with the shorter length). If you have previously taught that length is a vertical measurement and width is a horizontal measurement, then use these definitions. Tell students that the length is always perpendicular (at a right angle) to the width of a rectangle. If you have used the formula base x height = Area of a rectangle in previous lessons, then use these words in conjunction with length and width.
 The teacher will place 4 pieces of string around one square to show that it is a square inch.
 The teacher will direct students to the piece of chart paper with a larger version of the Area and Perimeter Recording Chart written on it.
 The teacher will fill in the first row's length, width, perimeter, and area with assistance from students. Write 1 + 1 + 1 + 1 = 4 inches (or 4 x 1 = 4 since it is a square) in the Perimeter cell and 1 x 1 = 1 square inch in the Area cell.
 The teacher will review the problem from the video. Project the inch grid paper and use one 12inch long piece of string to create a 1 x 5 inch rectangle.
 The teacher will trace the rectangle on the grid paper and remove the string. Next, the teacher will use the 12inch long string to create a 3 x 3 inch rectangle and trace it on the grid. Discuss with students that a square is a special kind of rectangle with 4 equal sides.
 The teacher, with the help of students, will fill in the Area and Perimeter Recording Chart with the measurements and calculations for both rectangles (A. Length  5 in., Width  1 in., Perimeter  5 + 5 + 1 + 1, or addends in any order = 12 in. OR (2 x 5) + (2 x 1) = 12 in., Area  5 x 1 = 5 sq. in.) (B. Length  3 in., Width  3 in., Perimeter  3 + 3 + 3 + 3 = 12 in. OR 4 x 3 = 12 in., Area  3 x 3 = 9 sq. in.).
 At this point, a discussion could be had about the Commutative Property of Multiplication and how you could have a 1 in. x 5 in. rectangle, which has the same area as a 5 in. x 1 in. rectangle.
 The teacher should clear up any misconceptions or confusion between area and perimeter before moving students into Guided Practice.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
 The teacher will distribute 2 pieces of inch grid paper, a 16inch long piece of string, crayons/colored pencils, and 2 copies of the Area and Perimeter Recording Chart to each student pair.
 The teacher will explain to students that they are going to investigate all the rectangles (remind students that a square is a rectangle) they can create with the string. The teacher should make sure students understand that there cannot be any gaps in the string because a rectangle is a closed figure. There also cannot be any overlaps of the string because the sum of the 4 sides' length must equal 16 inches (perimeter).
 The students will be following the steps that the teacher modeled with the 12inch piece of string to make the rectangle and fill out the recording sheet.
 Each time the student partners make a rectangle, they should have one of them trace it on the grid paper. The other partner should label the length and width (in inches) of each rectangle that they draw on grid paper. Together they should calculate and write the area (with square inches) in the center of their rectangles. This will reinforce the connection to arrays that they have used to learn about repeated addition and multiplication. They will then record the length, width, perimeter, and area on their own recording sheet.
 The teacher will circulate the room and check for accurate drawings and formula calculations.
 The teacher will bring the students back together to discuss the shapes they created and which had the greatest area. The rectangles would be 7 in. x 1 in. with an area of 7 sq. in., 6 x 2 and 12 sq. in., 5 x 3 and 15 sq. in., and 4 x 4 and 16 sq. in. The square had the greatest area. The perimeter column should have 16 in. written in every row as the answer with calculations to proving the answer, for example 7 + 7 + 1 + 1 = 16 in.
 Remind students that they did not have to fill in the whole Area and Perimeter Recording Sheet because some of the measurements would have been the same (for example, 7 x 1 and 1 x 7).
 The teacher can have students share any strategies they used for calculating their answers.
 The teacher will ask the guiding question "Why did the perimeter stay the same for each rectangle (we created) but the area changed?" before moving the students into Independent Practice.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
 The teacher will collect each students' Area and Perimeter Recording Sheet and provide feedback.
 The teacher will distribute a copy of Centimeter Grid Paper to each student. They will also need the crayons or colored pencils that were used in Guided Practice.
 Students will complete the problem on the Exit Ticket and show their work in their journals or on the paper. They must draw their rectangles on the grid paper and label the length and width in centimeters. They also must calculate and write the area (in square centimeters) inside each rectangle. Two copies of the same problem have been placed on the same page to save paper if you choose to print it out.
 The teacher will read the directions to the students for clarity. All gardens must have a perimeter of 24 centimeters (feet).
 The possible gardens are 6 ft. x 6 ft. = 36 sq. ft., 7 x 5 = 35, 8 x 4 = 32, 9 x 3 = 27, 10 x 2 = 20, and 11 x 1 = 11. The garden with the greatest area is the 6 x 6 square.
 The teacher should make observations about how the students calculated area to give information about their fluency with multiplication and use of strategies.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
 The teacher will ask the guiding questions "Which rectangle had the greatest area and why? Is this always true?"
 The teacher will ask students to look for patterns they noticed during the activities. Possible answers could include "As the length increased, the width decreased." or "As the width increased, the length decreased.", "The longest length was always 1 less than half the perimeter (because a side cannot be 0 units long), and "The square has the same length and width which will always create the greatest area when multiplied."
 The guiding question, "Why did the perimeter stay the same for each rectangle but the area change?" should be discussed. Possible answers include, "We had the same length of string. In the long rectangles the squares only shared one edge. We counted the outside edges and each garden had to have 24 feet. In the square shape the edges were shared so we didn't need as much string for the perimeter."

Summative Assessment
The teacher will have the students complete an Exit Ticket in their journals or on paper to determine if the students can find the area of several shapes having the same perimeter. The teacher will also be able to determine the strategies the students used for finding area. Are the students measuring area by counting individual squares, skip counting by the number of squares in each row or column, or by multiplying the length and the width? They could be using the Distributive Property to solve products that they don't know. This will determine each student's level of proficiency.

Formative Assessment
As the students are creating rectangles from the string and recording their data, the teacher will be able to determine if the students are correctly applying the formulas for area and perimeter. The teacher will also be able to check for accuracy of their calculations. The teacher will be able to check students' understanding that not all rectangles with the same perimeter have the same area as they prove that with this activity. The teacher can focus attention on any student struggling with discerning the difference between perimeter and area and what each is a measurement of, as well as offering strategies for calculating. Additional strategies for calculating area and perimeter can be found in the Accommodations section.

Feedback to Students
While completing the Guided Practice, the teacher will provide feedback while circulating around the room. The teacher will also bring the students back together to have them list all the possible areas they were able to find with the string. The teacher will pose questions to the class to will discuss why all the shapes have the same perimeter of 16 inches. The teacher will also pose questions to gather information about which shape had the greatest area. The feedback given to the whole class as these questions are discussed will help the students clear up any misconceptions prior to moving into Independent Practice.
Assessment
 Feedback to Students:
While completing the Guided Practice, the teacher will provide feedback while circulating around the room. The teacher will also bring the students back together to have them list all the possible areas they were able to find with the string. The teacher will pose questions to the class to will discuss why all the shapes have the same perimeter of 16 inches. The teacher will also pose questions to gather information about which shape had the greatest area. The feedback given to the whole class as these questions are discussed will help the students clear up any misconceptions prior to moving into Independent Practice.
 Summative Assessment:
The teacher will have the students complete an Exit Ticket in their journals or on paper to determine if the students can find the area of several shapes having the same perimeter. The teacher will also be able to determine the strategies the students used for finding area. Are the students measuring area by counting individual squares, skip counting by the number of squares in each row or column, or by multiplying the length and the width? They could be using the Distributive Property to solve products that they don't know. This will determine each student's level of proficiency.
Accommodations & Recommendations
Accommodations:
 Students who are experiencing difficulty with finding perimeter can use counters or base ten units placed along the outside of each rectangle. They can make a group out of the counters along each side. This will be helpful when they write the addition sentence and ensure that the perimeter remains constant with each rectangle.
 Students who are experiencing difficulty with finding area by multiplying can count the squares on the inside of each rectangle.
 Students who need more of a challenge can be encouraged to create nonrectangular shapes, as long as they are composed of all right angles, known as rectilinear figures (for example, an L or an E). They can decompose these figures into 2 or more nonoverlapping rectangles, multiply to find the area of each one, and add the partial areas together to find the total area.
Extensions:
 Students can play the PBS Kids Cyberchase Airlines Builder game on the computer.
 If students are able to find perimeter and area fluently, they can play FunBrain: Shape Surveyor on the computer. They can choose Perimeter, Area, or Area and Perimeter.
 Students can create rectangles, squares, or any other shape with only right angles on the National Library of Virtual Manipulative's Geoboard. Students can calculate the perimeter and area and then click the measures button to check their answer.
 On another day, students can investigate if shapes with the same area can have different perimeters.

Suggested Technology: Document Camera, Computer for Presenter, Computers for Students, Internet Connection, LCD Projector, Overhead Projector, Adobe Flash Player, Adobe Acrobat Reader, Microsoft Office, Java Plugin
Special Materials Needed:
 Inch Grid Paper
 Centimeter Grid Paper
 Exit Ticket
 Area and Perimeter Recording Sheet
 yarn or string cut into 16inch sections for each student pair
 string cut into 4 1inch sections
 string cut into a 12inch section
 colored pencils or crayons for students
 chart paper with a larger version of the Area and Perimeter Recording Sheet drawn on it
 markers
Further Recommendations:
 Have the yarn or string cut prior to the lesson.
 Prepare the string and the crayons or colored pencils for each student pair in baggies to save time.
 Prepare the large chart for the Area and Perimeter Recording Sheet with the headings Length, Width, Perimeter, and Area.
 Have the PBS Cyberchase video The Dumas Diamond set up prior to the lesson.
 Decide how you are going to have students answer the Exit Ticket. They can be given the half sheet of paper to write on, they can paste the half sheet in their journal and answer there, or students can copy the problem down.
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in Mathematical Practices MAFS.K12.MP.1.1 (Make sense of problems and persevere in solving them) and MAFS.K12.MP.7.1 (Look for and make use of structure) because students will be asked to analyze relationships, use different strategies to solve a problem, and will be looking for and making use of mathematical structure.
Source and Access Information
Contributed by:
Susanna Strickland
Name of Author/Source: Susanna Strickland
District/Organization of Contributor(s): Palm Beach
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.