Introduction to Triangle
and Parallelogram Area
Grade 7 math
(This lesson is to be covered in 2 periods)
General Outcome: Use direct and indirect measurement to solve problems.
Specific Outcome: Develop and apply a formula for determining the area of triangles and parallelograms.
Specific Cognitive Outcome: Students will manifest a spatial comprehension by representing, explaining and verifying geometric constructions such as squares, rectangles, parallelograms, triangles and trapezoids. Students will understand how these constructions have common elements and how to compose and decompose them.
Specific Affectivity Outcome: Students will share their reasoning for finding the various geometric shapes. Also since the problems of this lesson are puzzles, they will have fun while doing mathematics!
Basic Resource / Material Needed:
scissors, SMART board, cardstock pieces with tangram outline and grid printed (see Appendix 1), envelopes
(This lesson is to be covered in 2 periods)
General Outcome: Use direct and indirect measurement to solve problems.
Specific Outcome: Develop and apply a formula for determining the area of triangles and parallelograms.
Specific Cognitive Outcome: Students will manifest a spatial comprehension by representing, explaining and verifying geometric constructions such as squares, rectangles, parallelograms, triangles and trapezoids. Students will understand how these constructions have common elements and how to compose and decompose them.
Specific Affectivity Outcome: Students will share their reasoning for finding the various geometric shapes. Also since the problems of this lesson are puzzles, they will have fun while doing mathematics!
Basic Resource / Material Needed:
scissors, SMART board, cardstock pieces with tangram outline and grid printed (see Appendix 1), envelopes
(period 1)
Introduction – 5 minutes
I will explain to the students that we are doing a hands-on activity today and I will ask who has played with a tangram before. I will give a tangram cardstock piece to each student and show them which shapes to cut out and ask them to ignore the grid lines for now.
Activity 2 – 20 minutes
The students will cut out the tangram pieces and start with the first puzzle (presented on the SMART board). The students are expected to sketch their solutions in their notebook.
Activity 3 – 5 minutes
In a plenary group, I will ask for volunteers to come present their solution to the first puzzle on the SMART board, as the shapes are manipulable.
Activity 4 – 15 minutes.
We will continue with the second and third puzzles (repeat the same shapes but with the 5 smallest tangram pieces, then all 7 pieces). Finishing these puzzles will be homework. There is also an extra puzzle available for those who finish early. I will give envelopes to the students so that they can keep their tangram pieces safely.
While the students work, I will go around the room and check that they are making the right shapes. I will also provide encouragement for those frustrated ones!
(Next Class/period2)
Activity 1 – 10 minutes
I will ask the students to take out their sketches from yesterday and I will ask for volunteers to come up and construct them on the SMART board.
Activity 2 – 10 minutes
On the SMART board, I will show various website that use area (a plan of the Eiffel tower, a real estate listing from a house across the school, the specifications from a solar panel). I will lead a class discussion on what area is and how it’s connected to our lives. I will also discuss units of measure for area and how they differ from linear measures (i.e. a 125 m2 house vs. a 125 m house!)
Activity 3 – 20 minutes
On the SMART board, I will have 4 tangram pieces and I will ask for a volunteer to make a rectangle and then a parallelogram. I will also ask the students to make them out of their tangram pieces. I will then ask them to try to estimate the area of each shape by using the grid lines on the tangram shapes. Then I will ask them to repeat this with any 3 and 5 pieces. If some students finish fast, I will ask them to do it with all 7 pieces.
Activity 4 – 5 minutes.
In a plenary group, I will ask for a show of hands to see the various areas that have been found. I will close this lesson by asking if they are surprised that the areas are the same for both the rectangles and the parallelogram and if they think the formula to calculate the area of each will be similar.
While the students work, I will go around the room and check that they are making the right shapes and that they are on the right track to estimate the area of their shapes. If not, I will help them and if they are doing ok, I will encourage them to continue on. Also by going around the room, I will answer questions and offer additional help if necessary.
Introduction – 5 minutes
I will explain to the students that we are doing a hands-on activity today and I will ask who has played with a tangram before. I will give a tangram cardstock piece to each student and show them which shapes to cut out and ask them to ignore the grid lines for now.
Activity 2 – 20 minutes
The students will cut out the tangram pieces and start with the first puzzle (presented on the SMART board). The students are expected to sketch their solutions in their notebook.
Activity 3 – 5 minutes
In a plenary group, I will ask for volunteers to come present their solution to the first puzzle on the SMART board, as the shapes are manipulable.
Activity 4 – 15 minutes.
We will continue with the second and third puzzles (repeat the same shapes but with the 5 smallest tangram pieces, then all 7 pieces). Finishing these puzzles will be homework. There is also an extra puzzle available for those who finish early. I will give envelopes to the students so that they can keep their tangram pieces safely.
While the students work, I will go around the room and check that they are making the right shapes. I will also provide encouragement for those frustrated ones!
(Next Class/period2)
Activity 1 – 10 minutes
I will ask the students to take out their sketches from yesterday and I will ask for volunteers to come up and construct them on the SMART board.
Activity 2 – 10 minutes
On the SMART board, I will show various website that use area (a plan of the Eiffel tower, a real estate listing from a house across the school, the specifications from a solar panel). I will lead a class discussion on what area is and how it’s connected to our lives. I will also discuss units of measure for area and how they differ from linear measures (i.e. a 125 m2 house vs. a 125 m house!)
Activity 3 – 20 minutes
On the SMART board, I will have 4 tangram pieces and I will ask for a volunteer to make a rectangle and then a parallelogram. I will also ask the students to make them out of their tangram pieces. I will then ask them to try to estimate the area of each shape by using the grid lines on the tangram shapes. Then I will ask them to repeat this with any 3 and 5 pieces. If some students finish fast, I will ask them to do it with all 7 pieces.
Activity 4 – 5 minutes.
In a plenary group, I will ask for a show of hands to see the various areas that have been found. I will close this lesson by asking if they are surprised that the areas are the same for both the rectangles and the parallelogram and if they think the formula to calculate the area of each will be similar.
While the students work, I will go around the room and check that they are making the right shapes and that they are on the right track to estimate the area of their shapes. If not, I will help them and if they are doing ok, I will encourage them to continue on. Also by going around the room, I will answer questions and offer additional help if necessary.