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Algebra 1 Linear Functions {Bundle} in a PowerPoint Presentation

This is a bundle include the seven PowerPoint lessons below and two Quiz Show games, Jeopardy Style, for review.

Domain and Range of a Function 8.F.1, F.IF.1, F.IF.5

Discrete and Continuous Domains 8.F.1, F.IF.1, F.IF.5

Linear Function Patterns 8.F.1, 8.F.3, 8.F.4, F.BF.1a, F.LE.2

Quiz Show Game Linear Functions Domain, Range, & Patterns 8.F.1, 8.F.3, 8.F.4, F.BF.1a, F.IF.1, F.IF.5, F.LE.2

Function Notation (with Piecewise Functions) F.BF.3, F.IF.1, F.IF.2, F.IF.7b

Absolute-Value Functions F.BF.3, F.IF.1, F.IF.2, F.IF.7b

Comparing Linear and Nonlinear Functions 8.F.3, F.LE.1b

Arithmetic Sequences F.BF.2, F.IF.3, F.LE.2

Quiz Show Game Linear Functions, Notation, & Arithmetic Sequences 8.F.3, F.BF.2, F.IF.1, F.IF.2, F.IF.3, F.IF.7b, F.LE.1b, F.LE.2

Students often get lost in multi-step math problems. This PowerPoint lesson is unique because it uses a flow-through technique, guided animation, that helps to eliminate confusion and guides the student through the problem. The lesson highlights each step of the problem as the teacher is discussing it, and then animates it to the next step within the lesson. Every step of every problem is shown, even the minor or seemingly insignificant steps. A helpful color-coding technique engages the students and guides them through the problem (Green is for the answer, red for wrong or canceled numbers, & blue, purple & sometimes orange for focusing the next step or separating things.) Twice as many examples are provided, compared to a standard textbook. All lessons have a real-world example to aid the students in visualizing a practical application of the concept.

This lesson applies to the Common Core Standard:

Functions 8.F.1, 8.F.3, 8.F.4

Define, evaluate, and compare functions.

1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Functions Define, evaluate, and compare functions.

3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Use functions to model relationships between quantities.

4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

High School: Functions » Building Functions F.BF.1a, F.BF.2, F.BF.3

Build a function that models a relationship between two quantities.

1. Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Build new functions from existing functions.

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.

High School: Functions » Interpreting Functions F.IF.1, F.IF.2, F.IF.3, F.IF.5, F.IF.7b

Understand the concept of a function and use function notation.

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).

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

3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Interpret functions that arise in applications in terms of the context.

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.

Analyze functions using different representations.

7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

High School: Functions » Linear, Quadratic, & Exponential Models F.LE.1b, F.LE.2

Construct and compare linear, quadratic, and exponential models and solve problems.

1. Distinguish between situations that can be modeled with linear functions and with exponential functions.

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

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).

Please note that the PowerPoint is** not ** editable.

If you need an alternative version because your country uses different measurements, units, slight wording adjustment for language differences, or a slide reordering just ask.

** Are you looking for the Algebra 1 Curriculum Bundle? Coming Soon!** Click here!

**This resource is for one teacher only. ** You may not upload this resource to the internet in any form. Additional teachers must purchase their own license. If you are a coach, principal or district interested in purchasing several licenses, please contact me for a district-wide quote at prestonpowerpoints@gmail.com. This product may not be uploaded to the internet in any form, including classroom/personal websites or network drives.

This is a bundle include the seven PowerPoint lessons below and two Quiz Show games, Jeopardy Style, for review.

Domain and Range of a Function 8.F.1, F.IF.1, F.IF.5

Discrete and Continuous Domains 8.F.1, F.IF.1, F.IF.5

Linear Function Patterns 8.F.1, 8.F.3, 8.F.4, F.BF.1a, F.LE.2

Quiz Show Game Linear Functions Domain, Range, & Patterns 8.F.1, 8.F.3, 8.F.4, F.BF.1a, F.IF.1, F.IF.5, F.LE.2

Function Notation (with Piecewise Functions) F.BF.3, F.IF.1, F.IF.2, F.IF.7b

Absolute-Value Functions F.BF.3, F.IF.1, F.IF.2, F.IF.7b

Comparing Linear and Nonlinear Functions 8.F.3, F.LE.1b

Arithmetic Sequences F.BF.2, F.IF.3, F.LE.2

Quiz Show Game Linear Functions, Notation, & Arithmetic Sequences 8.F.3, F.BF.2, F.IF.1, F.IF.2, F.IF.3, F.IF.7b, F.LE.1b, F.LE.2

Students often get lost in multi-step math problems. This PowerPoint lesson is unique because it uses a flow-through technique, guided animation, that helps to eliminate confusion and guides the student through the problem. The lesson highlights each step of the problem as the teacher is discussing it, and then animates it to the next step within the lesson. Every step of every problem is shown, even the minor or seemingly insignificant steps. A helpful color-coding technique engages the students and guides them through the problem (Green is for the answer, red for wrong or canceled numbers, & blue, purple & sometimes orange for focusing the next step or separating things.) Twice as many examples are provided, compared to a standard textbook. All lessons have a real-world example to aid the students in visualizing a practical application of the concept.

This lesson applies to the Common Core Standard:

Functions 8.F.1, 8.F.3, 8.F.4

Define, evaluate, and compare functions.

1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Functions Define, evaluate, and compare functions.

3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Use functions to model relationships between quantities.

4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

High School: Functions » Building Functions F.BF.1a, F.BF.2, F.BF.3

Build a function that models a relationship between two quantities.

1. Write a function that describes a relationship between two quantities.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Build new functions from existing functions.

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.

High School: Functions » Interpreting Functions F.IF.1, F.IF.2, F.IF.3, F.IF.5, F.IF.7b

Understand the concept of a function and use function notation.

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).

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

3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Interpret functions that arise in applications in terms of the context.

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.

Analyze functions using different representations.

7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

High School: Functions » Linear, Quadratic, & Exponential Models F.LE.1b, F.LE.2

Construct and compare linear, quadratic, and exponential models and solve problems.

1. Distinguish between situations that can be modeled with linear functions and with exponential functions.

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

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).

Please note that the PowerPoint is

If you need an alternative version because your country uses different measurements, units, slight wording adjustment for language differences, or a slide reordering just ask.

Total Pages

*392

Answer Key

N/A

Teaching Duration

55 Minutes

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