Download Wayne County High School Daily Lesson Plan

Wayne County High School Daily Lesson Plan
Teacher: Baygents, Evans,
Overstreet, Shirley
Course: Transitions
Date(s): Aug. 19 -Aug.23 2013
Framework Competency and Objective
TRANSITION TO ALGEBRA
CONTENT STRANDS:
Number and Operations Algebra
Geometry Measurement
Data Analysis
Competencies and Objectives:
NUMBER AND OPERATIONS
1. Understand relationships between numbers and their properties and perform
operations fluently.
a. Compare and contrast the subsets of real numbers. (DOK 1)
b. Simplify and evaluate expressions using order of operations and use real number properties to justify solutions. (DOK 2)
c. Express, interpret, and compute numbers using scientific notation in meaningful contexts. (DOK 1)
d. Apply the concept of Greatest Common Factor (GCF) and Least Common Multiple (LCM) to monomials with variables. (DOK 2)
e. Use the inverse relationship to develop the concept of roots and perfect squares. (DOK 2)
ALGEBRA
2. Understand, represent, and analyze patterns, relations, and functions.
a. Given a literal equation, solve for a specified variable of degree one. (DOK 1)
b. Explain and illustrate how changes in one variable may result in a change in another variable. (DOK 2)
c. Solve and check multi-step equations and inequalities, including distributive property, variables on both sides, and rational coefficients.
(DOK 2)
d. Use real-world data to express slope as a rate of change. (DOK 2)
e. Graph solutions to linear inequalities. (DOK 2)
f. Write linear equations given slope and y-intercept or two points. (DOK 2)
g. Identify domain, range, slope, and intercepts of functions. (DOK 1)
h. Develop generalizations to characterize the behaviors of graphs (linear,
quadratic, and absolute value). (DOK 2)
i. Classify and determine degree of a polynomial and arrange polynomials in
ascending or descending order of a variable. (DOK 1)
j. Apply ratios and use proportional reasoning to solve real-world algebraic
problems. (DOK 2)
k. Add, subtract, multiply, and divide polynomial expressions. (DOK 1)
l. Analyze the relationship between x and y values, and determine whether a
relation is a function. (DOK 2)
GEOMETRY
3. Understand geometric principles of polygons, angles, figures.
a. Apply the Pythagorean Theorem to solve problems. (DOK 2)
b. Apply proportional reasoning to determine similar figures and find unknown measures. (DOK 2)
MEASUREMENT
4. Demonstrate and apply various formulas in problem-solving situations.
a. Solve real-world problems involving measurements (i.e., circumference, perimeter, area, volume, distance, temperature, etc.). (DOK 2)
b. Explain and apply the appropriate formula to determine length, midpoint, and slope of a segment in a coordinate plane (i.e., distance
formula, Pythagorean Theorem). (DOK 2)
DATA ANALYSIS
5. Interpret data.
a. Construct graphs, make predictions, and draw conclusions from tables, line graphs, and scatter plots. (DOK 3)
b. Use a given mean, mode, median, and range to summarize and compare data sets including investigation of the different effects that
change in data have on these measures of central tendency, and select the appropriate measures of central tendency for a given purpose.
(DOK 2)
c. Calculate basic probability of experiments and simulations to make and test conjectures about results. (DOK 3) Utilize critical thinking and
scientific problem solving in designing and performing biological research and experimentation.
Page 1
Common Core Standards
Seeing Structure in expressions a-SSe
Interpret the structure of expressions
1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
2. Use the structure of an expression to identify ways to rewrite it.
Write expressions in equivalent forms to solve problems
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions.
4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Arithmetic with Polynomials and rational expressions a-aPr
Perform arithmetic operations on polynomials
1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition,
subtraction, and multiplication; add, subtract, and multiply polynomials.
Understand the relationship between zeros and factors of polynomials
2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0
if and only if (x – a) is a factor of p(x).
3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function
defined by the polynomial.
Use polynomial identities to solve problems
4. Prove polynomial identities and use them to describe numerical relationships.
can be used to generate Pythagorean triples.
5. (+) Know and apply the Binomial Theorem for the expansion of (x+ y)n in powers of x and y for a positive integer n, where x and y are
any numbers, with coefficients determined for example by Pascal’s Triangle.1
Rewrite rational expressions
6. Rewrite simple rational expressions in different forms; write a(x)/b(x)in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are
polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples,
a computer algebra system.
7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Creating equations a-Ced
Create equations that describe numbers or relationships
1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and
quadratic functions, and simple rational and exponential functions.
2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with
labels and scales.
3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable
or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on
combinations of different foods.
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange
Ohm’s law V = IR to highlight resistance R.
Reasoning with equations and Inequalities a-reI
Understand solving equations as a process of reasoning and explain
the reasoning
Page 2
1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from
the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
4. Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) 2= q
that has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2= 49), taking square roots, completing the square, the quadratic formula
and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex
solutions and write them as a ± bi for real numbers a and b. Solve systems of equations
5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of
the other produces a system with the same solutions.
Monday
Focus of Lesson
(Student-Friendly Objective)
Bell Work
Learning Tasks/Activities
TSW determine the difference between inequalities and equations
TSW create and solve simple inequalities
TSW graph inequalities
(3-1-3-4) Inequalities (Adding, subtracting, multiplying, dividing)
Review Equations (Examples follow)
3/4x + 8 = ½
4(2x – 3) = 5(6x + 10) -2
1.
2.
3.
4.
5.
6.
7.
TSW complete bell work/class will discuss the bell work together
TCW discuss why solving inequalities is important to them
TCW discuss the differences in equations and inequalities
TTW ask Socratic questions to the class to see if students can differentiate between
equations and inequalities
TTW show students how to solve and graph simple inequalities
o Addition/subtraction/ multiplication/division
Students will come to the board and work inequalities
TSW work in ability groups to solve inequalities
Groups
Closure
Tuesday
Focus of Lesson
(Student-Friendly Objective)
Bell Work
Learning Tasks/Activities
Top: Inequality Handout/Inequality Enrichment Activity
Middle: Inequality Handout
Bottom: Remedial Inequality handout/Integers, order of operations, equations reteach
Exit Ticket: TSW solve an inequality and EXPLAIN the steps to take to solve it. The class will
discuss their explanations.
TSW create and solve multistep inequalities
TSW graph solutions to inequalities
3-4 (Multistep Inequalties)
Review Inequalities (Examples follow)
4x + 8 > 3
-5x – (-3) < 13
1. TSW complete bell work/class will discuss the bell work together
2. TCW discuss the differences in simple and complex inequalities
3. TTW show students how to create and solve multistep inequalities
4. Students will come to the board and work complex inequalities
5. TSW work in ability groups to solve inequalities
Groups
Top: Multistep Inequality Handout/Enrichment Activity
Page 3
Closure
Wednesday
Focus of Lesson
(Student-Friendly Objective)
Bell Work
Learning Tasks/Activities
Middle: Multistep Inequality Handout
Bottom: Remedial Inequality handout/Integers, order of operations, equations reteach
Exit Ticket: TSW solve a complex inequality and EXPLAIN the steps to take to solve it. The
class will discuss their explanations.
TSW write sets and identify subsets
TSW find the complement of a set
3-5 Working with Sets
Review inequalities
3/4x + 8 > ½
-5x – (-2) < 2x + 4
1. TSW complete bell work/class will discuss the bell work together
2. TCW review vocabulary words.
3. TCW use roster form and set-builder notation, inequalities and set-builder notation,
and find subsets.
4. Guided practice: pg. 211 1-3
5. Focus Question: How can you write sets and identify subsets?
6. Independent practice. See Groups
Groups
Top: Practice page: Working with sets/ Enrichment Working with Sets
Middle: Practice Page: Working with Sets
Bottom: Re-teach: working with sets
Closure
Thursday
Focus of Lesson
(Student-Friendly Objective)
Bell Work
Learning Tasks/Activities
Exit Ticket: TSW answer: How can you write sets and identify subsets?
TSW solve and graph inequalities containing the word and
TSW solve and graph inequalities containing the word or
(3-6) Compound Inequalities
Review writing and identifying sets and subsets
1. TSW complete bell work/class will discuss the bell work together
2. Watch video on Pearson
3. TCW review vocabulary words.
4. TCW write a compound inequality, solve a compound inequality involving and, write
and solve a compound inequality, solve a compound inequality involving or
5. Guided practice: pg. 217-219 1-4
6. Focus Question: How do you solve and graph inequalities containing the words and
or not?
7. Independent practice. See Groups
Groups
Top: Practice page: Compound inequalities/ Enrichment Compound Inequalities
Middle: Practice Page: Compound Inequalities
Bottom: Re-teach: Compound Inequalities
Closure
Friday
Focus of Lesson
(Student-Friendly Objective)
Bell Work
Learning Tasks/Activities
Exit Ticket: TSW answer: How do you solve and graph inequalities containing the words and
or not?
TSW solve equations involving absolute value
(3-7) Absolute value equations and inequalities
Review solving and graphing inequalities containing the words and/or
1. TSW complete bell work/class will discuss the bell work together
2. TCW watch Pearson video/discuss focus question
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3.
4.
5.
TCW solve absolute value equations with and without solutions
Guided Practice: pg. 223-225 1-22 even
The class will discuss answers
Groups
Closure
Top: Absolute Value Equations and Inequalities Handout/ Absolute Value Equations
and Inequalities Handout Enrichment
Middle: Absolute Value Equations and Inequalities Handout
Bottom: Re-teach: Absolute Value Equations and Inequalities Handout
TSW answer how is solving an equation with an absolute value similar to solving other
equations?
IEP Accommodation (if applicable)
Remediation/Intervention
Enrichment/Challenge for upper 25%
Assessment (pre and/or post)
Resources/Materials
http://www.mathplanet.com/education/algebra-1/exponents-and-exponentialfunctions/properties-of-exponents (Use on Wednesday/Thursday to explain power
properties.
Pearson Textbook
Handouts
Smartboard
Additional Notes:
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