The Ins And Outs Of Area And Perimeter

Designed by: Andress Carter-Sims , Burton Pack Elementary

1) Core Curriculum Objectives(s): Demonstrate the concept of perimeter and area using manipulatives.  (5GS5-1 )

Grade level: Five      Subject: Math

2) Overview: Students will explore area and perimeter through the exploration style of teaching using eatable and non-eatable manipulatives. Students will draw area and perimeter shapes to model the concept. Written explanations of how area and perimeter are found will be required. The modeling of how the formulas can be used to find the area and perimeter of regular shapes will also occur during the lesson.

3) Focus Essential Questions(s): How do you find the area and perimeter of regular and irregular shapes?  What process do you use to create a shape with a given area and perimeter?

4) Time Frame: Six One Hour Class Periods.

5) Resource Materials:

Paper towels

Overhead polyominoes

Ritz Cheese It Crackers or any square crackers

Centimeter grid paper

White drawing paper

Pencil

Crayon or Markers

Square tile manipulatives for students

Dry erase board for each small group

Dry erase marker

Cut out paper squares or magnetic square tiles *Note: used for modeling, discovery and exploration of lesson 

Houghton Mifflin glossary (optional) or dictionary to define the terms

http://www.funbrain.com/poly/index.htm/

6) Culminating Assessment: During the first task of the culminating assessment students will determine the area and perimeter of irregular and regular shapes. During the next task they will be asked to create regular and irregular shapes that have a specific area and perimeter. Students must label the length and width of their shape for evidence.  *Note: White plain drawing paper should be used to create or determine the area and perimeter of regular shapes.Centimeter or inch grid paper should be used for irregular shapes.

Finally, the students will be asked to write an explanation describing the process they used to determine the area and perimeter of irregular and regular shapes. *Note: A regular shape has four sides and the opposite sides must be the same lengths.  Irregular shapes may have more than four sides and all sides may but do not have to have the same length.

**While using square tiles in this activity they are referred to as irregular shapes and no formula is used to determine the area and the perimeter. 

** When a shape is drawn and the opposite sides are the same length they are referred to as regular shapes and the formulas provided may be used.

“The Ins and Outs of Area and Perimeter” Rubric

Assessment Charts

For drawing of specific area and perimeter, provide grid paper for irregular shapes.  Use plain white paper for regular shapes.

The teacher can decide the specific measurements.

7) INSTRUCTIONAL ACTIVITIES:

Activity One: The teacher will begin the activity through the discovery style of teaching.  The teacher will place a single magnetic square tile on the board or a cut out square.  The students should then be told that the area is one and the perimeter is four.  The teacher should then label this on the board so the students can see this visually. *Note:  During this time students are not required to provide a response.  Students should only listen very carefully.

The teacher will then provide another visual during the discovery phase.  Next two square tiles should be placed on the board. The second square tile may be placed so that the shape continues vertically or horizontally.  Place does not matter, the area and perimeter will be the same. *Note: Magnetic or cut out squares may be used during the demonstration. The tiles should touch each other and they must be side by side evenly.  The teacher will then tell the students that the area has changed as well as the perimeter with this new shape.  The students should be told that the area is now two and the perimeter is six.  *Note:  Students still do not need to do anything.  Once again the teacher should label the shape with its area and perimeter on the board so that students can view the change visually.

Now the third shape should be created on the board using three square tiles.  *Note:  If your second square was placed horizontally, continue your shape with the third square in the same direction. If your second square was placed in the vertical direction then continue vertically.  The teacher will again prompt the students by saying that the new area for this shape is three and the perimeter is eight.  A label should then be placed under the second shape.

The teacher is now ready to go on to the forth shape.  The teacher can actively engage the students in a “success maker” activity by asking the students “easy” questions. The success maker technique gives students the feeling that they will be able to learn new information.  *Example: How will the fourth shape look? How many squares do I need to use?  Will you come up and create the fourth shape for me?    Once the fourth shape has been created with all four squares side by side either vertically or horizontally the students are now ready to be questioned.  The teacher will not provide the area and perimeter for the fourth shape but will ask students for their predictions first.  The teacher should record several predictions on the board for all students to visually see.  After recording several responses the teacher will ask those students that did not provide a response do they agree with any answer that was placed on the board.  The teacher will then have some students to explain how they came up with their answer. The teacher will now provide the students with the answer. *Note:  The area for four squares is four.  The perimeter for four squares in a straight vertical or horizontal line is ten.

The teacher is now ready to guide the students through their own creation of a definition for area and perimeter.  Following the creation of their definition for area and perimeter they should refer to their math dictionary (located at the back of the students math books) to discuss their similarities.

The teacher will now explain with each model (irregular shape) on the board how the area and perimeter were found.  *Note:  The area is the number of squares that were used.  The perimeter is the number of sides on the outer shape or the distance around the shape.

Activity Two: Students should now be placed into groups of two or three.  Each group should have a total of ten squares. Students will begin to create irregular shapes and locate the area and perimeter. Taking turns one person in the group will start of with one tile placed on the desk.  They will explain and demonstrate how they found the area and perimeter to their group members.  Once they have shared with the group, they will record the area and perimeter on the group chart.  The next person will place two squares together and explain to the group what they think the area and perimeter are.  Once they have completed the discussion they may record the area and perimeter on the group chart.  The next person will place three square tiles together and again explain the process they used to get the area and the perimeter.  Once they have explained their process they may record on the group chart.  The teacher should monitor the groups during the activity and assist where needed.  The students should continue until they have completed the chart below. 

GROUP AREA AND PERIMETER CHART FOR IRREGULAR SHAPES

Once each group has completed the task the teacher should use cut out squares or the magnetic square tiles on the board to demonstrate the answer for each. 

Activity Three:

Now the teacher will guide the students into creating shapes using squares that are not going either vertically or horizontally.  *Note:  Although the squares will not be placed in a straight line they must be placed evenly beside, underneath or on top of the next square.  Example: The squares can be placed to form a “L”, “T”, “U” or an “E” shape etc.  Students can still use the same techniques to determine the area and the perimeter. 

To introduce students to locating the area and perimeter of shapes (squares) that are not going in a straight line the teacher will begin by using the overhead polyminoes.  After the students are shown all of the polyminoes they will figure out that the area for all of them are the same but the perimeters are different for some of them.

After the overhead demonstration, students will create a shape on their desks.  Next they will draw the exact shape on their centimeter grid paper.  The teacher will then instruct the students to label the inside of each square to model or display the area.  To display or model how the perimeter is located, they will place a number outside of each side around the outside of the shape.  *Note: Having the students go around the outside will demonstrate the distance around the shape.

The teacher should require that students create a minimum of ten shapes.  *Note:  Crayon or markers can be used during this time for the labeling of the area and perimeter.

Once each students has completed the task they should be placed into groups of four or less.  While in these groups students should check each other’s work and provide assistance where needed.

Activity Four: 

To introduce students to the formula for area and perimeter the teacher should draw a rectangle or a square on the board. *Note: The shape that the teacher chooses to draw must be drawn so that the opposite sides or the same length. (Regular Shapes)

After the teacher draws the shape, the opposite sides must be labeled with a measurement. *Example: The lengths may be labeled 7 inches and the width may be 9 inches.  Now the teacher is ready to place the formulas on the board.  The formula for area is length times width (L x W) and the formula for perimeter is two times the length plus the width 2x(L+W).

Once the shape has been placed on the board and has been labeled the teacher will model how to plug the numbers into the formula to determine the area and the perimeter.  *Example:  If the length is 7 inches and the with is 9 inches the teacher will explain how the “L” should be replaced with the 7 and the “W” should be replaced with the 9 to get an area of 63.  For the perimeter the same replacements should happen and the perimeter will be 32.

The teacher should model several shapes making sure that the opposite sides are the same lengths.  Any unit of measurement may be used such as foot, yard, inch, centimeter, meter, etc.  As long as students used the formulas and identified the unit of measure they should find success. *Note:  The teacher may remind students who are finding the task difficult to work the formula one step at a time.  First they should plug in the variables and then work the necessary mathematical operations.

Students should now be given centimeter grid paper and ask to create a regular shape with opposite sides the same length.  To reinforce the lesson students should create a minimum of ten.  They should label each with its length and width.  Once they have completed the task they should locate a partner and have the partner determine the area and perimeter of each shape.  Once the partner has completed that task they should check each other’s work.

Activity Five: 

During this activity students will be given a paper towel as well as approximately 45 crackers that must be square in shape.  Students will also be placed into groups of four or less and each group will be given a dry erase board and marker.  Students will take turns being the leader.  Starting with irregular shapes the leader will ask the group to make a shape with a specific area and perimeter. *Example: The leader may ask those persons in the group to make a shape with an area of 4 and a perimeter of 8.  *Note:  During this activity students must be told by the leader if they are creating regular or irregular shapes.  This signals the students to whether or not they need to use the formulas.  Students will use their crackers to create the specific dimensions.  Once each student in the group has completed the task the leader will ask one student to demonstrate what they created on the dry erase board. The group will check to see if the shape meets the specific dimensions.  The teacher will remind the students that some times there is more than one way to meet the specific requirements.  Note: Every one may have something different and they are all correct.  This is why it is important to share what students have created.  Each student in the group should have a minimum of four chances to be the leader in the group. 

Once the teacher feels that the concept as been mastered as best as possible the groups should move to making regular shapes.  *Note:  This is where students should recognize that the formulas for area and perimeter should be used.  Students should be asked by the leader to create a specific area and perimeter. *Example:  The leader may ask students to create a shape with an area of 15 inches and a perimeter of 16.  Note:  The leader must prepare his/her shape with the dimensions and answers before asking the group to create.  The activity will require students to use higher order thinking skills. The teacher should monitor this very closely.  During this activity students will also reinforce their addition and multiplication skills.  Remind students that there is more than one answer in some instances.  Each person should share the different ways they were able to come up with the same answer. 

This activity will take some time so each student should be allowed to be leader at least two times.  Students should again share their answers on the dry erase board.

Activity Six: The students should be assessed from the irregular and regular assessment charts provided.  The teacher should use the rubric to monitor student comprehension of this objective. Note: funbrain.com/poly/index.htm/ is a web site that can be used by students individually or in pairs.  This site can be used as practice during the conceptual phase of the lesson or reinforcement after students have mastered and been introduced to the concepts of regular shapes.