Around or All Over
I. Objectives:
Students will develop the concept of perimeter and area by using color tiles to build rectangles. Students will develop meaningful formulas for the area and the perimeter of both squares and rectangles and extend the concept to the perimeter and area of irregular figures.
II. MT Content and Performance Standards
-Mathematical Content Standard 4
Students demonstrate an understanding of shape and the ability to use geometry
-Benchmark 1
Identify, describe, construct, and compare plane and solid geometry figures
-Mathematical Content Standard 5
Students demonstrate understanding of measurement attributes and an ability to use
measurement processes
-Benchmark 3
Apply the concepts of perimeter and area
-Benchmark 6
Demonstrate relationships between formulas and procedures for determining
area and volume
III. Materials:
Color Tiles – a minimum of20 per group, Overhead Color Tiles, Around or All Over worksheet- one per student, Transparency of worksheet, transparency of graph paper, graph paper – one per student, overhead.
IV. Lesson Plan: Day 1
a. Lesson Objectives
1. Students use tiles to model figures with given dimensions and determine the figures perimeter and area.
2. Students will generalize their discoveries and write a verbal model for finding the perimeter and area of the figure.
3. Students will use their verbal model to write a formula to find the perimeter and area of a square and rectangle.
b. Students will work with a partner. Each pair of students will receive a bag of
Color Tiles.
i. Have students model 2 x 3 using their tiles. Ask students to compare their model with their partners. Ask for a volunteer to show their model on the overhead with the overhead color tiles. Discuss why the model has ‘2 rows of 3 tiles each’.
ii. Show how you build the rectangle – 2 rows of 3 tiles each. Help students make the connection that they are building rows of tiles. Discuss the connection between the model of 3 x 5 and the dimensions of a 3 x 5 rectangle. Ask students to explain the similarity of the models – 3 rows of 5 tiles each.
iii. Have students model a rectangle that is 3 x 3. Ask: “Is this a rectangle?” Review with students the terms: rectangle and square. NOTE: Watch students build the square. Be sure they are building 3 rows of 3 tiles – not building the outline and filling in the middle. This will help them when they find the perimeter and area of irregular figures.
iv. Have students determine how far it is around the square. Ask what term can be used to describe the distance around a figure.
v. Discuss how the term “area” describes the interior region of the figure. Have students count the number of tiles used to make up the interior of the square or how much space was covered.
vi. Review the following additional vocabulary: verbal model, variable expression.
c. Pass out the worksheets and explain the lesson objectives to the students. They will use the tiles to create rectangles and squares of specific dimensions, then complete the chart, and reflect on how to determine the perimeter and area of their models.
d. Have students begin the activity. The teacher should circulate around the room to facilitate students.
e. Last 7 minutes, have students reflect on how the building of models connects with the variable expressions they developed for finding perimeter and area...
V. Lesson Plan: Day 2
a. Lesson Objectives:
1. Review the verbal model and variable expressions for determining the perimeter and area of rectangles and squares
2. Determine the perimeter of irregular figures with right angles using the ‘combining smaller regions’ or ‘smaller area’ methods.
b. Review yesterdays work. Discuss the verbal models and the variable expressions that students developed the previous day.
c. Explain the objectives for Day 2. Find the perimeter for irregular figures with the ‘add-on’ and by using the ‘subtract' method.
d. Have students build a 2 x 4 rectangle and a 3 x 3 square. Observe students to see that they are building 2 rows of 4 tiles and 3 rows of 3 tiles. Have students determine their perimeter and compare their answer with their partners. Do the same for area. Discuss how the answers were determined.
d. Model the 2 x 4 and the3 x 3 models being put together. Discuss the perimeter and the area the new model. How did joining the figures change the perimeter and the area? Discuss how the ‘combining smaller regions’ strategy is helpful when finding the area of irregular figures with 90 degree angles but the strategy for finding the perimeter does not change.
e. Have students build a 4 x 5 rectangle as you model it on the overhead. Determine the area of the rectangle. Then remove a 1 x 3 section and have students do the same and determine the area of the section that was removed. Find the area of the remaining model. Discuss how an area can be found by either ‘Add-On’ or Subtract’ method.
f. Put the overhead of the grid paper on the projector. Ask for a volunteer to show how you could model the problem on the graph paper using the ‘Add-On’ method. Discuss. Ask for another volunteer to show how you would how model the problem on graph paper using the ‘Subtract’ method.
g. Have students turn to Part E. of the worksheet. Have students complete the problems using graph paper to model thee dimensions of each figure. They should do two problems using the ‘Add-On’ method and two doing the ‘Subtract’ method.
h. As students complete the worksheet, the teacher should facilitate the groups in their solving the remainder of the worksheet. Have students use a separate sheet of paper to journal the last question, “Explain why this worksheet is entitled “Around or All Over” and as to whether they prefer the ‘Add-On’ or the ‘Subtract’ method with irregular figures".
V. Summary
Students will learn how to find the area and the perimeter of squares and rectangles.
They will understand the concept of perimeter vs. area. They will apply this
Knowledge to irregular figures.
VI. Assessment
Day 1 Assessment: Observe students’ fluency building models and completing the chart correctly. Have student’s journal regarding the connections they made between building the models and calculating the perimeter and area with a variable expression. Lastly, verify the student’s ability to correctly chart in the lesson.
Day 2 Assessment: Observe students’ fluency in building and sketching models with ‘adding-on and taking off’. Have students journal about which method they prefer and why.
Overall Assessment: Continuing assessment of the activity will occur as students solve test questions on the chapter1 test and as they continue to work on problems dealing with the topic of area and perimeter throughout the year.
Around or All Over
A. Build each square and complete the chart.
Left Side Length / Right Side Length / Top Length / Bottom Length / Perimeter1 x 1
2 x 2
3 x 3
4 x 4
1. Write a verbal model explaining how to find the perimeter of a square.
2. Write a variable expression for the perimeter of a square. (Try to write the simplest expression possible.)
B. Build a rectangle with the following dimensions.
Left Side Length / Right Side Length / Top Length / Bottom Length / Perimeter1 x 2
1 x 3
2 X 3
2 x 4
3 x 4
1. Write a verbal model explaining how to find the perimeter of a rectangle.
2. Write a variable expression for the perimeter of a rectangle. (Try to write the simplest expression possible.)
C. Build each square and complete the chart.
Left Side Length / Right Side Length / Top Length / Bottom Length / Area1 x 1
2 x 2
3 x 3
4 x 4
1. Write a verbal model explaining how to find the area of a square.
2. Write a variable expression for the area of a square. (Try to write the simplest expression possible.)
D. Build rectangles with the following dimensions.
Left Side Length / Right Side Length / Top Length / Bottom Length / Area1 x 2
1 x 3
2 X 3
2 x 4
3 x 4
1. Write a verbal model explaining how to find the area of a rectangle.
2. Write a variable expression for the area of a rectangle. (Try to write the simplest expression possible.)
E. Use graph paper to draw each figure. Find the perimeter. (Drawings are not to scale.)
A. B. C. D.
A / B / C / DLeft Side
Right Side
Top
Bottom
Perimeter
On each of your drawings, show how you could divide each figure into smaller regions OR use the ‘Add On and Subtract’ model to calculate the total area. Find the area.
A / B / C / DArea
1. Explain why this worksheet is entitled “Around or All Over”