Selling Cake Pops Day 5 of 5

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Objective

Students will be able to explain what type of linear equations have one solution, no solutions or infinite solutions.

Big Idea

Extend writing expressions into solving equations through modeling a student run business. Linear modeling as entry point to build students' algebra confidence.

Lesson Author

Amelia Jamison

Caldwell, ID

Grade Level

Eleventh grade

Subjects

Math

Expressions (Algebra)

Algebra

modeling

Standards

HSA-CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HSA-REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*

MP3

Construct viable arguments and critique the reasoning of others.

MP7

Look for and make use of structure.

Warm up

5 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Selling Cake Pops Day 5, which asks students to explain why a specific equation has either infinite or no solutions.

Three Types of Solutions

15 minutes

This lesson was begun on previous day. Narrative for any unfinished portions can be found at Selling Cake Pops Day 4.

Here is how this activity runs. I pull up an equation and the students will need to determine whether it has one, none or infinite solutions without solving it first (Math Practice 7). It will start with pretty easy problems and then work up into trickier problems. I give them a chance to look at each problem (wait time) and then they will give a thumbs up for one solution, a thumbs down for no solution and a closed fist for infinite solutions. I then call on a student with the correct solution to explain the rationale for their answer.

I request that the students wait to show their answer until I ask them. Without that structure, the fastest students will shoot their answer up right away and the students who take a bit longer my just end up copying those answers. It is also good to have the students keep their answer right in front of their chest rather than high in the air as this also leads to more authentic answers.

Quiz on Expressions and Equations

12 minutes

This will be the first quiz the students will be taking in my class. I always make two versions, Quiz A and Quiz B and pass them out checkerboard style. When they finish they should start the assignment.

This quiz assesses how comfortable they are with our initial concepts. While I do provide one equation to solve, the remainder of the quiz assesses their ability to model with and reason about the skills we have discussed. These are equally, if not more, important as the ability to perform a skill in the Common Core.

Homework

1 minutes

This short assignment gives the students four equations with graphs of each side of the equation. They are asked to determine the solution from the graph and then solve it to reaffirm the solution. The goal is to reinforce the lesson from the last two days. This can be done after the students finish their quiz.