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Responsive Instruction

Responsive Instruction. Teaching & Assessing with the New Curriculum. Precalculus. Un-packing the Standard

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Responsive Instruction

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  1. Responsive Instruction Teaching & Assessing with the New Curriculum

  2. Precalculus • Un-packing the Standard • MA.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

  3. Precalculus • 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? • Students must be able to combine functions using operations and composition when the functions are presented graphically or symbolically. • Students must be able to describe the results of combining functions using operations and composition. • 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.

  4. Precalculus • Engaging Opening • To 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 ResourceYellow Text: External Resource

  5. Precalculus • Initial Instruction • Your 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 Questionsas constructive learning activities. • Problems from the book arranged in the style of Dan Meyer .

  6. Precalculus • Formative Assessment • Your 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. X

  7. Precalculus • Responsive Instruction • The Pre-calculus text provides leveled assignment sets for each section. • A level- routine, easy mechanics • B level-more difficult mechanics • C level- diff. mechanics, some theory • Some other sources for differentiation in your new text: • On-level practice: • Print practice sets fromMathzone.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. X X X

  8. Precalculus • Formative 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 X X X

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