Utecht – Culminating Project1. Five Day Plan:

Monday Tuesday Wednesday Thursday FridayCurve Shifters Linear,

Quadratic, and Exponential Transformations: Part 1 and 2

Linear, Quadratic, and Exponential Transformations: Part 2 and 3

Linear, Quadratic, and Exponential Transformations: Part 4 and 5

Linear, Quadratic, and Exponential Transformations: Part 6

2. Specific MMC content expectation(s) as a foundation,

A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s). A2.2.2 Apply given transformations to parent functions and represent symbolically. A2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical

representation; recognize that different families of functions have different asymptotic behavior. A2.3.2 Describe the tabular pattern associated with functions having a constant rate of change

(linear); or variable rates of change. A2.3.3 Write the general symbolic forms that characterize each family of functions. A2.4.1 Identify the family of function best suited for modeling a given real-world situation. A3.1.1 Write the symbolic forms of linear functions (standard, point-slope, and slope-intercept)

given appropriate information and convert between forms. A3.2.1 Write the symbolic form and sketch the graph of an exponential function given appropriate

information. A3.3.1 Write the symbolic form and sketch the graph of a quadratic function given appropriate

information. A3.4.1 Write the symbolic form and sketch the graph of power functions. A3.5.1 Write the symbolic form and sketch the graph of simple polynomial functions.

3. Outcomes for the mini-unit, o The student will be able to recognize and represent linear, quadratic, and exponential

functions, and their transformations, using various representations (tabular, graphical, verbal, and symbolic).

4. An Introduction or "Hook" to get students interested in the mini-unit's topic, o Students should have been introduced to the linear, quadratic, and exponential families of

functions prior to this unit. Combining these functions with the idea of transformations will allow the students to expand this idea and make recognizing a wider variety of functions easier. Discussion could also include how this could help with multiple choice (standardized) tests.

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5. At least one full lesson plan using the Lesson Plan Template (you may use one already developed for an Integration Assignment),

o Curve Shifters was Week 06 Integrated Assignmento Linear, Quadratic, and Exponential Transformations was Week 05 Integrated Assignment

6. Activities which could be from the course content modules or the social network to support the mini-unit's instructional focus,

o Linear, Quadratic, and Exponential Transformations was based on the Function Family Activity found at http://a4a.learnport.org/forum/topics/alg1-end-of-year-activity

7. At least one activity using a graphing calculator or some other technology (e.g. online resources)

o Curve Shifters uses the TI-Nspire calculator and was found at http://education.ti.com/calculators/downloads/US/Activities/Detail?id=13057

8. Problems and solution techniques incorporating multiple representations (verbal, symbolic, tabular, and graphical)

o Linear, Quadratic, and Exponential Transformations uses incorporates multiple representations (verbal, symbolic, tabular, and graphical)

9. Both formative and summative assessments. o Formative:

Depending on time, the students could be asked at the end of Monday or the start of Tuesday to sketch a parabola given in vertex form or to give the equation of a function graphed. This could be done as a ticket out the door on a note card or a warm-up on the TI-Nspire.

Part 2 of the Linear, Quadratic, and Exponential activity is a great formative assessment. While students prepare their presentation and when students discuss their results from part 1 the teacher can determine if there are misconceptions.

At the end of class Wednesday, after all students have completed part 3, they could be asked to restate their generalizations in a minute paper or to complete a muddiest point note card.

At the end of class Thursday student could be asked to create a verbal situation for any one of the function families that requires a transformation.

o Summative: Part 6 of the Linear, Quadratic, and Exponential Transformation packet would make a

nice summative assessment. In addition to the family, students could be asked to determine what type of transformation is needed to match the table.

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Algebra for All Online

Lesson Plan Template Mathematics Professional Development

Title: Curve Shifters

Content Expectation(s):

Strand: A; Algebra and Functions

Standard: A3: Families of Functions

Topic: A3.3 Quadratic Functions

Content Expectation:

A3.3.2 Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function.

Lesson Outcome: What will the students be able to do at the end of the lesson?

At the end of this lesson the student will be able to identify the elements of the quadratic functions and visualize the relationship between the coefficients and the graph.

Materials and Resources: List all supplies and resources to be used in the lesson, including texts, computers, calculators, software, web-based resources, manipulatives, art supplies.

This activity requires the use of the TI-Nspire calculator. The TI-Navigator or Connect-to-Class software are necessary to transfer the file to the students’ calculators.

Procedures: Describe the anticipatory set or “hook” to start the lesson, sample questions to students, and activities and tasks to be used in the lesson. The flow of the lesson, step by step, should be described, particularly in relation to what students will be doing.

Students will follow the steps provided on the attached activity sheet. This is provided by Texas Instruments for use with the TI-Nspire calculator. The teacher has downloaded the .tns file before class either through the TI-Navigator or the Connect-to-Class software. Students can work on this worksheet either individually, in groups, or as a whole class discussion. I would tend to have them in pairs as that would free up the teacher to observe and help students on an individual basis. Students should be encouraged to make predictions before trying the manipulations on the calculator. After the students have completed the assignment there are many ways to conclude this assignment. Students could share at the board via a document camera or the TI-Navigator and projector. Students could be asked to write a conclusion based on their predictions and observations. Pairs or groups could be given graphs and asked to determine the equation, or vice versa.

Assessment: How will you determine if the students have achieved the learning outcome(s).

Students could be assessed in a variety of ways. Students could be given a matching game of graphs and equations, they could be given graphs and instructed to construct the equation or vice

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versa, or students could be given a pair/group assignment where they construct graphs/functions and quiz each other.

Additional Notes: Fill in additional comments and considerations, such as special instructions, extension opportunities, differentiation strategies, re-teaching resources, etc.

There are no special instructions for this assignment. Differentiation could occur a variety of ways using the technology as well as various group scenarios.

Attachments: Provide copies of any worksheets, handouts, and other associated elements related to the lesson. Make a list of the attachments for reference in this space.

CurveShifters.pdf

CurveShifters_Student.pdf

CurveShifters.tns

http://education.ti.com/calculators/downloads/US/Activities/Detail?id=13057&ref=%2Fcalculators%2Fdownloads%2FUS%2FActivities%2FSearch%2FSubject%3Fs%3D5022%26sa%3D5022%26t%3D5035%26d%3D1008%26g%3Dauthor%23view-all

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NOTE:

Curve Shifters could not be copied into this document because the Word version has too many graphics. I will attach it separately or you can use the link from the lesson plan to go directly to the TI website.

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Algebra for All OnlineLesson Plan Template

Mathematics Professional Development

Title: Linear, Quadratic, and Exponential Transformations

Content Expectation(s):

Strand: 2: Algebra and Functions

Standard: A3: Families of Functions

Topic: A3.2: Exponential and Logarithmic Functions

Content Expectation:

A3.2.1 Write the symbolic form and sketch the graph of an exponential function given appropriate information.

A3.2.2 Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions; recognize the logarithmic function as the inverse of the exponential function.

A3.2.4 Understand and use the fact that the base of an exponential function determines whether the function increases or decreases and understand how the base affects the rate of growth or decay.

A.3.2.5 Relate exponential and logarithmic functions to real phenomena, including half-life and doubling time.

Lesson Outcome: What will the students be able to do at the end of the lesson?

At the end of this lesson the student will be able to distinguish linear, quadratic, and exponential function families, and their transformations, based on the equation model, the graph, the table, and the verbal situation.

Materials and Resources: List all supplies and resources to be used in the lesson, including texts, computers, calculators, software, web-based resources, manipulatives, art supplies.

The student will need colored pencils and some way to present the graphs to class (poster board, document camera, etc.).

Procedures: Describe the anticipatory set or “hook” to start the lesson, sample questions to students, and activities and tasks to be used in the lesson. The flow of the lesson, step by step, should be described, particularly in relation to what students will be doing.

Specific details are on the attached project, but the flow of the lesson is as follows:

This activity is intended for an Algebra 1 class. It could be used as an introduction to transformations or as a review. Linear, quadratic, and exponential functions should have been introduced prior to this time.

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Part 1: Transformations Explorations

Three different groups of students will each explore one of the function families, and make a large poster graph of 5 functions in that family, one being the parent function.

Part 2: Explanation

The students are told to be prepared to share and discuss their tables, graphs, and findings with the class. Each group of students will explain their graphs, what they can determine at that point in patterns, what the parent function is and looks like. The students will write each table of values on the poster.

Part 3: Observation

Now having access to all three explorations, the students will investigate each corresponding transformation in the various explorations and determine patterns.

Part 4: Shapes of Algebra!

The students will match the symbolic rules given with the appropriate graph, using the patterns discovered in the previous parts.

Part 5: Is it Linear, Quadratic, or Exponential ?

The students will identify which family of function each real situation represents.

Part 6: Table Time for Families

The students will identify which family of functions is represented by each table of values.

Conclusion:

Discussion of these results (how each family has common characteristics, how the “offspring” are different from the parents) and then possibly a quiz can follow this activity.

Assessment: How will you determine if the students have achieved the learning outcome(s).

Formative assessments can be from the presentations of the groups after the first part of the activity as well as based on teacher observation throughout this activity. Summative assessments could be either the end of this activity or a similar exercise that uses a variety of function families, transformations, and representations.

Additional Notes: Fill in additional comments and considerations, such as special instructions, extension opportunities, differentiation strategies, re-teaching resources, etc.

Depending on the class, this activity could be used for introduction or review of this concept. Remembering that this is intended to take 3-5 days, the teacher would have to plan this unit accordingly. Additionally, I would try to limit the use of calculators on Part 3, since I would want the students to be showing understanding the concepts of the different families instead of just typing it in the calculator. One method of differentiating would be to allow calculators at various points for some students, for example, the creating the tables would be a logical place for calculator use.

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Attachments: Provide copies of any worksheets, handouts, and other associated elements related to the lesson. Make a list of the attachments for reference in this space.

I have attached the original activity named: Alg1FunctionFamilyActivityendofyear. I have also attached my adjusted activity named: Utecht - linear, quadratic, and exponential transformations.

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Linear, Quadratic, and Exponential Transformations

This activity is intended for an Algebra 1 class. It could be used as an introduction to transformations or as a review. Linear, quadratic, and exponential functions should have been introduced prior to this time.

Part 1: Transformations Explorations Three different groups of students will each explore one of the function families, and make a large poster graph of 5 functions in that family, one being the parent function.

Part 2: ExplanationThe students are told to be prepared to share and discuss their tables, graphs, and findings with the class. Each group of students will explain their graphs, what they can determine at that point in patterns, what the parent function is and looks like. The students will write each table of values on the poster.

Part 3: ObservationNow having access to all three explorations, the students will investigate each corresponding transformation in the various explorations and determine patterns.

Part 4: Shapes of Algebra!The students will match the symbolic rules given with the appropriate graph, using the patterns discovered in the previous parts.

Part 5: Is it Linear, Quadratic, or Exponential ? The students will identify which family of function each real situation represents.

Part 6: Table Time for Families The students will identify which family of functions is represented by each table of values.

Conclusion: Discussion of these results (how each family has common characteristics, how the “offspring” are different from the parents) and then possibly a quiz can follow this activity.

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Part 1: Transformations Exploration #1 Name: Date: Group members:

Your group will:1. For each symbolic rule in the set, produce a table of (x, y) values with integer values of x.2. Draw the graph for each of the symbolic rules with the table of values that you made. Include each

table of values, a title and the axes labels. 3. Draw the parent function with black, and use a different color for other graphs, as indicated.4. Label each graph with its equation. Include a title.

1) y=x Parent Function for the _____________________ Family.

black

2) y=−x

red

3) y=2x

purple

4) y=( x−4 )

green

5.) y=(x+3)

blue

Part 2: ExplanationBe prepared to share and discuss your tables, graphs, and findings with the class.

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X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -6 -5 -4 -3 -2 -1 0

Y

Part 1: Transformations Exploration #2 Name: Date: Group members:

Your group will:1. For each symbolic rule in the set, produce a table of (x, y) values with integer values of x.2. Draw the graph for each of the symbolic rules with the table of values that you made. Include each

table of values, a title and the axes labels. 3. Draw the parent function with black, and use a different color for other graphs, as indicated.4. Label each graph with its equation. Include a title.

1) y = x 2 Parent Function for the _____________________ Family.

black

2) y=−x2

red

3) y=2 x2

purple

4) y=x2−4

green

5.) y = ( x + 3 )2

blue

Part 2: ExplanationBe prepared to share and discuss your tables, graphs, and findings with the class.

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X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -6 -5 -4 -3 -2 -1 0

Y

Part 1: Transformations Exploration #3 Name: Date: Group members:

Your group will:1. For each symbolic rule in the set, produce a table of (x, y) values with integer values of x.2. Draw the graph for each of the symbolic rules with the table of values that you made. Include each

table of values, a title and the axes labels. 3. Draw the parent function with black, and use a different color for other graphs, as indicated.4. Label each graph with its equation. Include a title.

1) y=2x Parent Function for the _____________________ Family.

black

2) y=−2x

red

3) y=(2)2x

purple

4) y=2x−4

green

5.) y = 2x+3

blue

Part 2: ExplanationBe prepared to share and discuss your tables, graphs, and findings with the class.

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X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -3 -2 -1 0 1 2 3

Y

X -6 -5 -4 -3 -2 -1 0

Y

Part 3: Observation Name: Date: Group members:

Answer the questions using the graphs &/or tables of all the explorations. Compare the tables, graphs, and symbolic rules in the explorations. Note similarities, differences, and connections between the symbolic rules, the tables, and the graph patterns.

1. In #1 of each exploration, state the rule for the parent function, and describe its graph.a. Exploration 1:

i. rule_________________________ ii. graph__________________________

b. Exploration 2: i. rule_________________________

ii. graph__________________________c. Exploration 3:

i. rule_________________________ ii. graph__________________________

2. In #2 of each exploration, identify what the “–“sign does for each exploration’s graph.a. Exploration 1: _____________________________________________________________b. Exploration 2: _____________________________________________________________c. Exploration 3: _____________________________________________________________d. Generalizing, how does the “–“sign affect graphs?

3. In #3 of each exploration, how does the coefficient a change the graphs?a. Exploration 1: _____________________________________________________________b. Exploration 2: _____________________________________________________________c. Exploration 3: _____________________________________________________________

4. In #4 of each exploration, how does subtracting 4 from the parent function change the graphs?a. Exploration 1: _____________________________________________________________b. Exploration 2: _____________________________________________________________c. Exploration 3: _____________________________________________________________d. Generalizing, how does subtracting at the end of a function affect (move) the graph?

e. How do you think adding a value at the end of a function affects/moves a graph?

5. In #5 of each exploration, how does adding 3 directly to x affect the graphs?a. Exploration 1: _____________________________________________________________b. Exploration 2: _____________________________________________________________c. Exploration 3: _____________________________________________________________d. Generalizing, how does adding a value directly to x affect (how does the graph move) each

graph?

e. How do you think subtracting directly to x would affect each graph?

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Part 4: Shapes of Algebra!

Use the information from parts 1 & 2 to help match the following graphs with the symbolic rules (equations).

Equation:________________ Equation:________________ Equation:________________

Equation:________________ Equation:________________ Equation:________________

Equation:________________ Equation:________________ Equation:________________

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y=2x−3 y=(x−3)2 y=x−3 y=2x+4 y=(x+4)

y=x2+4 y=−x+2 y=−(x+2)2 y=−2x+2

Part 5 : Is it Linear, Quadratic, or Exponential ?

Name: Date: Group members:

State whether the following situations would be best represented by a linear, quadratic, or exponential graph. Sketch what you think the graph would look like. Explain.

1. Mr. Bee’s free throw shooting (the flight of the ball).__________________________

2. Population growth of the number of snails in an aquarium.______________________

3. The flight of an arrow that is shot in the air on an upward angle._________________

4. The path of an airplane descending from 20,000 to 10,000 feet. __________________

5. The amount of water in an aquarium when filling up.__________________________

6. The total amount of money spent on prom tickets in relation to the number of people going.__________

7. The amount of money in a savings account that uses compound interest.__________________________

8. The flight of a dolphin jumping out of the water at Sea World._______________________

9. The population of pandas if the population is half of each previous year.__________________

10. The flight of a tee shot by Tiger Woods._______________________

11. The number of miles driven on a freeway when traveling at a constant speed.___________________

12. The value of a used Honda Accord over time._______________________

13. The height of a flea that jumps onto a cat. ___________________________

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Part 6: Table time for Families Name: Date: Group members:

Identify which family of functions is represented by each table of values. Explain in detail what are you looking for when identifing the correct function family.

Table A Table B Table C

Family_______________ Family_______________ Family_______________

Explanation:

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x -2 -1 0 1 2

y -7 -5 -3 -1 1