![be used in a Calculus course:
A.SSE.1
F.IF.4, 5, 7, 7c
F.BF.1
G.GMD.3
G.MG.1, 2, 3
Calculus course:
- Interpret and use information from figures and
graphs.
- Manipulate expressions and equations.
- Interpret and use information from graphs in the
coordinate plane.
-Analyze and draw conclusions based on
information from figures and graphs.
- Write expressions that require planning and/or
manipulating to accurately model a situation.
-Write equations that require planning,
manipulating, and/or solving.
- Identify characteristics of graphs based on a set of
conditions or on a general equation such as y = ax族
+ c.
-Solve problems integrating multiple algebraic
and/or geometric concepts.
-Analyze and draw conclusions based on
information from graphs in the coordinate plane.
- Draw conclusions based on a set of conditions.
-Solve multistep geometry problems that involve
integrating concepts, planning, visualization,
and/or making connections with other content
areas.
General In-class Activities/Strategies per Subject Area:
Activities:
Class discussion and brainstorming about how to solve certain difficult problems, short instructor
lectures/explanations giving hints on how to attack difficult problems, group and individual solving of
problems from text books or handouts from instructor (groups of distributed talent will sometimes be
assigned by instructor so that students can help other students out), confidence builders[ (1) students
solve problems on board and verbally explain to class their method and logic with other student and
instructor support, if necessary, and (2) practice in clearly explaining their method and logic used to solve
problems in writing by individual journaling], bell ringer warm up problems, entrance, and exit slips to
check student understanding , occasional fun change of pace games, computer lab work, using
Journey Through Calculus CD ROM (see textbook reference below) to supplement classroom
instruction, graphing calculator work.
Instructor Classroom Strategies:
(Sources--Table of High Leverage Practices as laid out in Doing Teaching: The Case of Ms. Gates, by
Dr. Ignacio Lopez, and my own classroom observations)
Stick with my designated time limits as laid out in my lesson plans. Keep the momentum going-crisp
transitions in and out of topics. Create a rapport with students so that they feel emboldened to share their](https://image.slidesharecdn.com/b1264b44-ebd5-4738-8182-9a2434aa995b-160101115505/85/Walker-Individual-Unit-Plan-2-320.jpg)
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Walker-Individual Unit Plan
- 1. High School Individual Unit Plan Name of Teacher: Stuart Walker Subject Areas: Math- AP Differential Calculus (first semester) Length of Unit: 5 weeks Dates: Last 2 weeks of September through end of 3rd week in October. Description of the Individual Unit: Students will learn Differential Calculus methods that will allow them to solve real world problems. To gain a broader perspective on Calculus, they will learn some history behind the development and applications of Calculus as well as visit a company or research facility that uses Calculus to solve problems. Essential Question of the Individual Unit: Why do I need to know Calculus? Objectives for Students: By the end of this Unit students will be able to: Apply Differential Calculus methods to solve real world problems. Topics emphasized will be: - Using derivatives to find rates of change in the natural, engineering and social sciences (e.g., physics, chemistry, thermodynamics, meteorology, biology, economics, psychology, sociology, mechanical engineering). - Related rates problems using the chain rule for differentiation. - Sketching of a curve y= f(x). (This includes finding the domain, range, x- and y- intercepts, symmetry, any asymptotes, intervals of increase or decrease, locations of local and absolute maximum and minimum points, concavity and location of any points of inflection.) - Optimization problems in various disciplines using the information learned in curve sketching. Describe orally and in writing their logic and reasoning to solve certain problems. Apply what they have learned to solve more difficult problems (e.g., Where Should a Pilot Start Descent?, The Calculus of Rainbows, The Most Economical Shape of a Can). Assign groups. Learn about an historical figure, who either added novel methods to Calculus or used Calculus in a novel way in his/ her discipline. Describe what they learned about Differential Calculus from the company or research facility that they visit towards the end of the unit. (Need to find out how to schedule a high school field trip.) ISBE/College Readiness Standards Per Subject Area (List all that apply) ISBE Standards for Subject Area College Readiness Standard (Social Studies and Language use Reading and Writing Standards) There are no specific standards for Calculus, but I have listed a few of the important ones that would There are no CRS for Calculus, but I have included upper level standards here that would be used in a
- 2. be used in a Calculus course: A.SSE.1 F.IF.4, 5, 7, 7c F.BF.1 G.GMD.3 G.MG.1, 2, 3 Calculus course: - Interpret and use information from figures and graphs. - Manipulate expressions and equations. - Interpret and use information from graphs in the coordinate plane. -Analyze and draw conclusions based on information from figures and graphs. - Write expressions that require planning and/or manipulating to accurately model a situation. -Write equations that require planning, manipulating, and/or solving. - Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax族 + c. -Solve problems integrating multiple algebraic and/or geometric concepts. -Analyze and draw conclusions based on information from graphs in the coordinate plane. - Draw conclusions based on a set of conditions. -Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas. General In-class Activities/Strategies per Subject Area: Activities: Class discussion and brainstorming about how to solve certain difficult problems, short instructor lectures/explanations giving hints on how to attack difficult problems, group and individual solving of problems from text books or handouts from instructor (groups of distributed talent will sometimes be assigned by instructor so that students can help other students out), confidence builders[ (1) students solve problems on board and verbally explain to class their method and logic with other student and instructor support, if necessary, and (2) practice in clearly explaining their method and logic used to solve problems in writing by individual journaling], bell ringer warm up problems, entrance, and exit slips to check student understanding , occasional fun change of pace games, computer lab work, using Journey Through Calculus CD ROM (see textbook reference below) to supplement classroom instruction, graphing calculator work. Instructor Classroom Strategies: (Sources--Table of High Leverage Practices as laid out in Doing Teaching: The Case of Ms. Gates, by Dr. Ignacio Lopez, and my own classroom observations) Stick with my designated time limits as laid out in my lesson plans. Keep the momentum going-crisp transitions in and out of topics. Create a rapport with students so that they feel emboldened to share their
- 3. answers with me and the class. Use No opt out--dont let a student pass on his/her original thought. If student gets confused, then ask appropriate questions to help him/her find the way. Use cold calling to keep students attention and to get all students participating. Facilitate students to stretch their thinking. Beware of teacher talking/ student doing ratio. Primary textbook: Calculus, 4th edition by James Stewart, which includes a CD ROM called Journey Through Calculus (JTC). This CD ROM contains 7 modules that include visual animation, problem solving techniques, and a symbolic computation program that will make topics come to life. It will help to keep students focused and interested in the concepts being studied. I will use modules 3, 4, 5 on derivatives, derivative calculations, and derivative applications respectively. In the book, I will cover chapter 3 on derivatives and their applications including rates of change in the natural, engineering and social sciences, and related rates problems (sections 3.1 3.9), and chapter 4 on applications of differentiation including optimization problems (sections 4.1 4.7). Assessment Suggestions per course: (List assessment you plan to use during the unit) Formative: Weekly quizzes, periodic examination of journal entries and feedback to students , student explanations to class on problem solving strategy and solution, daily class participation, homework quick check, entrance and exit slips. (20% of grade) Summative: End of unit written test (40% of grade) Portfolio to include solutions to and explanations of difficult problems, re-worked quiz problems, historical report, reasoning and logic journals, report on visit to company or research facility (40% of grade) Service Learning Component: Does this Individual Unit have a Service Learning Component: No Reflection: (Each member should complete this section individually then upload your IU to livetext) My EQ is not especially creative, but still very relevant and practical for the real world of science and mathematics. I think having the students learn about an historical figure in the world of Calculus and having them visit a company or research facility that uses Calculus are novel approaches that one would not find in a typical Calculus class curriculum. These two objectives and certain sections from the textbook also reinforce the idea that calculus underpins inter-disciplinary studies. For part of the summative assessment, I included the portfolio idea we used for the Integrated Unit Plan.