Congruent Figures

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SWBAT identify shapes that are the same size and shape by using transformations.

Big Idea

Students can move a shape into different positions in order to see if the shape is congruent.

Whole Class Discussion

15 minutes

In today's lesson, the students learn to determine if two figures are congruent by measuring the length of the sides or tracing one figure and putting it on top of the other figure to see if it fits exactly. 

To begin the lesson, the students are called to the carpet to sit in front of the Smart board.  (I like for my students to be close so that I can make sure that all of them are being attentive.)  To open the lesson, I show the students a video at the following site:

I tell the students that figures that are congruent are the same shape, the same size, and have angles with the same measurement.  Three ways to find out if the shapes are congruent are to 1) measure the sides of each shape, 2) trace the shape and put it on top of the other one to see if it fits perfectly, and 3) use a protractor to measure the angles.

I hold up two Kleenex boxes.  I ask the students to tell me about the two boxes.  Student responses:  One is small and one is large; one is thin and one is thick; they both are rectangles.  I let the students know that we need to see if these two boxes of Kleenex meet both requirements for being congruent:  1)  Are they the same shape, and 2) are they the same size?  I ask, Are they the same shape?  Student response:  Yes.   Are they the same size?  Student response: No.  Finally, I ask, Are these two boxes congruent?  Student response:  No.  I let the students know that these two figures are similar, but not congruent.

To give the students more practice, I let them work in pairs to practice the skill.

Skill Building/Exploration

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others.

For this activity, I put the students in pairs.  I give each pair an Congruent Figures Activity Sheet 1 activity sheet, a ruler, and a protractor.  The students must work together to find all of the shapes that are congruent by either measuring with the ruler or tracing the shapes (MP5).  

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.  

As they work, I monitor and assess their progression of understanding through questioning. 

1.  What strategies can you use to find the congruent figures?

2.  Which two figures are the same shape?  

3.  Are the two figures the same size?

Early Finishers: Use the ruler to draw congruent figures.


15 minutes

To close the lesson, I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples (Student Work - Congruent Figures), as well as work that may have incorrect information.  More than one student may have had the same misconception.  During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class. 


I had one pair of students tell me that they thought that figures F and J were congruent.  I asked the students to trace one of the figures.  Next, I had the students place the traced figure on top of the second figure.  I asked, "Are they congruent?"  The students knew that the shapes were not congruent.  I wanted to know why the students thought that they were congruent because we had already discussed that the shapes must meet both rules of being the same shape and same size.  One student said that he thought they were congruent because they were the same shape.  I reiterated to the students one more time that the shapes must be the same size and the same size shape.