Perimeter and Area of Irregular Shapes/Grade 5
What’s That Shape?
Grade Level: 5
Concept Addressed:
TN Curriculum Connection: Standard 4 Geometry and Measurement
GLE 0506.4.1 Use basic formulas and visualization to find the area of geometric figures. Checks for Understanding 0506.4.1 Develop the formula for the area of triangles as it relates to the area of a parallelogram/rectangle. 0506.4.2 Find the area of a convex polygon by decomposing it into triangles/rectangles. SPI 0506.4.2 Decompose irregular shapes to find perimeter and area.
Common Core Connection: Domain 5.NF Number and Operations - Fractions Cluster Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Standard 4.Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. B. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths to find areas of rectangles and represent fraction products as rectangular areas.
Introduction to the Lesson: (DI) (CE) (FA) Teacher will discuss real world applications to perimeter and area. Now that students are able to find perimeter and area, students should know that in the real world shapes would not always be squares or rectangles. Some examples are flooring, such as carpet or tile. Rooms such as kitchens may be square or rectangular to begin with, but once cabinets are put in, the section of the floor that needs to be tiled is no longer a regular shape. Teacher should draw an example of this. Show video from website: http://www1.teachertube.com/viewVideo.php?video_id=20966
Academic vocabulary required for lesson: area, parallel, perimeter,
Concept Development:
Review definitions for perimeter and area. Review formulas for the area of rectangles and triangles. http://www.mathsisfun.com/definitions/ Interactive, allows you to measure in centimeters with a ruler the perimeter of different shapes
Perimeter: The distance around a two dimensional shape
Area: The size of a surface. The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle.
Method 1 for finding area: Count the squares
Method 2 for finding area: L x W
What if the shape is irregular? Examples of Irregular shapes:
Image taken from: http://quake.ualr.edu/schools/guide/append1c.htm
Day 1 Perimeter of an Irregular Shape
Begin by showing the website: (TI) http://www.shodor.org/interactivate/activities/ShapeExplorer/
1. Students count the perimeter of the shapes generated. (These shapes are on a grid.)
2. Students should count the sides and draw representative pictures on computer paper with measurements labeled.
3. Give students geo-board or graph paper with examples of irregular shapes. Students can use markers, colored pencils, or crayons to color the lines of the shape. Students should color the same color lines that are opposite of each other. (Example: vertical lines: red, and horizontal lines: blue.) In this example students should color vertical lines one color, and color horizontal lines another color. Did you draw lines of the same length? Was the total of the broken lines the same as the opposite, unbroken line? (RQ) (SCA)
4. Students can create their own examples of irregular shapes on graph paper, label the measurements and find the perimeter. (They must use actual measurements, and not create their own.) Make sure to color vertical lines red and horizontal lines blue. (SCA)
Image taken from: http://www.ixl.com/math/grade-5/area-of-compound-figures
5. Finding perimeter when a measurement is missing. Students should see that the measurement for the left side is missing. The left vertical line should equal the two vertical measurements on the right. Since the two measurements on the left are 12 and 7 we add these two to get the measurement of the left side. 12 + 7 = 19
Step 1: Check to see if the length of every side is given.
One length is missing.
Step 2: Find the measure of the missing side.
The right side has two measurements: 12 and 7. The right side will equal the left side 12 + 7 = 19. 19 is the measurement of the left side.
Step 3: Add to find the perimeter
Start from the top and work clockwise.
4 yd + 12 yd + 15 yd + 7 yd + 19 yd + 19 yd = 76 yd
The perimeter of the figure is 76 yards.
5. Students can practice the skill on geo-boards, geo-board paper, or the online version http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities
First demonstrate for students
Step 1. Stretch rubber band vertically 8 units long. Move over a few units and stretch rubber band vertically 3 units long; move over a few more units and stretch rubber band vertically 5 units long from the bottom of the second to the bottom of the first. Then have students connect the remaining lines to create an irregular shape. (Horizontal and vertical lines only. Do not include diagonal lines) Students should see that however long their lines are they must match on the opposite side of the figure.
(SCA) Students can draw examples on geo-board paper from: http://illuminations.nctm.org/Lessons/Pick/Pick-AS-GeoPaper.pdf
Day 2 Perimeter of an Irregular Shape
1. Students can practice the skill at the following website. http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html
There are three levels. There is an introduction with review, lesson, and questions.
Practice, Assess, Reteach.
Lesson Wrap-Up: Students should journal the steps involved in finding the perimeter of an irregular shape. Rate from 1 star to 5 stars how well they understand the topic, and tell how they would help another student who was experiencing difficulty in the topic.
Day 1 Area of an Irregular Shape
Finding the area of an irregular shape. Decompose the figure into smaller figures. Then find the areas. (CE)
Begin by showing the website: http://www.shodor.org/interactivate/activities/ShapeExplorer/
1. Students count the area of the shapes generated. (These shapes are on a grid.)
2. Step 1. Divide the figure into two smaller rectangles. (Students should divide the shape using the shortest line possible.) To divide this figure into two separate rectangles the student could divide with a vertical line, or a horizontal line. Using a vertical line is preferable because it is a shorter divide.
3. Step 2. Find the dimensions of each rectangle.
a. The left rectangle is 7 cm by 21 cm.
b. The right rectangle is 12 cm by 5 cm.
4. Step 3. Find the areas of each rectangle.
c. Use the formula A = lw
d. Left A = 7 x 21 = 147 square centimeters
e. Right A = 12 x 5 = 60 square centimeters
5. Step 4. Add the areas
6. 147 + 60 = 207 square centimeters
The area of the figure is 207 square centimeters
Students will need practice in dividing shapes into separate figures, and identifying which measurements correspond with correct figures.
Class should complete together as many as possible before working alone.
Teacher can use http://www.ixl.com on a single computer to complete 20 questions a day.
***Another method for finding the area of an irregular shape is to subtract.
Area of Rectangle – Area of missing section
If the rectangle were not missing a section the area of the rectangle would be:
18 x 23 = 414
The area of the missing section is 7 by 10
7 x 10 = 70
Rectangle – missing section
414 - 70 = 344
The following website has two practice problems. One or both problems would work well to use addition or subtraction, Especially helpful for the subtraction is the problem with a section missing in the middle.
http://studymaths.co.uk/worksheets/40compoundshapes.html
Day 2 Area of an Irregular Shape
Students can practice the skill at the following website: (DI) (TI) (FA) http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html
There are three levels. There is an introduction with review, lesson, and questions.
Practice, Assess, Reteach.
Ø Instruction on curriculum expectations (CE)
Ø Formative Assessment strategies (FA)
Ø Questioning: Reflective of new assessments (RQ)
Ø Student-centered content activities (SCA)
Ø Common Core Connections (CCC)
Ø Technology Integration (TI)
Ø Differentiated Instruction (DI)
Materials Needed: Computer, projector, geo-board worksheets, graph paper, colored pencils are preferable, but markers or crayons will work, Overhead or online geo-board, rubber bands.
Lesson Wrap-Up: Students should journal the steps involved in finding the area of an irregular shape. Rate from 1 star to 5 stars how well they understand the topic, and tell how they would help another student who was experiencing difficulty in the topic.
Reflection: (What worked/what didn’t, Did I reach all students, How could I better check for understanding, were my questioning techniques on level with the new assessments, etc…)
How did students demonstrate that they connected the area of the individual shapes to the area of the larger shape? What words did the students use to demonstrate that they understood the connection?
Research References for Lesson:
TCAP Math Coach book
Interactive websites:
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/perimeter_and_area/index.html
http://nlvm.usu.edu/en/nav/frames_asid_172_g_2_t_3.html?open=activities
http://www.shodor.org/interactivate/activities/ShapeExplorer/
http://studymaths.co.uk/worksheets/40compoundshapes.html
Video:
http://www1.teachertube.com/viewVideo.php?video_id=20966
Worksheets:
http://www.analyzemath.com/geometry_worksheets.html
http://www.ngfl-cymru.org.uk/vtc-ks3-maths-worksheets-ssm
http://www.uen.org/Lessonplan/preview.cgi?LPid=21544
Figures for finding missing measurements for perimeter
Images taken from http://www.ixl.com
Figures for finding area of compound figures.
Images taken from http://www.ixl.com Similar images can be transferred to geo-board paper to make copies for students to draw on.
Math Journal
Rate yourself ______
Topic ______
What I learned ______
Steps: Example Problem:
If another student didn’t understand the lesson, I would:
http://www.primaryresources.co.uk/maths/pdfs/11arearecshape.pdf
http://www.ngfl-cymru.org.uk/vtc-ks3-maths-worksheets-ssm
http://www.suffolkmaths.co.uk/pages/Lesson%20Resources/Shape/20%20Mensuration/Questions%20-%20Composite%20Shapes%2056.pdf