Draw Shapes When Given an Area

Students work in partners on the Think About It problem.  After 3 minutes of work time, I have one student share how (s)he determined the dimensions of the figures they drew.  As the student is explaining, I show the work on the document camera.  I'm also making sure the student uses the language of dimensions, definitions of area and the appropriate units.

This lesson combines what students learned in the Coordinate Plane unit with what they've learned in this unit.

In this lesson, I lead students through Guided Practice problems.  Students will build their own geometric figures that have a given area by using what they know about the properties of shapes, and how we determine the area of each type of shape.

In this section, I ask kids to identify the constraints that each problem presents.  I then have students identify the formula needed to find the area of the figure in each problem.  Once we've identified the formula, students will then use a t-chart to list all of the factor pairs that meet the conditions.  The t-chart is the organizational tool that students learned to use in the Number Sense unit, and it helps to ensure that students list every factor pair.  Finally, students draw the shape on the coordinate grid, using one of the factor pairs they've listed.

Example 1 asks students to create a parallelogram.  The first time we work through the problem, I'll guide students to create a regular parallelogram by off-setting the top a height of 4 units from the base, to the right or left of where the base started.  Then, we'll draw a rectangle which meets the constraints of the problem.  I always was students thinking of alternative ways to represent the problems, and drawing a non-traditional solution is one way students can show a deep understanding of the content. 

For Example 2, I intentionally guide students in a convoluted way to get to the solution.  That is, I purposely construct a triangle that doesn't meet the constraints of the problem.  Once students identify the factor pairs that will result in a triangle with an area of 24 square units, I'll use one of the factor pairs to create a right triangle.  I want students to notice that I did not meet the constraints of the problem, because I didn't draw an acute triangle.  I'll ask students to help me fix what I've drawn.  The purpose of me making this 'mistake' is two-fold:  I want students to carefully make sense of the problems and pull out the key information, and I want students to see that making mistakes (and learning from them) is a normal part of learning math.

Students work in pairs on the Partner Practice problem set.  As students work, I circulate around the room and check in with each group.  I'm looking for:

• Are students plotting points correctly?
• Are students correctly creating the geometric figure given an area and additional constraints?  
• Are students correctly identifying the dimensions of each shape?
• Are students including units?
• Are students checking the area of the figures they drew?

I'm asking:

• How did you determine the dimensions of the shape?
• How did you draw the figure on the coordinate grid?
• Why did you use square units?

In the partner work example, you can see that the students used a t-chart to list all of the factors of 16, to ensure that they've created all of the possible rectangles.

Students work on the Independent Practice problem set.  

Problem 2 asks students to draw a triangle with an area of 16 square units.  In this sample, you can see that the student was able to make sense of the problem.  She found the factor pairs of 32, and then tested using a factor pair in the formula for the area of a triangle.  

A common misunderstanding for this problem is for students to use a factor pair of 16.  This tells me that students didn't consider the context of this problem - either they have a misconception about the area of triangles, or they did not take enough time to make sense of the problem.

After independent work time, I have students turn to their partners and talk through how they decided to solve Problem 6.  I want students to have the chance to articulate their problem solving strategies, as well as hear alternate methods for approaching the problem.

Students then work independently on the Exit Ticket to close the lesson.