Area of Shapes on the Coordinate Grid

Students work in pairs on the Think About It problem.  After 4-5 minutes of work time, I bring the class back together.  First, I ask for a volunteer to offer his/her paper for the document camera.  

I project the coordinate grid, and ask students to vote about whether the figure is graphed correctly.  Students have not had practice with graphing ordered pairs since our unit on the coordinate plane, so I will spend time talking through each vertex, if it seems like the class needs a refresher.

The goal of this problem is to get kids ready to work with perimeter and area on the coordinate grid. 

In this lesson, students will use their knowledge of the coordinate grid, along with the area formulas they've learned in this unit.  

These are the steps that students will follow, as they work through problems:

• Plot the vertices on the coordinate grid and label each vertex with a given letter
• Connect the points in the order in which they are plotted
• Check to ensure that the shape formed is the shape described in the problem
• Label the dimensions of the shape by counting the number of units that measure the dimensions
• Write the appropriate formula for calculating the area of the shape, substitute in the given information, and simplify to determine the area
• Include appropriate units on the answer 

Students may also calculate the area by counting the number of square units inside the shape when finding the area of squares and rectangles.  For other figures, they can count units to get an estimate of the number of square units, but they cannot rely on this strategy to come to the final area. 

For the first problem in the Intro to New Material section, I have students plot the points on their own, before showing my paper on the document camera.  Once students have drawn their trapezoids, I pepper the class with questions to have them lead us through finding the area (what's the formula, what are the lengths of the bases, how did you determine the lengths, what's the height, how would you simplify this, what are the units, etc.)

Students work in pairs on the Partner Practice section.  As they work, I circulate around the room and check in with each group.  I am looking for:

• Are students plotting points correctly?
• Are students labeling each point as they go?
• Are students connecting the points in the order in which they plot them?
• Are students correctly identifying or creating the geometric figure?  
• Are students correctly identifying the dimensions of each shape?
• Are students correctly applying the area formula and calculating the area of a figure?
• Are students showing all of their work, including the substitution, when they find the area of each figure?
• Are students including units on their answers?

I am asking:

• How did you determine the dimensions of the shape?
• When did you know this was going to be a (name of the specific shape in the problem)?
• Why isn't this a (a different quadrilateral)?
• How did you determine the area of the shape?  What is the formula for finding the area of this shape?
• Why did you use square units?

A trapezoid sample for Problem C is included.  The student's written work says "How I know the point I plotted represents the fourth vertex for a trapezoid is because it has one pair of parallel sides."

After partner practice time, students independently complete the Check for Understanding problem.  I pull a popscicle stick as a way to randomly select a student's paper to display on the document camera.  The class gives the student positive and critical feedback on the work. 

Students work on the Independent Practice problem set.  As shown in the student work sample, students graph and label the points and then show all of their work with the formulas in the space below the grid.

As students work on Problem 4, I ask students if they could have drawn the parallelogram in any other way.  Some students will draw a rectangle, and I ask them to prove to me that they have a parallelogram.

Problem 12 can be difficult for students because there is not a coordinate grid included with the problem.  I let students struggle a bit with this, as we'll talk about it at the end of independent work time. 

After 20 minutes of independent work time, I bring the class back together to discuss Problem 12.  I have students share out how they decided to attack the problem.  After hearing strategies from one another, I have students work in pairs to check their work and adjust their answers if they'd like.  

Students complete the Exit Ticket independently to close the lesson.