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The Algebra 1 Teacher's guide to the Common Core State Standards for Mathematics.

# Linear Equations

## Common Core Math says...

This unit is much more comfortable for me as the teacher. The focus feels clearer and the goals are more familiar. As is states in the Common Core State Standards in the Algebra introduction:

An equation can often be solved by successively deducing from it one or more simpler equations. For example, one can add the same constant to both sides without changing the solutions, but squaring both sides might lead to extraneous solutions. Strategic competence in solving includes looking ahead for productive manipulations and anticipating the nature and number of solutions.

Keep in mind that just because it is a linear equation chapter, you do not want the students to lose the information you have given them in unit 1. It is a wonderful thing to force students to think outside the units to solve problems.

## Standards for Mathematical Practice

• 4. Model with mathematics
• 8. Look for and express regularity in repeated reasoning
• ## Big Picture Lesson Planning for the Common Core

Big Picture Lesson Planning forces us as teachers to answer the question, "What do I want my students to be able to do in life with the skills they obtain from my class?" Or, "Why am I teaching this?"

The student will understand patterns in business, economics, environment and behaviors to predict future outcomes to make knowledgeable decisions for success. This includes researching and formulating the patterns and understanding the target audience and how that affects the results.

This goal is the same as Unit 1, but will be much more specific to linear equations.

• Can the student find a finish date for a project?
• Is the student able to take a situation and create a business proposal complete with reasoning and graphs showing future profit?
• Can the student decide how much to charge for a job done, such as painting a home?

What skills will they need to achieve this goal?

#### Week #5Slope

• Find the slope of a function from a graph or table (F.IF.6)
• Find the slope given an equation, including solving for y (F.IF.6)
• Based on the context of a situation, explain the meaning of the coefficient (slope) and intercepts in a linear function (F.LE.1a, F.LE.1b, S.ID.7)

#### Week #6 Linear functions and their inverses

• Graph linear functions and intercepts (F.IF.7a)
• Create a linear function given a table, graph or situation (F.LE.5)
• Construct arithmetic sequences (F.LE.2)
• Find the inverse of a function (F.BF.4a)

#### Week #7Translating Graphs

• Identify the effect on the graph of f(x) by f(x) + k, kf(x), f(kx), and f(x+k) (F.BF.3)
• Given the graphs above, find k (F.BF.3)

## Lesson Ideas

All of these resources and more can be found in the livebinder below.

## Common Core Standards

*Note that this chapter only deals with the linear part of each standard. The exponentials are dealt with in later units.

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F.IF.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.* (Emphasize quadratic, linear, and exponential functions and comparisons among them)

F.IF.5 Interpret functions that arise in applications in terms of the context. 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.*

F.IF.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.?

F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, give a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

F.BF.1a Write a function that describes a relationship between two quantities. (Emphasize linear, quadratic, and exponential functions). Determine an explicit expression, a recursive process, or steps for calculation from a context. Video explanation

F.BF.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. Video explanation

F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x3 or f(x) = (x + 1)/(x - 1) for x ? 1.

F.LE.1a Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.

F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-?-output pairs (include reading these from a table).

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

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