Finding the Area of a Parallelogram
Lesson 2 of 17
Objective: SWBAT find the area of parallelograms by using square units and the area formula.
The students will be working on a problem from NCTM’s illuminations. Students will need grid paper to help them visualize this problem. There is a chart to help keep track of their information. Allow students to read through the problem on their own. Begin by displaying a 1 x 2 rectangular table. (you can use pattern blocks or grid paper to do this.) Ask students “how many students can fit around the rectangular table?” Students should say 6. Then ask students “what does 6 represent?” Students should see that 6 represents the perimeter. If they don’t come up with this, then ask them this way “if 6 people fit around the outside of the table, what would this mean mathematically?” Then ask the students to look at the problem to figure out what perimeter Tanya will need to use. They should see in the problem that Tanya is using a perimeter of 18 because 18 people can fit around the rectangle. Students will be implementing MP2 by deciding what the numbers mean. Once students figure out that the perimeter must be 18, allow them time to work in their groups to determine the least amount of tables that Tanya will need. Students may need to know that they need to find the area of a rectangle with a perimeter of 18. They can use the grid paper and the chart to assist them with this problem (MP4). By drawing out the tables and determining the area, students should see that 1 x 8, or 8 tables would be the fewest amount of tables needed for this party.
Tools: Grid paper, square pattern blocks, Tables at a birthday party problem.
Students will be using the parallelogram in their notes as a guide. Tell students that we are going to use square units to determine the area of a parallelogram. Give each student a centimeter square (from the base 10 blocks) to find the base of the parallelogram. Students will place the square units on the parallelogram in their notes. As students are doing this, watch to see that they start and end at the appropriate place. Then tell students to continue building upon that bottom row. As students build to the top of the parallelogram, ask them what they notice? Students should see that they have created a rectangle. Ask students if they can tell how tall their parallelogram is? Students should be able to see that the height of the parallelogram is the same as the width of the rectangle. Show students the slide that has the triangle part of the parallelogram highlighted. Ask students what would happen if we cut off the triangle and moved it to the other side? Students should see that by doing this we changed the rectangle into a parallelogram. Therefore, finding the area of a parallelogram is similar to finding the area of a rectangle. The difference is that the height of the parallelogram must form a right angle to the base, just like a rectangle. Finding the height of a parallelogram, given both side length and height, is a common misconception with students. I like to say this to the students. When you go to the doctor and they want to measure your height, what do you do? Students will say they stand up straight and then get measured. I say, exactly. We don’t get measured on a slant (then I bend over and show them how this would look!) Then I say, when determining the height of a parallelogram, we need to look for the part that is straight up and down, or that forms a right angle to the base.
Tools: square unit manipulatives, finding the area of a parallelogram notes and power point.
Using the Area Formula
Show students the area formula. Ask them this, “can we use this formula to find the area of a rectangle?” Students should say yes, because the base and height of a rectangle meet at a right angle. The formulas are the same, they just look different. We proved this while using the square units earlier. There are three problems for the students to work on in their notes. Remind students that to be precise with their answers will require them to use a label.(SMP 6) They may get confused with the problem that has no unit of measure. Tell them that when this happens, we can use the generic term “units squared”.
Tools: Finding the area of a parallelogram power point and notes
Numbered Heads Together
I’m using Numbered Heads Together as an informal assessment. Students will use white boards to show me their solutions. During the NHT, students will need to apply the formula. I will be looking for them to use the appropriate base and height. I should see 2 numbers being multiplied together to get the solution and I will be looking for them to use the correct label.
Each of these problems gives them both side lengths and height. Students will need to determine which number to use. By using the formula and understanding what numbers to use, students will be implementing SMP 1 and SMP2. Applying the numbers to the formula will be implementing SMP4.
NHT also supports SMP3 by having the students justify their answers to a tablemate.
Tools: NHT questions (in the power point)
I would like the students to draw their own parallelogram, assign units of measure and then determine the area. Students will then need to explain in words how they know their solution is correct (SMP 3)
I chose this as the closure so I could see if students understood what a parallelogram looks like and if they could assign numbers to a base and height to determine the area. Students should then be able to explain that they multiply the base and height together to get the area of their parallelogram. They should also use the correct label as part of their solution.
Tools: Closure problems