Course Number: 316

SYLLABUS

Algebra 1

COURSE NUMBER: 316

COURSE DESCRIPTION

This is the first course in a college preparatory mathematics sequence for freshmen. Units of study include: linear equations and inequalities, linear functions and graphs, absolute value functions, systems of equations, quadratic equations and functions, laws of exponents, radicals, and probability and statistics. Technological tools, such as the TI graphing calculator, will be used for both discovery and problem solving; classroom sets will be provided. All students will be expected to bring a TI-30XIIS scientific calculator to class every day.

ENDURING UNDERSTANDINGS – After successfully completing this course, the student will understand that:

Real number calculations are a life skill.
Variables and expressions represent unknown quantities.
Formulas are used to find missing quantities.
Slope is the rate of change.
Linear, absolute value and quadratic functions can be used to model real-world situations.
Many real-world applications can be modeled and solved using a system of equations.
A graph is a visual representation of an equation.

CREDIT: 1 credit LEVEL: 9 - Regular

PREREQUISITES

Algebra 1 and Algebra 1-Extended are freshman level classes. Algebra 1 for Upperclassmen is specifically for sophomores, juniors and seniors who passed PreAlgebra with a grade of C or better.

AREAS OF STUDY

First Semester Second Semester

Solving Equations and Inequalities Systems of Equations and Inequalities

Graphing Linear Equations and Inequalities Quadratics

Statistics Exponents and Exponential Functions

Semester 1

UNIT 1: Solving Equations and Inequalities (30 Days)

Enduring Understanding:

· There is a systematic mathematical approach that can be applied when solving for an unknown.

· Variables represent unknown quantities.

· Simplifying expressions and solving equations allows us to take a complex situation and make it simple.

Essential Questions:

· How do you solve for an unknown quantity?

· What is a variable?

· How is solving inequalities the same and/or different than solving equations?

Knowledge and Skills

Pre-Skill: Students will apply order of operations (1.2 in the book)

Pre-Skill: Students will simplify expressions (Ch. 1 and 2)

Pre-Skill: Students will evaluate expressions (Ch. 1 and 2)

Pre-Skill: Students will translate words to mathematical expressions

Pre-Skill: Students will solve one-step equations (3.1)

Students will solve two-step equations (3.1) A-REI-3
Students will solve one- and two-step literal equations (3.1) A-REI-3, A-CED-1, A-CED-2, A-CED-4
Students will solve equations with variables on both sides (3.3) A-REI-3
Students will solve problems using proportions (3.4 and 3.5) A-REI-3, A-CED-1, N-Q-1
Students will solve single variable word problems (3.6) A-REI-3, A-CED-1, N-Q-1
Students will solve multi-step equations (3.2) A-REI-1, A-REI-3
Students will solve and graph one-step inequalities (4.1, 4.2, 4.3) A-REI-3

Students will solve two-step inequalities (4.4) A-REI-3
Students will solve inequalities with variables on both sides (4.4) A-REI-3
Students will solve multi-step inequalities (4.4) A-REI-1, A-REI-3

UNIT 2: Graphing Linear Equations and Inequalities (40 Days)

Enduring Understanding:

· Students will understand that there are multiple ways to represent the same solution

· A line represents an infinite solution set

· Equations can be used to model real world situations

Essential Questions

· How can I use a graph to make future predictions?

Knowledge and Skills

Pre-Skill: Students will be able to graph lines using a table of values (5.3)

Students will be able to interpret functions F-IF-1, F-IF-2, S-ID-7
Students will be able to write a linear equation given a table of values (5.4) F-BF-1a, F-LE-1a, F-LE-1b, F-LE-2, S-ID-7
Students will be able to calculate rate of change/slope algebraically (6.1) F-IF-6, F-LE-1b, F-LE-1c, S-ID-7
Students will be able to analyze the rate of change/slope from a given graph or table ( 6.1) F-IF-6, F-LE-1b, F-LE-1c, S-ID-7
Students will be able to create a table of values from a given equation or function F-BF-1
Students will be able to graph a linear equation, including those given in function notation, given in slope-intercept form (6.2) A-CED-2, A-REI-10
Students will be able to graph a linear equation given in standard form (6.4) A-CED-2, A-REI-10
Students will be able to create functions to model real-world situations A-CED-1, A-CED-2, A-REI-10, S-ID-7

Students will be able to create a linear equation from a graph (CH. 6) A-CED-2, A-REI-10
Students will be able to create a linear equation given a slope and a point (6.5) A-CED-2
Students will be able to create a linear equation given two points (6.5) A-CED-2
Students will be able to identify and write equations of parallel and perpendicular lines (6.6) G-CO-1, G-GPE-5
Students will be able to graph a linear inequality [given in slope-intercept form and standard form] A-CED-1, A-CED-2, A-CED-3

UNIT 3: Statistics (15 Days) [Supplementary Materials will be needed]

Enduring Understanding:

· Data can be represented in a variety of formats.

· Extreme data points (outliers) can skew interpretations of a set of data.

· Synthesizing information from multiple sets of data results in evidence-based interpretation.

· A line of best fit can be generated for a set of data to model the relationship between two variables.

· A line of best fit can be used to make predictions within the proximity of data.

Essential Questions:

· How do different representations of data lead to different interpretations of the data?

· Why are multiple sets of data used?

Knowledge and Skills

Students will be able to compare center (mean, median) and spread (range, maximum, minimum) from various data sets [e.g. box and whisker plots, scatter plots] (1.6 and Data Analysis p.52-53) S-ID-2 **Note: If time allows, continue with quartiles

Students will be able to identify and describe possible outliers in a data set (1.6) S-ID-3
Students will be able to interpret the slope and y-intercept of a best fit line in the context of a data set (6.7) S-ID-7, S-ID-6

Semester 2

UNIT 4: Systems of Equations and Inequalities

Enduring Understandings:

· The algebraic solution to a system of equations is the intersection point on the coordinate plane.

Essential Questions:

· When is it appropriate to solve a system algebraically?

· When is it appropriate to solve a system graphically?

Knowledge and Skills:

1. Students will be able to solve systems graphically (7.1)

2. Students will be able to solve systems algebraically when given two equations in standard form (7.3)

3. Students will be able to solve systems algebraically when given two equations in slope intercept form (7.2)

4. Students will be able to solve systems when given one equation in standard form and one equation in slope intercept form (7.2-7.3)

5. Students will be able to create a system of equations based on a graph (Ch. 7)

6. Students will be able to recognize a system with no solution (Ch. 7)

7. Students will be able to recognize a system with infinite solutions (Ch. 7)

8. Students will be able to create a system of equations based on real world problems (7.4)

9. Students will be able to solve a system of inequalities graphically.

UNIT 5: Quadratics

Enduring Understandings:

· A simplified algebraic expression has no common terms

· There can be at most two solutions to a quadratic

· There is a connection between factoring and polynomial multiplication

Essential Questions:

· How are the solutions of a quadratic represented graphically?

· What is the appropriate method to solve a quadratic?

· How can we use factoring to solve a quadratic equation?

Knowledge and Skills

10. Students will be able to add/subtract quadratic expressions (9.1)

11. Students will be able to multiply a monomial and a polynomial. (9.2-9.3)

12. Students will be able to multiply binomials to create a quadratic (9.2-9.3)

13. Students will be able to factor out a GCF ( 9.2)

14. Students will be able to factor trinomials with a = 1 (9.5)

15. Students will be able to factor trinomials with a ≠ 1. (9.6)

16. Students will be able to factor the difference of perfect squares. (9.7)

17. Students will be able to solve quadratic equations by taking square roots (10.3)

18. Students will be able to solve quadratic equations by factoring (10.4)

19. Students will solve quadratic equations by completing the square

(10-5)

20. Students will be able to solve quadratic equations using the quadratic formula (10.6)

21. Students will be able to solve quadratics graphically (Ch. 10)

UNIT 6: Exponents and Exponential Functions

Enduring Understandings:

· XXX

Essential Questions:

· XXX

Knowledge and Skills

22. Students will multiply monomials (8.3)

23. Students will be able to raise a monomial to a power (8.4)

24. Students will divide monomials (8.5)

25. Students will simplify monomials that have 0 as an exponent

26. Students will simplify monomial expressions with negative exponents

27. Students will classify Graphs, Tables, and sequences as exponential, linear or neither. Geometric vs Arithmetic sequences (8-6)

28. Students will distinguish between exponential growth and decay expressions, Ex - 2x, 2-x, 12x, 12x (8-7)

29. Student will solve real life problems involving exponential growth or decay including writing the explicit function to represent a real life scenario. (8-8)

UPDATED: Summer, 2014 BY: Kara Bucci, Janna Canning, Kevin Carlsen, Bill Flood, Jen Liaros, Kathleen McNeeley, Mike Osbourne, Matt Peccia