Objective

Discussion: What is Algebra?

Discussion: An Historic Problem - reasoning abstractly and quantitatively

Discussion: How do you know?

Homework

What is Algebra?

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Objective

Students will be able to explain why algebra needs definitions and axioms, what some of these first principles are, and what it means to "do algebra".

Big Idea

Algebra is built on axioms and definitions and relies on proofs just as much as geometry.

Lesson Author

Jacob Nazeck

Fort Collins, CO

Grade Level

Eleventh grade

Subjects

Math

Quadratic Equations

Algebra

modeling

Graphing (Algebra)

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-CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HSA-CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

HSF-IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP6

Attend to precision.

Discussion: What is Algebra?

10 minutes

Discussion: An Historic Problem - reasoning abstractly and quantitatively

10 minutes

A Common Mistake

Historic Problem Student Work.pdf

Discussion: How do you know?

15 minutes

Homework

10 minutes

Adjustments to Practice

A2 Weekly Workout box plot big.png

In the final 10 minutes of class, there are several things to accomplish.

First, I will assign the homework for the night, which is to complete the remaining two problems on the Historic Algebra Problems handout. This will be due at the beginning of class tomorrow.

Second, I will handout The Weekly Workout general guidelines along with the their first Weekly Workout 1. Quickly, I will explain the rationale behind the weekly workout - it's about staying strong through constant practice - and ask everyone to write the due date on the top of the assignment. It won't be easy, but I'll have to avoid getting side-tracked by lots of questions here!

Finally, I will pass out the class syllabus to all of the students, asking them to read it and share it with their parents. Their parents must send me an email sometime before Friday so that I know they are able to contact me if they need to, and so that I can contact them. This is another homework assignment!

It's important to write all of the assignments on the whiteboard and to make sure that the students copy the due dates into their planners, but it's also important to send them off with a smile and a big "Welcome to algebra!" at the end of class.

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