PYTHAGOREAM THEOREM

andLINEAR EQUATIONS

LESSON PLAN for VA., S.O.L., 8.10b and A.4fBY

GREGORY B. BLANCHARD

LESSON PLAN

VA. SOL. 8.106 AND A.4f

PYTHAGOREAN THEOREM AND EQUATIONS

Introduction:

Lesson Topic: Solving real-world problems involving equations and systems of equations.

Length of Lesson: 50 minutes.

Virginia Standards of Learning: 8.106, A.4f. Students will apply the Pythagorean Theorem and solve real-world

problems involving equations and systems of equations.

Cognitive Objectives:

Students will:

Understand the Pythagorean Theorem is used to find the measure of any one of the three sides of a right

triangle if the measure of the other two sides is known.

Develop the skills necessary to calculate the length of a side of a right triangle when given the length of the

other two sides.

Solve real-world problems involving the Pythagorean Theorem.

Materials/Technology and Advanced Preparation:

Set up Power Point (slide of ugliest tree house showing).

Divide chairs into four groups.

Provide small rafters to each station.

Rafter to have step method layout marred on surface.

Teaching and Learning Sequence:

Introduction/Anticipatory Set:

Explain Lesson for day. (Pythagorean Theorem, slope-rise over run.)

Have each group look at rafter and discuss.

Mingle, encourage, and guide (5 – 7 minutes).

Back to normal seating arrangements.

Lesson Development:

Draw student’s attention to Power Point screen.

Encourage students to compute calculations on their notes to mimic those in the presentation.

Give Power Point presentation.

Teacher should always walk among students to check progress on calculations and help as necessary.

Closure:

Go over dimensions on rafter handed out in class.

Encourage students not to have bad looking structures in yard

Homework:

Find structure and calculate the pitch of roof and length of rafters.

Students to attach a brief explanation of why they picked that structure and conclude if built sound (or not) and why.

Assessment:

Formative:

During class presentation and during time allowed for students to calculate, the teacher should always walk among

students to check progress. (Mingle…Encourage…Guide.)

Summative:

The teacher will mentally monitor (enter in journal at appropriate time) students demeanor and amount of input during present ation.

During the time, the teacher explains the small rafter and how it relates to rise over run and Pythagorean Theorem, mental notes taken on who seems to

Understand.

The teacher will review homework assignment

.

Appended Material:

Power Point Presentation.

Written Instruction for Power Point Presentation.

Instructional Content and Strategies Organizer.

Curricular Framework Document.

VA.,S.O.L., 8.106 http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml

VA., S.O.L., A.4f http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml

Algebra I Standard A.4f, Eighth Grade Standard 8.106 (50 minute Lesson Plan). The students will apply

the Pythagorean Theorem and solve real-world problems involving systems of equations.

Sample Problem:

Calculate the measurements and layout a rafter for a structure.

• Group discussion

• Power Point presentation.• Video presentation.

• Explain seat-cut

• Explain tails and overhang.

• Explain heel and heel height.

• Question ridge rafter and how

much to shorten rafter.

• Homework assignment.

• Small rafter sample.

• Manipulation of model rafter to

visually see rise over run.

• Background paper showing

overall rise over run.

Power Point Instructions

VA., S.O.L., 8.106, A.4f

Today’s lesson plan is about slope and the Pythagorean Theorem. (SLD. 10) “Why do I even care? I will never use this. Rise

over run, not in a million year”, are a few replies that are asked while pitching this lesson plan. Well, the one great exa mple of when

these math facts are needed, is building a roof. (SLD. 11, 12) Those of you who think you will never build a roof are mistaken. Some

time in your life you will attempt to assemble shelter for a lawnmower, firewood, or even the pet dog. (SLD. 13, 14) For the girls, you

may want a doll house for your daughters to play in. The boys, a tree house for your sons to play in. (SLD. 15, 16) Girls should pay

attention so when you’re married you will be able to help your husband with the calculations and prevent the lopsided structu re from

appearing in the yard. (SLD. 17, 18, 19, 20).

This lesson plan focuses on calculations needed to lay out a rafter, and an explanation of how to layout and cut the rafters. We have

Learned about the slope of a line and we have also referred to the slope as pitch or rise over run. (SLD. 21, 22) We have also studied the

Pythagorean Theorem. Let us review briefly and then try a real life problem (or two) using the concepts of pitch and the Pythagorean

Theorem. (SLD. 23)

Explain small model of truss handed to each student and calculate the rafter lengths. (SLD.24) Play video and discuss calculations

(SLD. 25). Try another problem for a building 28 feet wide with a five over twelve pitch.

PYTHAGOREAM THEOREM

andLINEAR EQUATIONS

LESSON PLAN for VA., S.O.L., 8.10b and A.4fBY

GREGORY B. BLANCHARD

HOW DO WE DESIGN RAFTERS?

RAFTERS

𝑎2+𝑏2=𝑐2

PYTHAGOREAN THEOREM:RATIOS:𝐴𝐵

=𝐶𝐷

PITCH:RISE/RUN

SLOPE:𝑦2−

𝑥2−

𝑦1

𝑥1

WHAT EQUATIONS MAY WE USE?

See Video