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J#J#J#6.1$1$1$1$1. TITLE OF THE LESSON
Shrinking Areas 3rd day of Fractal ITU
(57 minute lesson)
2. CURRICULUM AREA & GRADE LEVEL
Geometry (9th/10th graders)GENERAL STUDENT INFORMATION:
1.) Readiness Level
Reading at grade level, some students need some pronunciation help
1/3 of class gifted in math, 1/3 average, 1/3 below average
2.) Learning Profile
Most students are visual learners (needing models/representations), auditory and kinesthetic are also prominent
3.) Interest
Skateboarding, surfing, listening to music, socializing3A. STUDENT INFORMATION: English Language Learners
1.) Readiness Level
Alejandro writing/speaking academic language needs help, CELDT 4
2.) Learning Profile
Visual/kinesthetic learner, often needs repetition or rewording
3.) Interest
Basketball, skateboarding, technology3B. STUDENT INFORMATION: Students w/ Special Needs
1.) Readiness Level
Zach- ADHD, Need to build on his algebra skills while learning geometry, he is a good reader, and he needs organizational tools
Cindy Autistic, very good computational skills, good relationship with parents
2.) Learning Profile
Visual learner, likes to work alone
3.) Interest
Reading, drawing
4. RATIONALE
A. Enduring Understanding
Students will be able to measure and study the iterations of fractals, and develop a better sense of patterns.
B. Essential Questions
How can I generalize/simplify a seemingly complex fractal?
What are the patterns of fractal development and how can we describe them using Geometry/Algebra?
C. Reason for Instructional Strategies and Student Activities
Fractals range from very basic to complex, leaving me the ability to differentiate for the diverse students in our classrooms. Also, our theme appeals to different types of learners because fractals are visually stunning, can be created kinesthetically, and can be verbally analyzed quite easily.
5. CONTENT STANDARD(S)
-Common Core Mathematical Practice # 7 Look for and make use of structure
-Common Core: Geometry Measurement and Dimension 5: Determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. (CA standard Geometry 11.0)
6. ELD STANDARD(S)
Listening and Speaking/Vary Ways of Speaking: Consistently use appropriate ways of speaking and writing that vary accordingly to the purpose, audience, and subject matter (A)7. LEARNING GOAL(S) - OBJECTIVE(S)
A. Language
After discussing with groups how the are of the Koch Snowflake changes at each iteration, the students will be able to talk about the patterns to the class in a presentation style.
B. Cognitive
After discussing with groups how the are of the Koch Snowflake changes at each iteration, the students will be able to write the patterns
8. ASSESSMENT(S)
A. Formative-Progress Monitoring
- The teacher will walk around and make sure students are using their organizational charts and are finding the appropriate patterns
B. Summative
- the teacher will discuss with the class how what they learned today relates to the unit question
9A. EXPLANATION OF DIFFERENTIATION FOR
ENGLISH LANGUAGE LEARNERS
Content/Based on Readiness, Learning Profile or Interest
- Based on my ELs learning profiles, visuals help a lot so using the book to follow along and providing diagrams well help
Process/Based on Readiness, Learning Profile or Interest
Talking with peers and in front of the class, writing, and reading aloud are all things that will help improve second language acquisition.
Product/Based on Readiness, Learning Profile or
Interest
The completion of the math problems are assisted enough to meet students readiness.
9B. EXPLANATION OF DIFFERENTIATION FOR
STUDENTS WITH SPECIAL NEEDS
Content/Based on Readiness, Learning Profile or Interest
At the same level as the rest of the class, so ready for this lesson
Enough discussion to get help
Process/Based on Readiness, Learning Profile or Interest
Multiple visual representations used
Product/Based on Readiness, Learning Profile or Interest
At a mathematical level consistent with the rest of class so with my constant observing and checking, the students will be able to produce a competent product.
10. INSTRUCTIONAL STRATEGIES
A. Anticipatory Set/Into/Instruction
-Using the white board panel of information, review with students the information gathered so far and what they still need to know in order to find the area of the Koch Snowflake fractal.
C. Guided Practice/Through
-Work with students to create a chart with columns dealing with the individual triangles and total number of triangles ask whether each is necessary or if need more.
D. Independent (Group) Practice/Through
-Teacher walks around and looks for different ways students saw patterns and maybe different answers
-While students present the patterns they found, listen to student thinking and if something is unclear, ask the student to explain it again
-Remind students to be organized
E. Closure
-Teacher writes stuff down/adds anything necessary or offers hints after students are given ample wait time to the white board panel of information
F. Beyond
- Begin writing the sequence relating to the area of the Koch Snowflake11. STUDENT ACTIVITIES
A. Anticipatory Set/Into/Instruction
- Students add to white board by giving teacher information gained so far from unit
- Students write in journals: What do I need to do with these individual triangles areas in order to find the infinite stars total area?
C. Guided Practice/Through
- Think about: How can I organize the information about the triangle at each iteration in order to find a pattern, and ultimately find the area of the infinite star?
- Copy chart teacher creates with class
D. Independent (Group) Practice/Through
- In groups, students keep track of how many triangles are created in each iteration and find/write the pattern
-Some students present
- In groups, students keep track of total area of the infinite star each iteration in a table. Find/write the pattern.
-Students are chosen to present again.
E. Closure
-Students think about and tell teacher the new information they learned and can add to the big question white board panel.
Particular focus on how the total area changed at each iteration.
F. Beyond
- Begin writing the sequence relating to the area of the Koch Snowflake12. RESOURCES
(Attach any materials needed to implement the lesson, such as a power point presentation, graphic organizer, reading)
White board panel of the unit question, Yesterdays handout, New handout where students will make a table to organize: number of triangles at each iteration & area at each iteration
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