Alg1 Lesson 2.3: How Many Solutions?

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…

Part 1: Warming Up

Determine if each pair is a solution to this system.
Solve for y in the 2nd equation. Graph both equations.
What kind of relationship do these lines have? What
does this mean about the solution to the system?

Part 2: Exploring Linear

Systems with One Solution

Giving a Head Start

Jeanie and Frances want to start training for an upcoming bicycle race by riding on a flat bike path that has markings every mile. Since Jeanie is new to cycling, she will go more slowly than Frances, who is more experienced. The two girls decide that Jeanie will start at mile marker 3 to get a head start, and Frances will start at mile marker 0. Jeanie estimates that she will bike at a constant 10 miles per hour, but Frances will bike at a constant 16 miles per hour. When will the two girls meet if they start at the same time, and at what mile marker will they meet?

Questions & Answers

How can we find the solution to this system? We could make a table of values and
try to find the pair of numbers that works in both equations, or we could graph the
equations and find the intersection point of the lines.

What would the solution represent? The point at which the girls will meet (i.e.,
when and where they meet).

What is the intersection point of the lines? (0.5, 8)

What does this mean in the context of the problem? Frances will catch up to
Jeanie after 0.5 hours (30 minutes) at mile marker 8.

Plug point (0.5, 8) into formulas: 8 = 10(0.5)+3 and 8 = 16(0.5)

Part 3: Systems with No

Solutions and Infinite
Solutions in Context

Jeanie & Frances Go Riding Again

Several months later, Jeanie and Frances go bike
riding again. This time Jeanie has been practicing and
now can go the same speed as Frances. However,
Frances doesn’t know that Jeanie has improved and
gives her a 3-mile lead again. Based on this
information, when will the two girls meet if they start at
the same time, and where will they meet?

Riding Together

Now that Frances knows that Jeanie can also bike at
16 mph, it isn’t necessary to give her a head start. In
fact, Frances thinks that it would be nice if the girls
ride together.

Part 4: Review

Main Focus

Students should be able to analyze a system of equations by examining the slope
and y-intercepts of the associated graphs.

Handout 2.3: Practice Classifying Systems of Linear Equations

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.