Alg1 Lesson 2.1: A Geometric Approach to Systems

Lesson 2.1: A Geometric

Approach to Systems of Linear

Equations

Obj: 3G: I can graph equations and find their
intersection.

EQ: How do I find the intersection of 2 equations?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Poll

What are you doing during this lesson?

• Facilitator

• Scribe

• Resourcer

• Includer

Part 1: Balancing an

Irregular Triangle

Bob the Balancer

One of your friends is known as “Bob the Balancer” because he can
balance plates on his finger. He does this by carefully placing his
finger exactly in the middle of the plate and staying as still as
possible.

You find an irregular triangular plate at home and bring it to Bob the
Balancer for him to show off his skills. You say, “Bob, balancing a
round plate is easy, because finding the center of a circular plate is
pretty straightforward. Can you balance this triangular plate by
placing your finger under its center?”

Centroid

The triangle’s center of mass

Trace/Draw this Triangle and Grid on Paper, Estimate and
Label the Centroid.

Part 2: Finding the Centroid

Median

The middle, half; A median of a triangle is a
line segment from a vertex of the triangle to
the midpoint of the opposite side.

Multiple Choice

How many medians does a triangle has?

• 3

• 1

• infinitely many

• 6

Multiple Choice

Suppose we drew two medians. Would they intersect?

• Always

• Sometimes

• Never

Drag and Drop

If you draw any two medians of the triangle on your paper, what o you notice? The medians ​

Placeholder

at or near the ​

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that they estimated as the ​

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of ​

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.

Drag these tiles and drop them in the correct blank above

intersect

point

center

mass

plane

Multiple Choice

What is the centroid of the triangle?

• (2, 1)

• (3, 1.5)

• (0, 3)

• (6, 0)

• (0, 0)

Multiple Select

Which lines contain the medians?

• $$-4x\ +\ \frac{2}{3}=y$$

• $$\frac{1}{2}x=y$$

• $$-\frac{1}{4}x+\frac{3}{2}=y$$

• -x + 3 = y

• 2x = y

Plug In (2, 1) to Check Solutions

-(2) + 3 = 3 - 2 = 1

-¼(2)+ 3/2 = -2/4 + 1.5 = -0.5 + 1.5 = 1.5 - 0.5 = 1

½(2) = 2/2 = 1

All 3 equations are true statements.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

Part 3: City Planning

Handout 2.1: City Planning

Draw a diagram of Algebra
Town and sketch the
trenches.

Labelling

Label each letter.

Drag labels to their correct position on the image

Gas Distribution Center

Where the two trenches cross

Power Plant

New Hospital

New Apartment Building

Drag and Drop

Electric Trench Eq: ​

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Gas Trench Eq:  ​

Placeholder

Intersection: ​

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and ​

Placeholder

of Town Center

Drag these tiles and drop them in the correct blank above

y = -(1/3)x + 3

y = -(5/3)x + 5

1.5 E

2.5 N

y = -(1/3)x + 5

y = -(5/3)x + 3

1.5 W

1.5 N

2.5 S

2.5 E

Draw

Draw a floorplan for your dream house layout in the rectangle provided. Label things such as bedrooms, bathrooms, closets, etc.