Lesson+Plan+4

** Lesson Title ** : The Power of Notation ** Learning Targets: ** To formalize and consolidate Previous of NOW-NEXT equations, particularly through the use of subscript notation and the introduction of recursive formulas. **Math EALR 1:** **Student understands and applies the concepts and procedures of mathematics.** 1.1 Number Sense: Understand and apply concepts and procedures from number sense. GLE 1.1.7 Applies strategies and uses tools to complete tasks involving computation of real numbers. 1.5 Algebraic Sense: Understand and apply concepts and procedures from algebraic sense. GLE 1.5.3 Recognize functional relationships presented in words, tables, graphs and symbols. ** Math EALR 2: ** **Student uses mathematics to define and solve problems.** 2.1 Define Problems GLE 2.1.2 Analyze a situation and describe the problem(s) to be solved. 2.2 Construct Solutions GLE 2.2.4 Use logical reasoning and mathematical knowledge to obtain and justify mathematically correct solutions. ** Math EALR 3: ** The student uses mathematical reasoning. 3.1 Analyze Information GLE 3.1.1 Model situations and relationships using a variety of basic functions (linear, quadratic, logarithmic, cubic, exponential, and reciprocal) and piecewise‑defined functions. 4.2 Organize, represent and share information. GLE 4.2.1 Use symbols, diagrams, graphs, and words to clearly communicate mathematical ideas, reasoning, and their implications. 5.2 Relate mathematical concepts and procedures to other disciplines. GLE 5.3.1 Use mathematical ideas and strategies to analyze relationships within mathematics and in other disciplines and real life situations.
 * Instructional Lesson Plan **
 * Daniel Schmidt **
 * High School **
 * Date Taught: November 18, 2008 **
 * EALRS: **
 * Math EALR 4: **   **  The student communicates knowledge and understanding in both everyday and mathematical language.  **
 * Math EALR 5: The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real‑world situations. **

** Assessment Strategies: ** While students are working on their investigation in groups of 2 to 3, the teacher will circulate around the classroom and ask questions as an informal assessment. The teacher will also look at the students work to get an idea of each student and group’s understanding and methods. The teacher will also offer suggestions to guide the students. The investigation will consist of five related problems from their book and a checkpoint. Students will be selected at random to present to the class an answer to a problem and how they derived their answer. The presentation will be informally (i.e. not graded) assessed by the teacher using the following criteria: using correct mathematical language and mathematical correctness. The assignment will be due at the beginning of the next day’s class. ** Grouping of Students for Interaction ** : Students will be placed in groups of 2 to 3, and will complete problems 1-5. ** Learning Experience: ** Introduction: Teacher will begin class with a warm-up exercise. The warm-up exercise will ask students to complete a question that covers material learned over the previous couple of days. Whole Class: The teacher will act as a facilitator, as students work in small groups completing all five problems from their text. The presentation will be informally (i.e. not graded) assessed by the teacher using the following criteria: using correct mathematical language and mathematical correctness. If the student presents the wrong answer, the teacher will explain to the rest of the class; why it was wrong, and help guide the students toward the correct answer. Learning Activity: Students will be placed in groups of 2 to 3 and will be asked to complete five related problems from their book. Closure: Teacher will present the solutions to the class that weren’t presented by the student presenters. The teacher will also answer any final questions that the students may have regarding the investigation group activity. Independent Practice: The students will work on the remaining problems from the book and also the checkpoint. They are encouraged to work together outside of the classroom to complete the assignment. They are also encouraged to meet with the teacher if they need additional help. ** Instructional Materials, Resources, and Technology: ** >   **__  Instructional Plan Rationale  __** ** Assessment Strategies: **
 * Whiteboard/Chalkboard
 * Markers/Chalk
 * Projector
 * Transparent worksheets
 * Worksheets
 * Student Textbooks
 * Ti-83 Calculator
 * Learning Targets: **
 * 1)  The learning targets for this lesson are tied in with the EALRs and GLE’s listed above. The EALRs are there to prepare students for standardized tests such as the WASL and SAT. They also prepare students for life after their academic career.
 * 2)  The learning targets use past mathematical knowledge and will prepare students for the next unit. The lesson will reinforce prior knowledge and critical thinking, as well as cooperative learning.
 * 3)  The learning targets will use different teaching techniques, so that all students have an equal chance at gaining the knowledge needed to be successful, both during and after this lesson. Students are encouraged to participate in the class discussion, work within a group setting in order to create a math community.
 * 1)  While students are completing their bookwork, the teacher will circulate around the room conducting an informal assessment of each groups understanding of the material.
 * 2)  Each student will turn in a copy of the worksheet for the teacher to grade.
 * 3)  Students will be assigned the five related problems from the book as well as the checkpoint to be completed as homework, to be turned in at the beginning of the next class period. The students have been given a rubric, so they are aware of exactly how they will be assessed.


 * Learning Experiences: **
 * 1)  During the investigation, students will be encouraged to ask questions.
 * 2)  Prior to the lesson, students will be asked if they have any questions regarding the previous day’s lesson, and homework assignment. If they do have questions the teacher will review and reinforce those skills.
 * 3)  Students who feel that they may need extra help are encouraged to make arrangements with the teacher to meet before or after school, or during lunch.
 * 4)  Students working in groups will reinforce cooperative learning skills. They are expected to work together and help any student who may need extra attention. The teacher, while circulating around the room, will also help in that regard.
 * 5)  During the whole group discussion, the teacher will ask students to discuss questions posed to them, have students present their own questions, and share thoughts. All thoughts will be given respect and students will feel at ease sharing their thoughts, as they will see how it all plays a role to a better understanding for all students.
 * 6)  Students with disabilities and/or 504 students will be accommodated as necessary.


 * Family Interactions: **
 * 1)  A letter will be sent home at the beginning of each quarter to the parents or guardians of each student. It will include contact information for the teacher, grading procedures, course outline, and tentative schedule. If there are any issues that need to be brought to the teacher’s attention, parents are encouraged to contact the teacher at their earliest convenience. This letter should be signed and returned to the teacher by the end of the first week of the quarter. Students who return a signed copy will be given a hint card, which can be cashed in any at point throughout the quarter. The card will allow the student a hint on any quiz, homework, or test problem throughout the quarter.

**Reflection 4:** This was a great lesson that the students really enjoyed. There were a couple of problems that I tried to deal with. One was the notation itself. Pn-1 was very difficult for some of the students. I had some difficulty explaining this notation to these students but eventually we were able to work through it. The other problem was using the Ti-83 calculators in the sequential mode. Again a few students really struggled with this. I thought I had helped all the students through this but then today in class there was one that was still struggling. On the bright side most of the students really did understand and the lesson went fairly smoothly. Students were excited to read when I asked for readers and that pleased me. If I was to change anything I would try to find a couple of more ways to explain the two problem areas. Also the dynamic of the classroom was a little different because my master teacher was not there and I had a substitute teacher that was trying to learn the lesson from me so he could teach it the following period. This was somewhat distracting but it worked out alright. Overall I enjoyed this experience and the learning goals seemed to be attained.