Complementary, Supplementary, and Angles in a Triangle Lesson Plan (7th grade)

Lesson Plan

Subject/Topic: Math/Complimentary, Supplementary, and Triangle Angles 

Time (minutes) required for lesson: 135 minutes    

                         

CC Georgia Performance Standards for this lesson:

MCC7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Essential Question(s):

·         How can protractors be used to create and describe angle measurements?

·         How can angle relationships be described as supplementary or complimentary?

·         Why does the sum of the angles within a triangle always equal 180 degrees?

 Purpose/Relevance:

·         Understanding relationships between angles is necessary to facilitate missing angle measurement problem solving later in the geometry curriculum.

Goals of lesson aligned with CC Georgia Performance Standards:

·         Students will accurately find angle measurements using protractors.

·         Students will determine angle relationships as being complimentary and/or supplementary.

·         Students will understand the relationship between the sum of angles in a triangle and supplementary angle measurements.

    

Materials/Equipment/Technology Required:

·         < 10 geo-boards

·         < 100 rubber bands

·         < 2 sets of “ang-legs” (Substitute with Popsicle sticks, etc., if necessary)

·         Class set of protractors

·         Paper and pencils

·         Computer with projector and internet connection to go to: http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html for protractor modeling  OR large protractor for modeling OR document camera for modeling protractor usage

PROCEDURES

Introduction: 20 minutes

Protractor Review I DO- WE DO- YOU DO format. This is a general review for using protractors, because students should have already been exposed to this already. Students need to know how to use protractors so that they can explore the properties of angles and identify relationships between angles later on.

·         Ask students: What is the protractor used for when making shapes? (Expected response would be to measure angles.)

* I do- We do- You do: Exercise for protractors*

o   Estimate to one or two degrees.

1.  I do: Several examples from: http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html (This website is just a digital version of a protractor. The teacher can set parameters as to the degree of accuracy accepted for determining angle measurements using a protractor, as well as other versions of protractor usage outside of finding angle measurements.)

2.  We do: (On the white board with the wooden protractor)

§  Make a 45 degree angle.

§  Make a 105 degree angle.

3.      You do:

§  Make an acute, obtuse, and right angle.

Format of the lesson- Direct Instruction: 15 minutes  

1.      Supplementary and complementary note taking- definition, examples, and real-world examples. What are supplementary angles? Give clue for the “S” in supplementary as being able to turn into an 8 for 180 degrees. What are complimentary angles? Give clue for the “C” in complimentary as being able to turn into a 9 for 90 degrees.

2.      Review angle measurements of triangles by asking students how many degrees are in a triangle and clarifying any misconceptions that may occur.

3.      Provide detailed instructions for the following independent “centers”.  Students will break into six groups (decided on by the teacher). There will be three centers duplicated so that there will be two of each center ongoing at all times. Co-teaching model will provide students with one teacher per three centers for monitoring and assistance purposes. Directions for each center will be posted at each individual center.

Centers: Complimentary Angles, Supplementary Angles, and Angles of a Triangle (20 minutes for each center)

1.       Geo-board Supplementary Angles Task: Investigate what makes two angles supplementary.

a.       Use a protractor to measure the angle formed by one long rubber band piece, stretched over at least 5 pegs. What kind of an angle is this called? (Straight angle).

b.      Create a scalene triangle using the original long rubber band piece (straight angle), and two shorter pieces and then add a fourth orange piece to the center of the long rubber band piece, up through the vertex of the shorter two rubber band pieces. 

c.       Remember how many degrees were in the straight angle formed by the first single long rubber band. Measure and record each of the angles formed at the center connector of the first long piece.

d.      What do you notice about these angles? How do they relate to the measurement of the degrees in the single long piece, straight angle?

e.       Try this again one more time with different sized rubber band pieces. Is there a similar relationship?

f.       What kind of angles are these?

Geo-board Complimentary Angles Task: Investigate complimentary angles.

g.      Make medium-large sized square to begin.

h.      Measure and record the angle at the lower left vertex. *Use the protractor to measure angles.

i.        Use another connecting piece to divide the angle you just measured into two angles as shown.

j.        Measure both angles created by the new connecting piece, the angle bisector.

k.      What do you notice about these angles? How do they relate to the measurement of one of the angles in the square?

l.        Find an equation that explains the mathematical relationship between the original angle of the square and the two acute angles.

m.    Try this again one more time with different color pieces. Is there a similar relationship?

n.      What kind of angles are the two acute angles?

2.      “Ang-Legs” Triangle Sum Task: Investigate the properties of the angles of a triangle.

a.       Build three congruent scalene triangles.

b.      Identify a different vertex on each triangles (arrows).

c.       Connect all three vertices together and align triangle legs.

d.      What do you notice about the degree measurement when all three angles are connected?

e.       Repeat with equilateral and isosceles triangles.

f.       Does this work for all triangles, or only certain triangles?

Closure: 20 minutes

·         What are supplementary angles?

·         What are complementary angles?

·         How many degrees are in a triangle?

·         Find examples of complementary and supplementary angles in the classroom.