Responsive Instruction

Teaching & Assessing with the New Curriculum

Name of Lesson: Operations on Functions: Composition (Lesson 3-5)Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson:

Engaging Opener:

Initial Instruction:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Practice: Re-teach:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

Un-packing the StandardMA.1.1 Describe characteristics of functions, translate among verbal, numerical, graphical, and symbolic representations of functions including polynomial, rational, power, trigonometric, exponential, logarithmic, and piece-wise functions.Identify elements of the standard used TODAY:• Characteristics of functions: Result of combining functions

using operations, composition, and real world modeling of combination of functions• Representations: verbal, symbolic, graphical, & numerical• Type of functions: linear, quadratic, polynomial, rational

and power functions.

Write the standard as it applies to today’s lesson:• Today we will describe the results of combing linear,

quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Unpacked-standard

Precalculus

Name of Lesson: Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson: • Perform operations on functions given in symbolic and graphical form.• Describe the results of performing operations on functions.• Perform composition of functions given in symbolic and graphical form..• Describe the results of performing composition of functions.• Interpret the result of combining functions appearing in the real world.

Engaging Opener:

Initial Instruction:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Practice: Re-teach:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

Identify Learning Targets:Unpacked Standard: Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

What are the distinct skills, processes, and learning outcomes associated with the un-packed standard?1. Students must be able to combine functions using operations and

composition when the functions are presented graphically or symbolically.2. Students must be able to describe the results of combining functions using

operations and composition.3. Students must be able to apply combination of functions to real-world

situations and interpret the results of the composition within the context of the problem.

One source for identifying learning targets is the bulleted list appearing beneath the section heading for each section. Check the example headings in the text. Are all of the learning targets addressed? If not, supplement the text with outside resources, guided questioning, or by

enriching student notes.

Precalculus

Engaging OpeningTo create an engaging opening, consider including one of the following resources:• Look at the Group Activity

provided at the end of each chapter. Previewing this problem without soling it may be a good starter.

• Consider finding a problem from the text and making it “come to life” by removing the scaffolding, some of the given information, or making it more interesting as demonstrated by Dan Meyer in the video clip.

Orange Text: Text Resource Yellow Text: External Resource

Precalculus Name of Lesson: Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson: • Perform operations on functions given in symbolic and graphical form.• Describe the results of performing operations on functions.• Perform composition of functions given in symbolic and graphical form..• Describe the results of performing composition of functions.• Interpret the result of combining functions appearing in the real world.

Engaging Opener:

Initial Instruction:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Practice: Re-teach:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

Initial InstructionYour initial instruction may include a traditional approach:• Formative assessment of pre-

requisite skills: • Look at the first couple of

questions in the exercises for the section. These are designed to be reflective/ summary questions and can be used as “KWL” questions.

• Delivery of lesson content from the textbook. Pay close attention the “>>>CAUTION>>>” boxes to address common student errors.

Or a constructionist approach:• Assign Explore-Discuss Questions

as constructive learning activities. • Problems from the book arranged

in the style of Dan Meyer .

Precalculus Name of Lesson: Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson: • Perform operations on functions given in symbolic and graphical form.• Describe the results of performing operations on functions.• Perform composition of functions given in symbolic and graphical form..• Describe the results of performing composition of functions.• Interpret the result of combining functions appearing in the real world.

Engaging Opener:

Initial Instruction:• Explain that in life there are so many variables to consider that often a single function cannot fully represent a

situation. Ask for past math experiences that have used more than one function at a time (piece-wise functions, linear systems, matrix operations). Present the definition of the operations performed on functions found on page 224 in the call-out box. Assign groups of students to explore and present one of parts (A), (B), (C), and (D). Debrief as a class to ensure that each of the presentations is complete and correct.

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Practice: Re-teach:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

Formative AssessmentYour formative assessment may include observing student performance on:• Group presentations or written

summary of constructed learning (e.g. Dan Meyer, or Explore-Discuss Questions)• Student performance on online

quiz at Mathzone.com • Student responses to

“Matched Problems” provided in the text for each section.• Student responses to high-level

questions from first few exercises.

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Precalculus Name of Lesson: Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson: • Perform operations on functions given in symbolic and graphical form.• Describe the results of performing operations on functions.• Perform composition of functions given in symbolic and graphical form..• Describe the results of performing composition of functions.• Interpret the result of combining functions appearing in the real world.

Engaging Opener:

Initial Instruction:• Explain that in life there are so many variables to consider that often a single function cannot fully represent a

situation. Ask for past math experiences that have used more than one function at a time (piece-wise functions, linear systems, matrix operations). Present the definition of the operations performed on functions found on page 224 in the call-out box. Assign groups of students to explore and present one of parts (A), (B), (C), and (D). Debrief as a class to ensure that each of the presentations is complete and correct.

Formative Assessment: Have students solve “matched problems” 1-2. Observe student performance to assess concept attainment.

Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Practice: Re-teach:

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

Name of Lesson: Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson: • Perform operations on functions given in symbolic and graphical form.• Describe the results of performing operations on functions.• Perform composition of functions given in symbolic and graphical form..• Describe the results of performing composition of functions.• Interpret the result of combining functions appearing in the real world.

Engaging Opener:

Initial Instruction:• Explain that in life there are so many variables to consider that often a single function cannot fully represent a

situation. Ask for past math experiences that have used more than one function at a time (piece-wise functions, linear systems, matrix operations). Present the definition of the operations performed on functions found on page 224 in the call-out box. Assign groups of students to explore and present one of parts (A), (B), (C), and (D). Debrief as a class to ensure that each of the presentations is complete and correct.

Formative Assessment: Have students solve “matched problems” 1-2. Observe student performance to assess concept attainment.

Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Teacher will present the “Function Machine” graphic found on page 226. Be sure to emphasize that

Students will solve and summarize the Explore-Discuss problems 2 and 3.

Practice: Teacher will present the “Function Machine” graphic found on page 226. Be sure to emphasize that when computing f °g, it’s important to know that the first letter that appears is not the first function applied.

Teacher will present Examples 5, 7, and 8. Students will refer to examples 3, 4, and 6 in order to complete their matched problems.

Re-teach: Students still struggling to comprehend operations on functions will form a group and take a prepared online quiz on the Smart Board utilizing the “show me” and “guided practice” functions to assist them if they get stuck. Quiz will cover composition,.

Formative Assessment: Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

Responsive InstructionThe Pre-calculus text provides leveled assignment sets for each section. A level- routine, easy mechanicsB level-more difficult mechanicsC level- diff. mechanics, some theory

Some other sources for differentiation in your new text:On-level practice:• Print practice sets from

Mathzone.com for additional practice.• Assign Review Exercises located at the

end of each chapter.

Remediation & Extension:• If students are still struggling, have

them complete exercises on Mathzone.com using the “Show Me” and “Guided Practice” features. Students may write a process summary, V.I.P., or short presentation to demonstrate understanding.• Advanced students may learn and

present the calculator functions available for the lesson using the “Technology Connections” in each text section.

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Precalculus

Name of Lesson: Standard Number(s):

MA.1.1Unpacked Statement of Standard(s):Today we will describe the results of combing linear, quadratic, power, polynomial, quadratic, and rational functions using sums, differences, products, quotients, and composition. These results will be numeric, algebraic, graphical, and will have verbal representations of real-world scenarios.

Learning targets addressed in this lesson: • Perform operations on functions given in symbolic and graphical form.• Describe the results of performing operations on functions.• Perform composition of functions given in symbolic and graphical form..• Describe the results of performing composition of functions.• Interpret the result of combining functions appearing in the real world.

Engaging Opener:

Initial Instruction:• Explain that in life there are so many variables to consider that often a single function cannot fully represent a

situation. Ask for past math experiences that have used more than one function at a time (piece-wise functions, linear systems, matrix operations). Present the definition of the operations performed on functions found on page 224 in the call-out box. Assign groups of students to explore and present one of parts (A), (B), (C), and (D). Debrief as a class to ensure that each of the presentations is complete and correct.

Formative Assessment: Have students solve “matched problems” 1-2. Observe student performance to assess concept attainment.

Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Responsive Instruction (Differentiation):Enrichment: Teacher will present the “Function Machine” graphic found on page 226. Be sure to emphasize that

Students will solve and summarize the Explore-Discuss problems 2 and 3.

Practice: Teacher will present the “Function Machine” graphic found on page 226. Be sure to emphasize that when computing f °g, it’s important to know that the first letter that appears is not the first function applied.

Teacher will present Examples 5, 7, and 8. Students will refer to examples 3, 4, and 6 in order to complete their matched problems.

Re-teach: Students still struggling to comprehend operations on functions will form a group and take a prepared online quiz on the Smart Board utilizing the “show me” and “guided practice” functions to assist them if they get stuck. Quiz will cover composition,.

Formative Assessment: Observe student presentations and summaries from the responsive instruction session. Use results to assign differentiated HW:Struggle: Students work on “A” level assignment, page 232 #2-28 even, 91Practice: Students work on “B” level assignment, page 232 #30-64even, 93Advanced: Students work on “C” level assignment, page 232 #66-88 even, 94

Process Standard(s):Problem SolvingReasoning & ProofCommunicationConnectionsRepresentation

Student Learning Summary:Students Exceeding Learning Targets:

Students Meeting Learning Targets: Students Reaching for Learning Targets:

PrecalculusFormative Assessment

Formative assessment at the end of the class period may take the form of:•Mathzone.com or ALEKS HW

Quiz. ALEKS is a supplemental online program that coordinates with the Pre-calculus text. You may sign up for a free trial at www.aleks.com • Exit Slip formulated from

unused “Explore-Discuss” problems.•Word problems provided in the

text exercises for each section. Especially those marked with the “Preparing for Calculus” icon.• Student Response System or TI

Navigator problem on the SMART Board

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