Coordinate Plane and Shapes

3 teachers like this lesson
Print Lesson

Objective

SWBAT use ordered pairs to create shapes.

Big Idea

Students find the perimeter and area of rectangles using a coordinate plane.

Do Now

10 minutes

Students have prior knowledge creating a coordinate plane, plotting ordered pairs, and finding the distance between two points. The Do Now is a quick assessment of their understanding of these concepts.  Students will be provided with graph paper and a ruler.

Do Now

Locate and label (4,5) and (4,-3). Draw the line segment between the endpoints given on the coordinate plane.  How long is the line segment that you drew?

After about 5 minutes, I will have students compare their coordinate plane with their group and verify that they agree on the distance of the line segment.  If there are any discrepancies, students should discuss and come to an agreement.

Common Mistakes

- Students may number the coordinate plane incorrectly.

- Students may have switched the negative and positive sides of the number lines.

- Students may plot the ordered pair incorrectly, reversing the x and y coordinates.

- Students may have subtracted to find the distance, rather than add the absolute values of the y coordinates.

Mini Lesson

20 minutes

In this lesson students will use their knowledge of plotting ordered pairs and distance to find the area of rectangles.

I will model example 1 on the board as students complete the problem.  Students should continue the problem on the same coordinate plane as the Do Now.  The steps for example 1 will be posted on the board. We will work through and discuss each step.

Example 1 

Draw a horizontal line segment starting at (4,-3).  It should be west of (4,-3) and have a length of 9 units.

Which direction is west of (4,-3)?  What is the coordinate of the 2nd point?

Find the coordinate of the fourth vertex of the rectangle.

How can we determine where the fourth vertex lies?  

Students may realize that the coordinate should be a reflection of (4,5) over the y axis and therefore have the coordinates of (-5,5).

Draw the remaining sides of the rectangle.

What are the lengths of the sides of the rectangle?  What are two ways we can find the length?

Most students will rely on the strategy of counting the squares in the coordinate plane.  However, students should know that they can verify their answer using absolute value.

Using the vertices that you have found and the lengths of the line segments between them, find the perimeter of the rectangle.

Students should have prior knowledge of how to find the perimeter of the rectangle.  We will review what perimeter is and how to find it.

What are two strategies for finding the perimeter of the rectangle?

Most students will add the lengths of the sides.  Some students will choose to count the squares on the exterior of the rectangle.  For students who choose this strategy, they should be careful that they don't count the corner squares, or the perimeter will be wrong.

Find the area of the rectangle.

Students should have prior knowledge of how to find the area of a rectangle.  We will briefly review the concept.

What are two strategies for finding the area of the rectangle?

Most students will choose to multiply the length times width.  Some students may choose to count the squares in the interior of the rectangle.

 

 

 

Independent Practice

10 minutes

For the Independent Practice, students will receive a series of directions to follow, that will assess their knowledge of ordered pairs and perimeter and area.

 

Independent Practice

Construct a rectangle on the coordinate plane that satisfies each of the criteria listed below.  Identify the coordinate of each of its vertices.

  • Each of the vertices lies in a different quadrant.
  • Its sides are either vertical or horizontal.
  • The perimeter of the rectangle is 28 units.

Using absolute value, show how the lengths of the sides of your rectangle provide a perimeter of 28 units.

After about 10 minutes, students will trade papers with a member of their group, who will check their work and verify that they met the criteria listed in the problem.

Exit Ticket

5 minutes

The exit ticket is an assessment of students' understanding of the coordinate plane and distance.  I will use the results to plan future lessons and groupings.

 

 Exit Ticket 

The coordinates of one endpoint of a line segment are (−3,−5). The line segment is 10 units long. Give three possible coordinates of the line segment’s other endpoint.