WOODLAND HILLS HIGH SCHOOL LESSON PLAN
SAS and Understanding By Design Template
Name _Irene Runco______Date Feb 2, 2015 _ Length of Lesson __25 days(total)_ Content Area Honors Algebra 2 _
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STAGE I – DESIRED RESULTSLESSON TOPIC:
Unit 5: Polynomials:
· Monomials and operations
· Polynomials, adding and subtracting
· Dividing polynomials
· Factoring polynomials
· Roots and real numbers
· Radical expressions
· Rational exponents
· Radical equations
· Complex numbers / BIG IDEAS:
Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
KEYSTONE ANCHORS:
A2.1.1.1 Represent and/or use imaginary numbers in equivalent forms (e.g., square roots and exponents).
A2.1.1.2 Apply the order of operations in computation and in problem‐solving situations.
A2.1.2.1 Use exponents, roots, and/or absolute values to represent equivalent forms or to solve
problems.
A2.1.2.2 Simplify expressions involving polynomials.
A2.1.3.1 Write and/or solve non‐linear equations using various methods.
A2.2.1.1 Analyze and/or use patterns or relations.
A2.2.2.1 Create, interpret, and/or use polynomial, exponential, and/or logarithmic functions
and their equations, graphs, or tables.
.
ELIBIBLE CONTENT:
M11.D.2.2.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial X a trinomial).
M11.A.1.1.3 Express numbers and/or simplify expressions using scientific notation (including numbers less than 1).
M11.A.1.2.1 Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is not equal to 0).
M11.A.1.2.2 Find the Greatest Common Factor (GCF) for sets of monomials and/or factor polynomial expressions using the greatest common monomial factor.
M11.A.1.2.3 Simplify algebraic fractions.
M11.A.2.2.2 Simplify expressions involving multiplying with exponents (e.g., x6 x7 = x13), powers of powers (e.g., (x6)7=x42) and powers of products (2x2)3=8x6 (positive exponents only).
UNDERSTANDING GOALS (CONCEPTS):
· Basic operations with monomials, polynomials, radical expressions, and complex numbers
· Using the distributive property
· Using properties of exponents
· Using properties of radicals
· Solving polynomial equations by factoring
· Solving radical equations
· Solving radical inequalities
· / ESSENTIAL QUESTIONS:
How can you extend algebraic properties and processes to quadratic, exponential and polynomial expressions and equations and then apply them to solve real world problems?
What are the advantages/disadvantages of the various methods to represent exponential functions (table, graph, equation) and how do we choose the most appropriate representation?
VOCABULARY
· Monomial (2)· Binomials (2)
· Polynomial (2)
· FOIL (1)
· Conjugate (3)
· Complex number (2)
· sy nthetic division (3)
· rationalizing the denominator (3)
· extraneous solutions (3)
· /
STUDENT OBJECTIVES (COMPETENCIES/OUTCOMES):
Students will be able to:1. Express numbers in scientific notation.(2 days )
2. Apply the laws of exponents to simplify expressions. (2 days)
3. Add, subtract, multiply, and divide polynomials. (6 days)
4. Factor polynomials using various factoring techniques, including (10 days)
a. Finding Greatest Common Factor
b. Difference of Two Squares )
c. Sum and Difference of Two Cubes
d. Perfect Square Trinomials )
e. General Trinomials
i. c > 0
ii. c < 0
iii. a 1
f. Factoring by grouping )
5. Review, quizzes, and test ( 4 days)
STAGE II – ASSESSMENT EVIDENCE
PERFORMANCE TASK:
Students will participate in
1. class discussions,
2. guided notes & practice,
3. computer work,
4. whiteboard activities / OTHER EVIDENCE:
· Daily warm up or exit polls ,
· homework,
· Keystone Diagnostic Tool,
· Study Island and Glencoe.unit tests,
· quizzes,
· formative assessments.
· Student work in portfolio
STAGE III: LEARNING PLAN
INSTRUCTIONAL PROCEDURES:
(Active Engagement, Explicit Instruction, Metacognition, Modeling, Scaffolding)
ACTIVE ENGAGEMENT USED:
· Cooperative learning
· Think pair share
· Notetaking
· Higher level thinking
DESCRIBE USAGE
Students will work from basic procedures to solve equations
Solving world problems
Solving real world applications
Proving properties of algeb
SCAFFOLDING USED
:
· Chunking
· Building on Prior knowledge
· Providing Visual Support
MINI LESSONS:
· Using algebra tiles
· Distributing when subtracting polynomials
· Synthetic division and its limitations
· What discriminants tell you
· Quadratic formula song / MATERIALS AND RESOURCES:
Unit 1 Chapter : Systems of Equations and Inequalities
( Glencoe Text )
Warm ups & Exit polls(daily)
Homework (daily)
Guided practice and Enrichment from Glencoe Grab & Go workbooks
Curriculum Binder: Algebra 1 before books This has very good additional practice for students in these area
Glencoe teacher works…chalkboard is
Good for Promethean Board use. / INTERVENTIONS:
Study Island
A+ Math
Math Lab
Khan Academy Videos
Keystone Diagnostic Tool
National Library of Virtual Manipulatives is an excellent site for use with promethean boards for this unit.
On line activities are very good in this chapter for finding a pattern and making predictions based on your observations.
Also www.shodor.org has good interactive material
Linear Function Machine is a good activity from this site
Truly struggling students will be referred to guidance/SAP (RTI)
• Small group/ flexible grouping will occur if necessary.
• Students will be encouraged to stay for or find help with a math teacher during free time, after school, or lunch. / ASSIGNMENTS:
Note: all assignment are from the same page, but different questions are assigned based on grouping by teacher.
· Weekly blogs
· Word problem practice from 2008 copy of Algebra 2 (on line form Glencoe.com)
· Enrichment from 2008 Glencoe ( advanced)
· Khan Academy videos
§5-3 pp 236-238
§5-4 pp 242-244
§5-5 pp 248-249
§5-6 pp 254-256
§5-7 pp 260-262
§5-8 pp 266-267
§5-9 pp 273-275
Note: Reading with Mathematics pages from Grab & Go are especially good for standard classes.
Note: Algebra tiles can be very helpful in this chapter for factoring
Monday 97A / Tuesday 98B / Wednesday 99A / Thursday 100 B / Friday 101 A
Do now: factoring walk around activity – 10 minutes
Review of simplifying radical expressions
Rationalizing the denominator
/ · Do now:
· Slide 178 from chalkboard
· Simplifying radical expressions
· Emphasis: (1) simplify each radical (2) combine like terms (3) put in proper order / · Do now:
· Explain the retention of signs when working with radicals… how does it change from even to odd roots?
· Conjugates of radical expressions
· Review of (a+b) times (a-b) / · Do now:
· 6√x3
· Can you suggest another form for this answer?
· What will it take to get the x out of the radical?
· How does that relate?
· Rational exponents / · Do now:
· What can you do now with rational exponents that you could not do previously? Give an example.
Quiz on first half of chapter 5.
· Complete p 718# 1 – 57 / · P 254 # 25 - 34 / P 254 # 35 - 45 / · P 261 @ 21- 49
Math Lab – Tuesday, Thursdays