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Too many grades of D or F in math?. Kids only get one chance at receiving a good education, we are working to ensure they get it!. Axiom. The more math you know, the easier math gets!. Way of Thinking. Math is more than just a body of knowledge,
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Kids only get one chance at receiving a good education, we are working to ensure they get it!
Axiom The more math you know, the easier math gets!
Way of Thinking Math is more than just a body of knowledge, it is a way of thinking that affects the way we live.
Decisions • Computation; 4 x 13 x 25 • Algorithm (rule) • Properties of Real Numbers
Decisions • Finding a common denominator • Multiply denominators • Write multiples • Factor Tree, LCM • Reducing Method
Decisions • Systems of Equations • Graphing • Substitution • Linear Combination • Cramer’s Rule
Decisions • Quadratic Equations • Zero Product Property • Completing the Square • Quadratic Formula • Rational Root Theorem
Answering the Question • The “5+1” answers the fundamental question parents want to know ~ What are you doing to help my child learn?
“5+1” • Implementing the “5+1” results in students being more comfortable in their knowledge, understanding, and application of mathematics. • The “5+1” organizes and focuses students so they can study more effectively and efficiently.
Organizing Student Learning5 +1 • Instruction/Preparation, Concept Development-Linkage • Note Taking • Homework • Test Preparation • Assessment Student-Teacher Relationships My Kid Standard
Student-Teacher Relationships • Treat your students the way you want your own children treated. • Build success on success. • Talk to your students. Be friendly. • Talk positively to your students about their opportunity to be successful. • Call home early with information and good news. • Make testing as much a reflection of your instruction as their studying.
Student-Teacher Relationships • Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time). • Tell them you like them. • Go over expectations explicitly and give examples. • Build trust, make sure they know you are there for them by telling them you are. • Tell them you want them to succeed. • Continually answer the question; “What am I doing to help my students learn?”
The Phone Conversation • Introduction • Pleasure teaching your son/daughter, nice young man/lady • Explanation, how I intend to help your child succeed – Instruction • Clear instruction, linkage, memory aids • Notes, * system, very prescriptive • Homework, comes from notes & instruction • Oral recitation, procedures & formulas • Practice tests, * system • Study/flash cards • Reviews
The Phone Conversation • Permission to use those strategies/consequences • Parental help • Know when tests are scheduled • Examine student notebooks • Use flashcards to help study
Preparation Preparation Creation of a practice test before instruction begins suggests that teachers prepared for the unit; knowing where students traditionally experience difficulty and having resources and strategies ready to address those difficulties.
Preparation • Practice test • Cover curriculum appropriately (rigor) • Grades - Fair & Portable • Benchmarked • Unit questions reflect questions on: • Curriculum • Unit • HSPE • Semester exams • College Entrance exams (ACT & SAT)
When will I ever use this? • Pythagorean Theorem • Parabola • Circumference
Balance Balance in mathematics has been defined as: • Vocabulary & Notation • Concept Development & Linkage • Memorization of Important Facts & Procedure • Applications • Appropriate Use of Technology Balance should be reflected in assessmentsand in the delivery of instruction.
Vocabulary & Notation There is no more single important factor that affects student achievement than vocabulary and notation
Vocabulary • Find the degree of the monomial 4x2y3z5
Language Acquisition • Double meanings area volume operation power mean feet product
Greek to Me • Theorem In a right triangle, the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments.
Use simple straight forward examples that clarify what you are teaching. Do not get bogged down in arithmetic.
Show them how - Linkage • Introduce new concepts using familiar language • Review and reinforce • Compare and contrast • Teach in a different context
Add / Subtract Rational Expressions
1 2 3 6 1 3 + + 2 6 5 6
1 5 1 + = 2 6 3 1 9 1 + = 5 20 4 1 7 1 + = 4 12 3
1 8 1 + = 15 5 3
1 13 2 + = 5 3 2 29 3 + = 3 10 15 30
1 3 + = 5 4 20 1 19 3 + = 5 4
3 2 + = Y XY X 3 2Y + 3X 2 + = Y XY X
+ = D BD B C A C AD + BC A + = D BD B
2 3 + = x+3 (x-1)(x+3) x-1 2 3 3(x+3) + 2(x-1) + = x+3 (x-1)(x+3) x-1
Axiom The more math you know, the easier math gets!
6 7 2 = 6 10 + 7 10 + 2 2 6 n + 7 n + 2 2 6x + 7x + 2 2 6(100) + 7(10) + 2(1)
5 3 2 + 3 4 1 = (5 +3)(100) + (3 + 4)(10) +(2 + 1)(1) = (8)(100) + (7)(10) + (3)(1) = (800) + (70) + (3) = 8 7 3
362 412 + + (8)(10) + (7)(1) = + (80) + + (7) = Addition - Left to Right 213 = (4 +3+2)(100) + (1+6+1)(10) + (2+2+3)(1) = (9)(100) (900) 9 8 7
5 3 2 + 3 4 1 = 8 7 3 (5x + 3x + 2) + (3x + 4x + 1) 2 2 (5x + 3x ) + (3x + 4x) + (2 + 1) 2 2 = 8x + 7x + 3 2
Axiom The more math you know, the easier math gets!
Title • Date • Objective • Vocabulary & Notation • Pattern Development • Rule • Examples • Variation