Finding the Area of a Trapezoid
Lesson 4 of 17
Objective: SWBAT find the area of a trapezoid by decomposing it into triangles and using the formula
The students will be completing a memory box. Give students this prompt: in a few moments I’m going to ask you to write down everything you remember about finding the areas of triangles, parallelograms and rectangles. Once you write down everything you remember, put your pencils down. Give students some time to think about what they want to write down. Then ask them to write. I would give them 3 – 4 minutes to write. Once all pencils are down, have them take out their notes to review. This is done independently. Then have them put their notes away and write for one more minute. Once this is done, have the students do an “I have that”. One student will say what is written down in their memory box. If the students have it, they will say out loud “I have that” and mark it off their list. If students don’t have it, they should add it to their memory box. This should continue until all thoughts are crossed off the list. I like this activity because it reinforces concepts that have already been learned. Students feel a sense of responsibility when they are required to “remember” things!
The memory box supports mathematical practices:
SMP1: thinking deeply about a concept
SMP3: using assumptions and previously established results
Before discussing how to find the area of a trapezoid, it may be a good idea to go over the definition of a trapezoid: quadrilateral with 1 set of parallels and can have up to two right angles. Students may want to have a visual for their notes so that is recommended as well.
Students will be using the triangle formula to help them figure out the area of a trapezoid. Instruct students to draw a diagonal within the trapezoid to create two triangles. Then have them find the area of each triangle. Students may have difficulty finding the height. Remind them that the base and height meet at a right angle. Ask them where they see that in the shape? Students should see that the height and base are located outside of the shape using the dotted line. Once they calculate the area of both triangles, ask them how they could find the area of the trapezoid? Students should respond that we would add the two triangles together to get the area of the triangle. (SMP2: understanding what the numbers mean)During this time students should show an understanding of how to use the triangle formula: A = ½(b x h). If they are struggling with this, have them refer to their notes or ask them to recall how we found the area of a triangle. They should know that we composed it into a rectangle and then divided the rectangle in half because we only needed one triangle.
Give students time to practice one on their own. This time the height is indicated by a right angle and it is one of the sides (just in case they don’t see it)
Tools: Using triangles to find area problems, finding the area of a trapezoid notes and power point.
Before discussing the formula for the area of a trapezoid, ask the students what they did when they decomposed the trapezoid into triangles. Students should say they found the area of both triangles and then added them together. This will help them relate to the area of trapezoid formula: Area = the sum of the bases times the height, divided by 2
In this formula, the bases are always the parallel sides. The height is perpendicular to the base and they can add the bases, then times the height, and finally divide. They can also divide any part by 2 and get the same answer. For example: they can add the base divide by two and times the height. They can divide the height by two and then add the bases. Since we didn’t overlay the trapezoids with squares, it is suggested that students say what unit of measurement would be used for a trapezoid. Students should say they will use square units because they are finding the area and we used square units for triangles which make up a trapezoid. (SMP4: using a model to represent the math)
Once you have discussed the formula, have the students practice using the formula to find the area.
Tools: Practice problems, Finding the area of a trapezoid notes and power point
Students will be working on a round table. Each student will be responsible for solving their own problem and then having it checked by a tablemate for accuracy. I chose problems that will increase with difficulty. In the first problem, students will need to recall how to multiply/divide with decimals. In the second problem students will be using whole number lengths. In problems 3 and 4, the students will be dealing with more decimal numbers. Students may need some recall to help them appropriately multiply and divide. The last two problems are real life application problems. The last problem asks the students to use an approximate number. This would be a good time to ask students why they worded the problem like that. The students should recognize that the state of Arkansas is “like” a trapezoid, therefore an exact area cannot be calculated, but an approximate answer will do.
Roundtable supports the following practices:
SMP1: Making sense of the problem
SMP2: Finding out what the numbers tell us
SMP3: Justifying and critiquing the work of others
Closure + Homework
I’m going to have the students writing about the two ways to find the area of a trapezoid. I want the students to be able to say in their own words that the area can be found by decomposing the trapezoid into two triangles. Then finding the area of each triangle and finally adding the two triangle areas together. I want them also to say that they can apply the formula by adding the bases together, multiplying by the height and dividing by two. Asking students to use precise, mathematical language supports MP6. If time permits, the students can share their reflections with a tablemate or partner.
We will be assessing learning for the next lesson, so the students will be given a study guide to help them prepare for their assessment.
Tools: Closure question and study guide