Relations and Functions

1. Relations and Functions
a. Distinguish between linear and nonlinear data.
b. Distinguish between relations and functions.
c. Identify dependent and independent variables, domain and range.
d. Evaluate a function using tables, equations or graphs” CCSSI, OK standard).
Lesson Goal(s):
Students will be able to graph linear equation by using table.

Lesson Objective(s):

Vocabulary learned: Solution of an equation, Graph of an equation.
Learn what verify the solution to an equation means and then the process of substitution of the point into the equation of the line to check.
Graph a linear equation using a table by first rewriting the equation in function form by solving for y then choosing a few values of x and making a table of values. Finally, plotting the points and drawing a line through them.
Learn the equations of Horizontal and vertical lines and how to graph them.
MATERIALS AND RESOURCES

Instructional Materials:

Textbook, Overhead, Pencil and paper, chalkboard

Resources:

Walle, J.A; Karp, K.S., (2010), Elementary and Middle School Mathematics: Teaching Developmentally.

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

INSTRUCTIONAL PLAN

Sequence of Instructional Procedures/Activities/Events (provide description and indicate approximate time for each):

1. Identification of Student Prerequisite Knowledge and/or Skills: 15min
It is expected that students are able to plot ordered pairs on a coordinate system and to create a table of values from an equation.
2. New Knowledge and/or Skills To Be Taught:
Students will learn about the linear equation and graphing them by using tables. They will learn how to rewrite the linear equation in function form by finding y.

3. Modeling: I Do
I will explain what linear equations are? Is the equation in the standard from like ax + b = c where a, b, and c are any value. We are looking for the value of variable x to solve the equation. How do you solve linear equations? Detail explanation of how to graph linear equations can be done in guided practice.

4. Guided Practice: We Do (15min)
I will use the following the worksheet for guided practice.

……..Desktoplinear equation worksheet.pdf
5. Independent Student Practice: You Do (15 min)
Students will do the worksheet of solving linear equations using graphic calculator.
Name ________________________
Date ________________________
Show all work clearly for full credit. Round to the nearest hundredth if necessary.
1. Find the average speed of a person boating 126 miles in 5 hours. (4points).
2. Convert 250 pesos to dollars. The exchange rate is 9.99 pesos per United States dollar. (4points)
3. What percent of people were in favor of a survey question if 162 people voted NO out of a total of 525 voters? (5 points)
4. 6x-2y=10
a. solve this equation for y.
b. use the equation from part a) to make a table of values for x=-5 , x=-2 and x=1, x=4
c. plot the points and draw the line. Make sure to label the line appropriately.

6. Culminating or Closing Procedure/Activity/Event: (15min)
I will have my students to pair up at their desks and create and solve their own linear equations using table. Make sure to walk around and answer the questions if they have any. Once they are done with that then give them worksheets for homework.
Pedagogical Strategy (or Strategies):
I will hold a class discussion to address the portion of the task that the students having difficulty with. I will ask questions like; what you don’t understand about the work? What method did they use? If it was clear or accurate?
What kind a error did they make?
How can they improve their understanding?
“Algebra 16.0: Students understand the concepts of a relation and a function, determine whether a given relation defines a function and give pertinent information give relations and functions.
Algebra 17.0: Students determine the domain of independent variables and the range of dependent variable defined by the graph, a set of ordered pairs, or a symbolic expression.
Algebra 18.0: Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion” (CCSSI, OK standard).

Lesson Objective(s):
Students will discover various ways of describing and recognizing functions and relations. 1) By thinking of a rule and having their partner(s) try to guess. 2) By learning how to use function notation. 3) By seeing how graphs of functions and relations compare.
MATERIALS AND RESOURCES

Instructional Materials:
We will use text book, pencil, paper and overhead projector.
Resources:
Supplementary information and/or places where you found information for the lesson
Walle, J.A; Karp, K.S., (2010), Elementary and Middle School Mathematics: Teaching Developmentally.

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

INSTRUCTIONAL PLAN

Sequence of Instructional Procedures/Activities/Events (provide description and indicate approximate time for each):

1. Identification of Student Prerequisite Skills Needed for Lesson:
Operate with the real numbers to solve problems. Find, identify, and interpret the slope and intercepts of a linear relation.
2. Presentation of New Information or Modeling:
1. Teacher presents the students with some simple rules for combining numbers and lets students attempt to guess the rules (See Functions and Relations Worksheet). The teacher says, “If you say 2, I say 11. If you say 7, I say 26.” (The rule is to multiply the first number by 3 and add 5). Students can suggest numbers for the teacher to process and try to use these as clues in determining the rule.
2. Students in pair groups then try this exercise with each other, taking turns making up rules. Student #1 thinks of a rule such as multiply a number by 2 and adds 5. Then they say, “If you say 4, I say 13. If you say 10, I say 25.” Then Student #2 suggests number for Student #1 to process. Student #2 tries to determine the rule. Once this is done, Student #1 and #2 switch roles.
3. Guided Practice:
Functions and relations can be written in many forms. Some of the possible forms include using: words, algebra, or a table. For example:
Words: Take a natural number, double it and add seven.

Algebra: f (x) = 2x + 7 for x N
x f(x)
1 9
2 11
3 13
4 15
… …

Table:

 
4. Independent Student Practice:
Function Notation Practice
1. Write the following word notation into Algebra notation: Take a real number, triple it and subtract thirteen.
2. Draw a table showing at least 5 solutions for the function f(x) = 4x + 2.
3. Draw an arrow diagram to represent the set of ordered pairs: {(5, -3), (6, -5), (2, 3), (3, 1)}.
4. What is the rule in word notation for the ordered pairs in #?
5. What is the rule in Algebra notation for the ordered pairs in #4?

5. Culminating or Closing Procedure/Activity/Event:
The lesson is designed to prepare the students for the notation used in linear and quadratic functions. Algebra is a language that can be very useful in describing relationships. Students will also need some review with the graphical representation of functions and the vertical line test.

Pedagogical Strategy (or Strategies):
After students have had time to explore, the teacher can lead a discussion on the difference between a function and a relation and then begin discussing the various ways of representation, (e.g. ordered pairs, a table and a mapping diagram). This would lead into some drills in having the students practice representing some of their rules. A worksheet or selection of problems from text would be most useful at this time as a follow-up.
Differentiated Instruction:
I will make easy one variable equation worksheet for the students that need more help compare to my regular student

Student Assessment/Rubrics: The lesson is designed to prepare the students for the notation used in linear and quadratic functions. Algebra is a language that can be very useful in describing relationships. Students will also need some review with the graphical representation of functions and the vertical line test.
Please show all work clearly and write your answers in complete sentences.

1. Decide whether or not the following set of ordered pairs is a function or not. Give a reason for your conclusion.
{(13, 4), (14, 3), (15, 6), (18, 3), (4, 9)}
2. Decide whether or not the following set of ordered pairs is a function or not. Give a reason for your conclusion.
{(1, 4), (2, 3), (3, 6), (5, 7), (3, 8)}
3. Draw a table showing at least 5 solutions to the function f(x) = 3x – 5.

 
4. List five ordered pairs that would belong to the function f(x) = 2x + 3
5. Use an arrow diagram to illustrate the ordered pairs you found for #3.
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Relations And Functions

Week 5 – Discussion 1

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses.

Relations and Functions

In this discussion, you will be assigned two equations with which you will then do a variety of math work having to do with mathematical functions. Read the following instructions in order and view the example to complete this discussion. Please find the two equations assigned to you in the table below:

If the last letter of your last name is    On pages 708 – 711, solve the following problems
A or B    22 and 30
C or D    24 and 32
E or F    26 and 34
G or H    28 and 36
I or J    12 and 46
K or L    14 and 48
M or N    16 and 50
O or P    18 and 52
Q or R    20 and 54
S or T    2 and 56
U or V    4 and 58
W or X    6 and 60
Y or Z    8 and 64
•    First, graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.
•    Mention any key points on the graphs, including intercepts, vertex, or start/end points.  (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)
•    Discuss the general shape and location of each of your graphs.
•    State the domain and range for each of your equations. Write them in interval notation.
•    State whether each of the equations is a function or not giving your reasons for the answer.
•    Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.
•    Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):
o    Function
o    Relation
o    Vertical Line test
o    Transformation
Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

Relations And Functions

Week 5 – Discussion 1

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses.

Relations and Functions

In this discussion, you will be assigned two equations with which you will then do a variety of math work having to do with mathematical functions. Read the following instructions in order and view the example to complete this discussion. Please find the two equations assigned to you in the table below:

If the last letter of your last name is    On pages 708 – 711, solve the following problems
A or B    22 and 30
C or D    24 and 32
E or F    26 and 34
G or H    28 and 36
I or J    12 and 46
K or L    14 and 48
M or N    16 and 50
O or P    18 and 52
Q or R    20 and 54
S or T    2 and 56
U or V    4 and 58
W or X    6 and 60
Y or Z    8 and 64
•    First, graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.
•    Mention any key points on the graphs, including intercepts, vertex, or start/end points.  (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)
•    Discuss the general shape and location of each of your graphs.
•    State the domain and range for each of your equations. Write them in interval notation.
•    State whether each of the equations is a function or not giving your reasons for the answer.
•    Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.
•    Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work.):
o    Function
o    Relation
o    Vertical Line test
o    Transformation
Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.