Quadrilaterals and the Coordinate Plane

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Objective

Students will be able to: • Define congruent. • Classify a rectangle, parallelogram, trapezoid, square, and rhombus by its characteristics. • Plot and identify a point on the coordinate plane. • Find the length of sides of a quadrilateral on a coordinate plane. • Calculate the area of quadrilaterals on a coordinate plane.

Big Idea

A fun and challenging lesson on quadrilaterals

Do Now

5 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  For this lesson I want students to review plotting coordinate points.  Common student mistakes are switching the x and y coordinate and not paying attention to negative signs.  Some students struggle when there is a zero as a coordinate, such as in problem 5 and 6.  We will review answers and go over any common mistakes I saw when I was walking around.  I ask students to share out strategies they have for remembering how to plot coordinate points.

Classifying Quadrilaterals

20 minutes

After the Do Now, I have a student read the objectives for the day. This section of the lesson may be a review for your students, or it may be introduction to new material.  Change the length/depth of this section of the lesson depending on the needs of your students.

I ask students to share out what a prefix is.  I am looking for students to tell me that a prefix is a group of letters that is placed at the beginning of a word that has a specific meaning.  Many students will be able to share that the prefix “tri” means three.  I have my students think-pair-share about words that begin with “tri” and “quad” for 2-3 minutes.  Some examples may include triangle, tripod, triathlon, trio, triplet, trilingual, quadrant, quadruplet, and quadruple.  See my video on Think Pair Share in my Strategy folder for an explanation.

I want students to make a connection between the prefix of “quad” and the meaning of quadrilateral.  My hope is that with knowledge of prefixes, students will have an easier time recalling the meaning of some mathematical terms. 

I have students read through the definitions on the Quadrilateral Notes page.  Here are some questions I may ask:

  • How are all the quadrilaterals similar? (By definition they all have 4 sides)
  • What is the difference between a rectangle and a square? Use the word congruent in your answer.
  • What is the difference between a parallelogram and a rhombus?
  • Can you call a rectangle a square?  Why or why not?
  • Can you call a square a rectangle? Why or why not?
  • Can you call a square a rhombus?  Why or why not?
  • Can you call a rhombus a square?  Why or why not?

If students struggle with these questions, have them draw a Venn diagram for each question.  Students can then organize the specific similarities and differences of the two shapes.  Some students struggle with questions like the last 4 listed.  A square can be called a rectangle because it meets the criteria of a rectangle (4 sides, 2 sets of parallel sides, and 4 right angles).  It is important that students understand that although a square can be called a rectangle, the best and most specific name for the quadrilateral is a square.  A rectangle cannot be called a square because it does not have 4 congruent sides.

It is important to me that students use the Mathematical Practice 6: Attend to precision with their language throughout this lesson.  Students need to be using specific mathematical terms to describe the characteristics of quadrilaterals and how they compare to other quadrilaterals.  I push students to use terms like: angles, parallel, and congruent. 

I pass out the Naming Quadrilateral reference sheet.  We fill in the missing descriptions on the back.  I go over how to use the series of questions to identify the first quadrilateral on the Practice page as an example.  I walk around to make sure students are writing the specific characteristics of the rhombus under “How do you know?” 

I give students 3-5 minutes to classify and write their answers.  I walk around and monitor student progress.  Some students may struggle with number 2 and 4 if they compare the side lengths visually.  I have rulers available if students want to use them to compare side lengths.

When most students are finished we quickly review a couple of the examples and reasoning behind the answers.

Quadrilaterals on the Coordinate Plane

25 minutes

We work through number one together.  I remind students that they have their Naming Quadrilaterals reference sheet and I have rulers available if needed.  For part (a) I want students to explain that the missing coordinate must be (8,9) because a rectangle must have 2 sets of parallel sides.  If you place a point at (7,9) or (9,9) the quadrilateral will only have 1 set of parallel sides, making it a trapezoid.  We review perimeter and area of a rectangle and calculate them accordingly.  I have students think-pair- share about part (d).  See my video on Think-Pair-Share in my Strategy folder for an explanation.  Some students may say no, since the quadrilateral has 4, sides, 4 right angles and 2 sets of parallel sides, it is a rectangle.  Other students may say that it meets the criteria of a parallelogram, since it has 4 sides and 2 sets of parallel sides.  Both of these arguments are correct.  If I asked what would be the most specific name for this quadrilateral, the answer would have to be rectangle.

Students work on numbers 2-5 independently.  I tell students that if they are stuck to 1) use their reference sheets, 2) ask a neighbor, 3) ask the teacher.  During this time I am also looking to see what strategies students are using on problem 3 so I can have students share during the closure.  When students have completed a problem, they raise their hand.  I quickly scan their work.  If their work is adequate, I send them to the posted keys to check their answers.    See my video Posting A Key in my Strategy folder for more details.  If students are struggling here are a few things I may do:

  • Tell them to go back and use their Naming Quadrilaterals sheet to help them.
  • Give them the MCAS Reference Sheet to find formulas for area and perimeter.
  • Have them pair up with someone to help trouble shoot.
  • Have them join other students who are struggling and work with me at a small table.

If students are successful on these problems and finish early here are some options:

  • Ask them to create and plot 3 different rectangles that have the same perimeter as Carrie’s garden in problem 4.  What do they notice about the area of the different rectangles?
  • Ask them to create and plot a parallelogram and trapezoid that have the same area as the rhombus in problem 5.
  • Ask them to serve as a helper for students who are struggling.

Closure and Ticket to Go

10 minutes

Together we work through problem 3.  I ask a student to share the most specific name of the quadrilateral and have other students add details/terms if needed.  I ask a student to share how he/she found the answer to parts (c) and (d).  I choose 1-2 students to display their work under the document camera and explain how they found the area for the trapezoid.  Some students may split it into a square and a triangle and find the areas.  Other students may split the trapezoid into two triangles and find the area.  Students who struggle with using formulas may count the full squares and ½ squares and add them up.  I encourage students to use formulas to find the area.

With the remaining time I pass out the ticket to go and have students complete it.  I also collect their work so that I can see how individual students tackled the problems.