Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 47331
Area of a Right Triangle
This lesson uses a discovery approach to explore how find the area of a right triangle by using the formula for finding the area of a rectangle. To
activate prior knowledge, the students will use white boards to draw a rectangle and then cut it into 2 right triangles. To hook the students, review the
Ticket Out the Door responses from the day before. Then, the students will find the area of their rectangles using the formula: A = l x w. Next, as a
whole class, discuss how to find the area of a triangle but multiplying the area of the rectangle by 1/2. Finally, the students will complete a brief
summative assessment.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Suggested Technology: Document Camera,
Computer for Presenter, Computers for Students, LCD
Projector
Instructional Time: 45 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: area, rectangle, triangle, right triangle, formula, vertex, diagonal
Instructional Design Framework(s): Structured Inquiry (Level 2)
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
MAFS.6.G.1.1 Answers Sum Assess1.docx
MAFS.6.G.1.1 Poster and practice sheet.docx
MAFS.6.G.1.1 Sum Questions.docx
MAFS.6.G.1.1AofRectposterREV.docx
LESSON CONTENT
Lesson Plan Template: Confirmatory or Structured Inquiry
Learning Objectives: What will students know and be able to do as a result of this lesson?
By the end of this lesson, students will gain a stronger understanding of finding the area of a right triangle. Students will view a triangle as part of a parallelogram
composed of two copies of that triangle.
Students will compose triangles into rectangles and decompose rectangles into triangles to determine their areas, and justify and find relationships among the formulas
for the areas of different polygons (cognitive level of complexity: level 2).
Students will understand that area is additive.
Students will accurately use multiplication and division to calculate area.
Students will accurately record the area of each right triangle.
page 1 of 4 MAFS.6.G.1.1 A of Rect poster.docx
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should:
be able to calculate the area of a rectangle using the formula: A = length x width and know why this formula works.
know the unit of measurement used for area is the square units, including what is meant by square units.
be able to solve multiplication and division of whole numbers.
recognize geometric figures, including triangles and rectangles.
be able to label the vertices of a rectangle.
have some ability to make sense of problems and persevere in solving them as they do math.
address different cases for rectangles: a length is a side of a rectangle and the width is perpendicular to the length.
Guiding Questions: What are the guiding questions for this lesson?
How can you find the area of a rectangle? (length x width) Why does this formula work? Does it always work?
What unit of measurement is used for area?
How can we use the area of a rectangle to find the area of a right triangle? (once we know the area of a rectangle, we multiply by 1/2) What are we trying to find in
this problem?
Introduction: How will the teacher introduce the lesson to the students?
The "Hook" and Activation of Prior Knowledge
Open the lesson with the Formative Assessment: ticket out the door from yesterday. Ask them to tell you how to find the area of a rectangle and explain why their
strategy or formula works.
Tell them the results of Ticket Out the Door. Respond to any errors by mentioning the error and asking if any student can find the error, explain why a student might
make this error, and provide the correct answer.
Be sure to stress that the unit of measure for area is "square units". For example, if a student miscalculates a multiplication fact, ask the group how it can be corrected.
Investigate: What question(s) will students be investigating? What process will students follow to collect information that can be
used to answer the question(s)?
Explain to the students that our class was challenged with making a 6th grade banner to hang in the front office. Tell the students that the principal gave you a template
so the first thing they need to figure out is the shape of the flag and how much material to purchase. Ask the students to tell you the shape of the template. (triangle)
The teacher should create a 15 in. x 10 in. rectangle template to display and show the students.
Ask the students how they would figure out how much material to purchase. (find the area of the template) Tell the students to work with their partner to find the area
of the triangular template. (One possible solution is to trace the template onto a sheet of graph paper and count the squares. Another solution strategy would be to turn
the triangle into a rectangle. They can then use the formula to find the area of the rectangle and multiply by ½ to find the area of the triangles.
Ask selected students to report their answers and explain the strategies for finding the area. Finally, have the students tell you the area in inches of the template.
(Solution: ½ x 15 x 10 = 75 inches squared)
Ask students if they know of another strategy to find the area of a triangle once they find the area of a rectangle. (length x width divided by 2)
How is this like/different than the area of a rectangle? Why?
Ask the students why they should use that strategy.
Analyze: How will students organize and interpret the data collected during the investigation?
Circulate around the room to observe and help students. As you circulate, make notes of the specific examples you wish to show during the closure.
The following discusses Student Feedback that can be given. Questions might include,
"How are you organizing your work so that you can clearly see your answers?"
"How do you use rectangles to find triangles?"
"How do you find the area of a rectangle?"
"What is the formula for finding the area of a right triangle?" "Why does it work?"
"What operation do you use to calculate the area of rectangle? Why do you use this?"
"What 2 operations do you use to find the area of a triangle? Why do you use this?" "What roadblock is stopping you from finding the area of the triangle?"
"Once you find the area of the rectangle, how do you find the area of the triangles?"
"What piece of knowledge about area does this activity point out?"
Check to see the students are recording their work in an organized efficient manner. They could be using the formulas to calculate the area. If so, be sure they
understand why the formulas work.
Scaffolding questions might include,
"Which number is the length? Width?"
"What operation do you use to find the area of a rectangle? Why?"
"Once you find the area of a rectangle, how do you find the 2 triangles?"
Closure: What will the teacher do to bring the lesson to a close? How will the students make sense of the investigation?
Using the document camera, show one of the students' work. Ask the student to explain his/her thinking on how they found the area of a triangle.Use the Guiding
Questions to help clarify student thinking and the ability to explain.
Be sure to discuss the necessity of finding the 2 congruent triangles. Write the response on the board so the students can copy it into their notebooks. Be sure to show
the most efficient strategies (when multiplying the product of the length x width, they can multiply by 1/2 or divide by 2).
page 2 of 4 Ask the students why someone would want to solve the problem these ways. While the students may note some worthy similarities, the following should be
highlighted:
Every strategy involves breaking apart (decomposing) the area of the rectangle into 2 equivalent pieces/triangles.
Some strategies for finding area are more efficient (strategic) than others.
Be sure students have pieces of knowledge written in their notebooks and applaud their hard work and brilliant thinking. Suggest they go home and tell everyone they
are math superstars.
Administer the summative assessment. This attachment is found in the Summative Assessment section of this lesson.
Summative Assessment
Listening to student conversations during the Guided Practice and the Closure will provide a teacher information on the students' understanding. A more formal
assessment is attached. The questions require reasoning and explanations. Answering 3 out 4 questions would indicate a strong understanding of the topic. Please see
the answer key for model responses to the explanations, including the correct unit of measure.
Summative Assessment
Summative Assessment Answers
Formative Assessment
The day before you plan to implement this lesson, conduct a quick assessment that focuses on the students knowledge of finding the area of a rectangle. On a sticky
note, ask the students to draw a rectangle, label the length 8 cm and the width 3 cm. Then, calculate the area. When finished, they give you their sticky note (their
Ticket Out the Door).
A quick check the day before will give you time to assess which students are confused and what misconceptions some students still have. The students who still do not
know how to identify the length and width, or calculate the area of a rectangle, should be pulled into a small group before the whole group lesson the next day and
shown how to identify length and width and calculate the area using the formula A = l x w. They must include the label for measurement of area, which is square units.
Feedback to Students
During the activity, circulate among the students to monitor their work, probe their thinking and scaffold the task for students needing assistance.
For example, if the students cannot calculate the area of a rectangle, ask them to explain the meaning of area then write out the formula. If the students have difficulty
calculating the area of a right triangle, ask them to write out what part of the formula they do know.
If a student cannot multiply a whole number by 1/2, ask them to tell you what happens when you cut a rectangle in 1/2. How many pieces to you get? Tell them they
divided the rectangle into 2 equivalent pieces.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations: A teacher could create additional Area of Rectangles practice sheets to be done.
A model/paper could be created which scaffolds how to finding the area of a rectangle, followed by finding the area of a triangle. Posters of the formulas for area of a
rectangle and area of a triangle.
Check for understanding.
Visually organize the formula - put a box around the width and a circle around the length.
MAFS.6.G.1.1 Poster and practice sheet.docx
Extensions: When students show they understand how to find the area of a right triangle, they are ready for more area practice. Have the students go to the Web
site http://nlvm.usu.edu/en/nav/vlibrary.html Go to Geometry and click on grades 6-8. Next, scroll down and click on Geoboard. Instruct your students to use the virtual
geoboard to draw 5 rectangles. Then, they must find the area of each figure and then divide it into 2 congruent triangles. Find the area of each triangle. You may need
to demonstrate the use of the virtual geoboards.
Suggested Technology: Document Camera, Computer for Presenter, Computers for Students, LCD Projector
Special Materials Needed:
math notebooks/journals, pencils
Further Recommendations: You may wish to keep a clipboard nearby to record which students struggled with the concept so you can work with them in a small
group later. You may also want to make note of specific students to spotlight.
Classroom Management Tips:
You may let those who complete the activity practice their communication skills by helping another student.
Using the camera to take and post pictures of student work helps motivate students to record clearly.
Additional Information/Instructions
page 3 of 4 By Author/Submitter
This lesson also addresses Math Practice Standards: MAFS.K12.MP.1.1; MAFS.K12.MP.4.1; MAFS.K12.MP.6.1 by: Math Practice 1: make sense of problems and persevere in
solving them = is evident in this resource as students ask questions and reflect on their work Math Practice 4: model with mathematically = is evident in this resource as
students use formulas to find Area and include square units. Math Practice 6: attend to precision = is evident in this resource as students think about the problem before
starting to solve it. They demonstrate this by correctly labeling their rectangles with length and width.
SOURCE AND ACCESS INFORMATION
Contributed by: Cassie Meyers
Name of Author/Source: Cassie Meyers
District/Organization of Contributor(s): Flagler
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.G.1.1:
Description
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and
mathematical problems.
page 4 of 4