Pearson Assessments



381 Lesson

FOUNDFUN1 (2 instructional Days)

Introduction to Functions and Multiple Representations

|Enduring Understandings |

|The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. |

|The student understands that data representing real-world situations can be collected, organized, and interpreted in order to solve problems. |

|The student understands that functions can be used to model real-world situations. |

|Vocabulary |

|function, independent, dependent, discrete, continuous, domain, range, input, output, mapping, scatterplot |

|A.1A(S) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is |

|expected to describe independent and dependent quantities in functional relationships. |

|The student will know… |The student will be able to… |

|The difference between the independent and dependent |Identify the independent and dependent quantities in a function and/or situation. |

|quantities. |Verify that a point is on a function by substituting (x, y) into the function equation. |

|That not all relationships are functions (height vs eye |Verbalize functional relationships. |

|color). |“y” depends on “x” |

|An ordered pair can represent a point on the function. |“y” is a function of “x” |

| |“x” determines “y” |

| |“y” is a result of “x” |

| |Use related vocabulary for functional relationships. |

| |Input, output |

| |If, then |

| |Cause, effect |

|A.1B(S) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is |

|expected to gather and record data and use data sets to determine functional relationships between quantities. |

|The student will know… |The student will be able to… |

|Not all data sets represent functional relationships. |Gather and represent data from situations (Ex: build a table of data from a problem situation). |

|The characteristics of a functional relationship in its |Represent data in a graph, table, set of ordered pairs, mapping, and verbal description. |

|various forms (graph, table, set of ordered pairs). |Use data to determine if a relation is a function, including vertical line test. |

|A function may or may not contain an infinite number of | |

|ordered pairs. | |

|A.1C(S) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is |

|expected to describe functional relationships for given problem situations and write equations [or inequalities] to answer questions arising from the |

|situations. |

|The student will know… |The student will be able to… |

|Algebraic expressions can be used to represent |Verbally describe the relationship among quantities (Ex: As the term number increases by 1, the |

|generalizations. |value decreases by 3). |

|Symbols can be used to represent unknowns or variables. |Create a graph from a given equation, table of data, concrete models, or a given situation. |

|A table is a graphic organizer used to represent |Complete a table of data from a given equation, a graph, concrete models, or a given situation. |

|relationships among quantities. |Use graphing calculator to verify table of data, equation, and/or graph. |

|Patterns in a table create patterns in a graph. |Recognize and connect the various representations of a situation (i.e. graph, table, equation, |

| |verbal description). |

| |Create a situation from a table of data, an equation, or a graph. |

| |Define what a variable(s) represents in a problem situation. |

| |Generate equation from scenario and from table. |

Prior Knowledge (from 371):

• Determine if a set of data describes a function.

• Determine a linear function equation from a table.

• Represent a functional relationship with a table, graph, equation, and scenario/verbal description.

• Solve 1 and 2 step equations containing one variable.

• Interpret scatterplot data and make predictions.

Materials needed

• Graphing Calculators

• Scissors

• Glue or Tape

• Markers/Colored Pencils

• 1 class set of Break the Code – Decoder on cardstock (Day 1)

• 1 Secret Code Message per student – 5 messages per page (Day 1)

• 1 copy of Function or Not Notebook Sort per student (Day 1)

• 1 copy of Fiddling with Functions per student (Day 1)

• 1 pre-cut class set of Function or Not Representation Cards (Day 2)

• 1 copy of Function poster – to be hung on wall (Day 2)

• 1 copy of Not A Function poster – to be hung on wall (Day 2)

• 1 copy of Representation Stations per student (Day 2)

Procedure

|Day 1 |

|Use the MATH_0381_FOUNDFUN1_MAT_FUNCTIONSPRESENT1_02 notebook file to guide this lesson. |

|Use the Function or Not A Function Notebook Sort for the interactive student notebook. |

|[pic] |Slide 1: This slide contains words and descriptions that |Use this column to write your own notes: |

| |students were exposed to in 371 during the Foundations of | |

| |Functions unit after STAAR. | |

| | | |

| |Inform students that over the next few days we will | |

| |revisit these words. | |

|[pic] |Slide 2: Students have done this “Break the Code” activity| |

| |in 371, but decoded different messages. Give each student| |

| |a secret code to decipher, and allow students 2 – 3 | |

| |minutes to decipher their code. | |

| | | |

| |Possible Questions/Statements to recall prior knowledge: | |

| |For those of you that had the same message, did you get | |

| |the same or different answers? Same | |

| |Why do you think that is so? The same input gave the same| |

| |output. | |

| |Did you have any input values that were repeated in your | |

| |message? Yes | |

| |Was your output value the same or different for that input| |

| |letter? Same | |

| |What would happen if you had more than one possible output| |

| |value for those repeated input values? For example: How | |

| |would your message change if for the input letter B the | |

| |output could be R or L or S? What would happen to your | |

| |message? It would change. It wouldn’t make sense. | |

| |So each input value should only have one output value. | |

|[pic] |Slide 3: This is a fun introduction slide into recalling | |

| |the definition of a function. | |

|[pic] |Slide 4: This slide contains a Candy Vending Machine which| |

| |can be used to create a mapping to help students recall | |

| |the definition of a function. | |

| | | |

| |If you push each button on the vending machine it will | |

| |direct you to the kind of candy you will get. On the | |

| |candy slide you press the word candy on the lower right | |

| |side of the screen to get back to this slide and use | |

| |arrows to create the mapping of the candy vending machine | |

| |(as shown below). | |

| |[pic] | |

|[pic] |Slide 5: This slide gives students the definition of a | |

| |function by relating it to the candy vending machine. | |

| | | |

| |It is okay to have two different buttons on a vending | |

| |machine vend the same candy. | |

|[pic] |Slide 6: This slide presents students with a situation | |

| |that is not a function, because each input does not have | |

| |only one output. Button #2 vends two different candies. | |

| | | |

| |Students explored last year that it is not possible to | |

| |press one button (on a CD player) and get two different | |

| |outputs. | |

|[pic] |Slide 7: This slide presents students with multiple | |

| |definitions of a function using words in which they | |

| |learned during the foundations of functions unit in 371. | |

| | | |

| |This slide also ties the definitions back to the candy | |

| |vending machine. | |

|[pic] |Slide 8: Use this slide to work with students to determine| |

| |which graphs are functions and which are not. | |

| | | |

| |If they are not functions, highlight the data that makes | |

| |it not a function. | |

| | | |

| |[pic] | |

|[pic] |Slide 9: Use this slide to work with students to determine| |

| |which set of ordered pairs are functions and which are | |

| |not. | |

| | | |

| |If they are not functions, highlight the data that makes | |

| |it not a function. | |

| | | |

| |[pic] | |

|[pic] |Slide 10: Use this slide to work with students to | |

| |determine which tables are functions and which are not. | |

| | | |

| |If they are not functions, highlight the data that makes | |

| |it not a function. | |

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| |[pic] | |

|[pic] |Slide 11: This slide shows students how to set up their | |

| |interactive notebook. Have students title their page and | |

| |set up a t-chart as shown. Then give students 3 – 5 | |

| |minutes to cut out their Function or Not Notebook Sort | |

| |cards and sort them as described on the slide and above | |

| |their cards. | |

|[pic] |Slide 12: This slide provides an interactive way for | |

| |students to check their answers. Have students come to | |

| |the board and drag each representation to the correct | |

| |location. | |

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| | | |

| |The undo button will undo the last action. | |

| | | |

| |The reset button will move all cards back to their | |

| |original location at the bottom or the screen | |

| | | |

| |When students believe they have all representations in the| |

| |correct place press the Submit button. [pic] | |

|[pic] |Slide 13: Allow students 5 minutes to process what they | |

| |remember about functions using the question stems provided| |

| |on this slide. | |

|Assign students Fiddling with Functions as independent practice/homework. |

| |

|[pic] |

|Day 2 |

|Use the MATH_0381_FOUNDFUN_MAT_FUNCTIONSPRESENT1_02 notebook file to guide this lesson. |

|[pic] |Slide 1: Title Slide |Use this column to write your own notes: |

|[pic] |Slide 2: Give each student one representation card and | |

| |have them determine if it is a function or not. They will| |

| |go stand by the correct poster with other students who | |

| |believe they share the same functionality. | |

| | | |

| |Once all students have decided, have them discuss (and | |

| |share) the characteristics that make each representation a| |

| |function or not. | |

| | | |

| |Have “function” and “not a function” posters posted on the| |

| |wall before students enter the room. | |

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| |Answer Key | |

| | | |

| |Function | |

| |Not A Function | |

| | | |

| |C, D, F, I , J, K, M, N, O, Q, R, V, W | |

| |A, B, E, G, H, L, P, S, T, U, X | |

| | | |

|[pic] |Slide 3: This slide has students determine if two things | |

| |create a dependency relationship. | |

| | | |

| |Yes | |

| |No | |

| |Yes | |

| |Yes | |

|[pic] |Slide 4: This slide reviews descriptions of the | |

| |Independent Variable. | |

| | | |

| |Students drag the blue words from the bottom of the page | |

| |into the correct blank in the description. | |

| | | |

| |[pic] | |

|[pic] |Slide 5: This slide reviews descriptions of the Dependent | |

| |Variable. | |

| | | |

| |Students drag the words from the bottom of the page into | |

| |the correct blank in the description. | |

| | | |

| |[pic] | |

|[pic] |Slide 6: Students will drag the green and blue boxes over | |

| |the statement to review the independent and dependent | |

| |quantity in a functional relationship statement. | |

| | | |

| |[pic] | |

|[pic] |Slide 7: Students will drag the green and blue boxes over | |

| |the statement to review the independent and dependent | |

| |quantity in a functional relationship statement. | |

| | | |

| |[pic] | |

|[pic] |Slide 8: Students will drag the green and blue boxes over | |

| |the statement to review the independent and dependent | |

| |quantity in a functional relationship statement. | |

| | | |

| |[pic] | |

|[pic] |Slide 9: Students will drag the green and blue boxes over | |

| |the statement to review the independent and dependent | |

| |quantity in a functional relationship statement. | |

| | | |

| |[pic] | |

|[pic] |Slide 10: Transition Slide | |

|[pic] |Slide 11: This slide is an example to be worked with | |

| |students to review multiple representations of a function.| |

| | | |

| |This should be completed by allowing students to come to | |

| |the smart board and fill in the representations. | |

| | | |

| |Graphing calculators can be used to verify the equation, | |

| |graph, and table in this activity. | |

| | | |

| |[pic] | |

| |Students learned about discrete and continuous during 371 | |

| |Foundations of Functions so this would be a great place to| |

| |discuss why you used dots and did not draw a line. | |

|[pic] |Slide 12: Pass out the Representation Stations to each | |

| |student. Allow students 20 minutes to complete these | |

| |scenarios. | |

| | | |

| |Students may sit with a partner to discuss their work but | |

| |each student must complete their own activity. | |

| | | |

| |Graphing calculators are required for this activity. | |

|Assign Revisiting Multiple Representations as individual practice/homework. |

| |

|[pic] |

BREAK THE CODE - Decoder

You’ve been given a secret message. Determine the

message by using the code grid. Look at the input letter then map it to the corresponding output letter.

Secret Code Messages

|Determine the secret message by using each of the input values and following it to the black square, then find the corresponding output value. |

|K V Q O L B K B Y M U C ! |

|Determine the secret message by using each of the input values and following it to the black square, then find the corresponding output value. |

|P B O C R W O X B E V O ! |

|Determine the secret message by using each of the input values and following it to the black square, then find the corresponding output value. |

|P B O C R W O X B Y M U ! |

|Determine the secret message by using each of the input values and following it to the black square, then find the corresponding output value. |

|S’ W K W K D R C D K B ! |

|Determine the secret message by using each of the input values and following it to the black square, then find the corresponding output value. |

|B Y M U S X’ D R O K V Q O L B K R Y E C O ! |

Function or Not Notebook Sort

Cut out each of the cards. Sort the cards into two groups. One group represents functions while the other group represents non-functions. Highlight the part that makes the representation not a function. Do not glue your cards into your notebook until we go over them as a class.

|[pic] |[pic] |[pic] |[pic] |

|[pic] |{ (-1, 2), (0, 2), (1, 2), (2, 2) } |[pic] |

| |{ (2,-1), (2,0), (2, 1), (2, 2) } | |

Function or Not Notebook Sort

Cut out each of the cards. Sort the cards into two groups. One group represents functions while the other group represents non-functions. Highlight the part that makes the representation not a function. Do not glue your cards into your notebook until we go over them as a class.

|[pic] |[pic] |[pic] |[pic] |

|[pic] |{ (-1, 2), (0, 2), (1, 2), (2, 2) } |[pic] |

| |{ (2,-1), (2,0), (2, 1), (2, 2) } | |

Fiddling with Functions Practice

For problems 1 through 8, if the graph, relation, or mapping represents a function,

circle yes. If the graph, relation, or mapping does NOT represent a function, circle no.

Then explain your answer choice in the space below the problem.

1. 2. 3.

Yes or No Yes or No Yes or No

4. (3, 5) (2, 4) (1, 3) (0, 2) (-1, 1) Yes or No

5. (4, 12) (5, 18) (4, 24) (5, 30) Yes or No

6. (2, 6) (3, 6) (6, 6) (7, 6) Yes or No

7. Yes or No 8. Yes or No

For problems, 9 and 10, follow the directions given.

9. Create a table of values that represents 10. Create a table of values that does

a function. NOT represent a function.

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|x |y |

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Fiddling with Functions Practice – Answer Key

1. Yes; A vertical line will touch the graph in only one place at a time.

2. Yes; A vertical line will touch the graph in only one place at a time.

3. No; A vertical line will touch the graph in more than one place at a time.

4. Yes; Each x-value has exactly one y-value.

5. No; 4 has two different y-values, and 5 has two different y-values.

6. Yes; Each x-value has exactly one y-value.

7. No; 8 is paired with two different y-values.

8. Yes; Each x-value has exactly one y-value.

9. Answers vary; Each x-value has exactly one y-value.

10. Answers vary; One x-value should have two different y-values.

Function or Not Representation Cards

|A. |B. |

| |[pic] |

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|(-1, 5), (0, 8), (-1, 9) | |

|C. |D. |

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|x |x |

|2 |2 |

|4 |5 |

|5 |7 |

| |3 |

|y | |

|-5 |y |

|-9 |1 |

|-11 |2 |

| |2 |

| |4 |

| | |

|E. |F. |

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|[pic] |[pic] |

|G. |H. |

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| |[pic] |

|x | |

|3 | |

|5 | |

|7 | |

|3 | |

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|y | |

|1 | |

|2 | |

|3 | |

|4 | |

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|I. |J. |

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|[pic] | |

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| |(-1, 5), (0, 5), (1, 9) |

|K. |L. |

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| |Independent |

|x |Dependent |

|2 | |

|3 |-4 |

|5 |16 |

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|y |-2 |

|1 |4 |

|3 | |

|7 |0 |

| |0 |

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| |2 |

| |4 |

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| |-4 |

| |-16 |

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| |7 |

| |49 |

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|M. |N. |

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| |[pic] |

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|(2, 4), (3, 5), (4, 6), (5, 8) | |

|O. |P. |

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|[pic] |Input |

| |Output |

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| |0 |

| |1 |

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| |0 |

| |2 |

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| |0 |

| |4 |

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| |0 |

| |8 |

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| |0 |

| |16 |

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| |0 |

| |32 |

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|Q. |R. |

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| |x |

| |1 |

|(1, 4), (2, 3), (3, -6), (-3, 6) |2 |

| |3 |

| |4 |

| |5 |

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| |y |

| |5 |

| |7 |

| |9 |

| |11 |

| |13 |

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|S. |T. |

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| |[pic] |

|[pic] | |

|U. |V. |

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|[pic] |[pic] |

|W. |X. |

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|[pic] | |

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| |(1, 6), (1, 3), (3, -4), (-8, 7) |

[pic]

Scenario 1

The carnival has a $5 entrance fee and each ride ticket costs $1.50.

_____________________________________ depends on __________________________________.

|Table |List of Ordered Pairs |

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| |Equation |

|Mapping |Graph |

| |[pic] |

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[pic]

Scenario 2

The total bill for each customer is a function of the number of slices of pizza they bought. This relationship can be represented by

f(x) = {(1, 2.5), (2, 5), (3, 7.5), (4, 6)}

_____________________________________ depends on __________________________________.

|Table |List of Ordered Pairs |

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|PROCESS | |

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| |Equation |

|Mapping |Graph |

| |[pic] |

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[pic]

Scenario 3

Johnny is making a frame for a picture he drew. He knows that the length is triple the width, w. The equation to find the area of the frame is a = (w)(3w) = 3w2.

_____________________________________ depends on __________________________________.

|Table |List of Ordered Pairs |

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|PROCESS | |

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|Don’t forget your order of operations! | |

| |Equation |

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| |A = 3w2 |

|Mapping |Graph |

| |[pic] |

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[pic]

Scenario 4

Use the information in the graph to complete the remaining representations.

|Table |List of Ordered Pairs |

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| |Equation |

|Mapping |Graph |

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Could height be on the y-axis instead of the x-axis???

Why was there no dependency statement above the representations?

[pic]

1) Russell went to a farm with his grandmother to pick blueberries. It cost $9 to enter the farm and $1.50 per pound.

_____________________________________ depends on __________________________________.

|Table |List of Ordered Pairs |

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|Don’t forget your order of operations! | |

| |Equation |

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|Mapping |Graph |

| |[pic] |

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2) Denny Construction Company charges $0.80 for each cubic foot of mulch, plus $6 to deliver the mulch.

_____________________________________ depends on __________________________________.

|Table |List of Ordered Pairs |

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|Don’t forget your order of operations! | |

| |Equation |

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|Mapping |Graph |

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-----------------------

One copy per student

(on light colored paper)

x y

5

7

-2

3

-5

2

7

-3

6

8

-3

6

8

12

x y

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