Algebra 1 Accelerated

Course Description

Open to: Grade 8 One Year Course
Prerequisite: Instructor/Counselor Approval/Accelerated Mathematics 7
Content: Students will study the structure of the real number system and will apply it to steps involved in solving algebra problems. Equations and inequalities will be solved using math axioms. Graphic and algebraic analysis of equations, inequalities, and systems of equations will be studied. Emphasis will be placed upon factoring, algebraic fractions, radicals, and problem solving.

Adopted Materials

Title: Algebra-Structure and Method Book 1
Edition: 2000
Publisher McDougal Littell
ISBN: 0-395-97722-3

Resource Materials:

Textbook:
Brown, Dolciani, Sorgenfrey, and Cole. Algebra I. Structure and Method Book 1 McDougal Littel, Houghton Mifflin Company 2000. (PH)

Additional Resources:
Taylor, Harold and Loretta. Developing Skills in Algebra I Book A. Palo Alto, Ca. Dale Seymour. 1984. (DS-A)
Taylor, Harold and Loretta. Developing Skills in Algebra I Book B. Palo Alto, Ca. Dale Seymour. 1984. (DS-B)
Taylor, Harold and Loretta. Developing Skills in Algebra I Book C. Palo Alto, Ca. Dale Seymour. 1984. (DS-C)
Taylor, Harold and Loretta. Developing Skills in Algebra I Book D. Palo Alto, Ca. Dale Seymour. 1984. (DS-C)
Marcy, Steve and Janis. Middle School Math with Pizazz C revised. Chicago. Creative Publications, 1996. (CP-C)
Marcy, Steve and Janis. Middle School Math with Pizazz D revised. Chicago. Creative Publications,1996. (CP-D)
Marcy, Steve and Janis. Middle School Math with Pizazz E revised. Chicago. Creative Publications,1996. (CP-E)
Marcy, Steve and Janis. Algebra with Pizazz revised. Chicago. Creative Publications, 1996. (CP-A)

Mathematics Curriculum Map
Course overview, activities, vocabulary, supplemental materials in pdf format.

Copyright Resources

Course Scope

• For specific Standard References please see: Idaho State Assessment Standards
• Download this curriculum and standards documentation as a "Printer Friendly" pdf file

Unit 0

Preparation and Review

1 week

0813.01 Review arithmetic skill prerequisites from previous years.

Standard Reference
9.M.1.1.2, 9.M.1.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Demonstrate proficiency at performing basic arithmetic skills using fractions and decimals.

Text p. 43, p. 92
(Maint. Skills end of Chap)

TMA

Back to Top

Unit 1

Introduction to Algebra

2 weeks

0813.02 Understand and use procedures for operating on algebraic expressions.

Standard Reference
9.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate an algebraic expression using rational numbers.

Ch. 1-1, 1-2

TMA, EOC

0813.03 Use the proper order of operations. Perform operations with real numbers.

Standard Reference
9.M.1.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use the order of operations to simplify numerical expressions.

Ch. 1-1, 1-2, 1-3

TMA, EOC

0813.04 Understand and use variables, expressions, equations, and inequalities.

Standard Reference
9.M.3.1.1

No.

Resource Reference

Assessment Correlation

01

Translate an English phrase or sentence into an algebraic expression and vice versa.

Ch 1-4, 1-5

TMA, EOC

0813.05 Use a variety of methods, including common mathematical formulas, to solve problems drawn from daily life.

Standard Reference
9.M.1.3.1, 9.M.2.1.2

No.

Resource Reference

Assessment Correlation

01

Use a problem-solving model to develop and apply problem-solving strategies. (e.g., guess and check, draw a diagram, make a list, work backwards, identify a simpler problem.)

Ch. 1-6, 1-7

TMA, EOC

Back to Top

Unit 2

Working with Real Numbers

2 weeks

0813.06 Understand properties of the real number system.

Standard Reference
9.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Recognize and use a property of real numbers (associative, commutative, distributive, and equality) in an algebraic expression.

Ch. 2-1

TMA, EOC

02

Identify and use identity and inverse properties in algebraic expressions.

Ch. 2-2

TMA, EOC

0813.07 Understand and use positive and negative numbers, fractions, decimals, percentages, and scientific notation.

Standard Reference
9.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Understand and perform basic operations on positive and negative numbers.

Ch. 2-2, 2-3, 2-4, 2-5, 2-6, 2-8, 2-9

TMA, EOC

0813.08 Use a variety of methods, including common mathematical formulas, to solve problems drawn from daily life.

Standard Reference
9.M.1.3.1

No.

Resource Reference

Assessment Correlation

01

Use a problem-solving model to develop and apply problem-solving strategies. (e.g., guess and check, draw a diagram, make a list, work backwards, identify a simpler problem.)

Ch. 2-7

TMA, EOC

0813.09 Make and evaluate logical arguments.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Make and evaluate logical arguments (e.g. explain why it is not possible to divide by zero.)

Ch. 2.9

EOC

Back to Top

Unit 3

Solving Equations and Problems

3 weeks

0813.10 Understand and use appropriate procedures to solve linear equations and inequalities such as:
3x – 4 = 2
or
3x – 4 > 2

Standard Reference
9.M.3.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve linear equations with one variable for computational or word problems.

Ch. 3-1, 3-2, 3-3, 3-4, 3-5

TMA, EOC

0813.11 Use a variety of methods, including common mathematical formulas, to solve problems drawn from daily life.

Standard Reference
9.M.2.1.2, 9.M.1.3.1

No.

Resource Reference

Assessment Correlation

01

Use a problem-solving model to develop and apply problem-solving strategies. (e.g., guess and check, draw a diagram, make a list, work backwards, identify a simpler problem.)

Ch. 3-4, 3-6, 3-7

TMA, EOC

0813.12 Solve problems that involve varying quantities with variables, expressions, equations, inequalities, and absolute values.

Standard Reference
9.M.3.6.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve problems that involve varying quantities variables, expressions, equations, inequalities, and absolute values.

Ch. 3-4, 3-5

TMA, EOC

Back to Top

Unit 4

Polynomials

3 weeks

0813.13 Use the proper order of operations. Perform operations with real numbers.

Standard Reference
9.M.1.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use the order of operations to simplify numerical expressions.

Ch. 4-1

TMA, EOC

0813.14 Understand and use procedures for operating on algebraic expressions.

Standard Reference
9.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate an expression using exponents.

Ch. 4-1 through 4-4

TMA, EOC

02

Simplify expressions involving exponents.

Ch. 4-5 through 4-7

TMA, EOC

0813.15 Use a variety of methods, including common mathematical formulas, to solve problems drawn from daily life.

Standard Reference

No.

Resource Reference

Assessment Correlation

01

Use a problem-solving model to develop and apply problem-solving strategies. (e.g., guess and check, draw a diagram, make a list, work backwards, identify a simpler problem.)

Ch. 4-8 through 4-10

TMA, EOC

Back to Top

Unit 5

Exponents and Polynomials

5 weeks

0813.16 Use number theory concepts (divisibility rules, factors, multiples, primes) to solve problems.

Standard Reference
9.M.1.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Apply definitions of prime and composite numbers to solve mathematical problems.

Ch. 5-1, 5-2, 5-3

TMA, EOC

0813.17 Make and evaluate logical arguments.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Make and evaluate logical arguments (e.g., explain why it is not possible to divide by zero.)

Ch. 5-2

EOC

0813.18 Use appropriate procedures to simplify and solve polynomial equations and inequalities such as
x² + 3x = 7
or
x² + 3x < 7

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Factor simple polynomials.

Ch. 5-3, 5-5, 5-6, 5-7, 5-8, 5-9, 5-10, 5-11

TMA, EOC

02

Factor the difference of two squares or perfect square trinomials.

Ch. 5-5, 5-6

TMA, EOC

03

Solve polynomial word problems with or without factoring.

Ch. 5-12, 5-13

TMA, EOC

Back to Top

Unit 6

Fractions

2 weeks

0813.19 Understand and use procedures for operating on algebraic expressions.

Standard Reference
9.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate an algebraic expression using rational numbers.

Ch. 6-1, 6-2, 6-3

TMA, EOC

0813.20 Model real-world phenomena using polynomial, rational, and basic exponential functions, noting restricted domains.

Standard Reference
9.M.1.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Model real-world phenomena using polynomial, rational, and basic exponential functions.

Ch. 6-2, 6-3, 6-5, 6-6, 6-7

TMA, EOC

Back to Top

Unit 7

Applying Fractions

2 weeks

0813.21 Understand and use procedures for operating on algebraic expressions.

Standard Reference
9.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate an algebraic expression using rational numbers.

Ch. 7-1 through 7-3

TMA, EOC

0813.22 Understand and use proportions, ratios, and scaling.

Standard Reference
9.M.2.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Calculate the solutions to number problems using ratio, proportion, and percent.

Ch. 7-1, 7-2, 7-5, 7-6

TMA, EOC

0813.23 Understand and use appropriate procedures to solve linear equations and inequalities such as:
3x – 4 = 2
or
3x – 4 > 2

Standard Reference
9.M.3.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve fractional equations

Ch. 7-3, 7-4

TMA, EOC

0813.24 Make and evaluate logical arguments.

Standard Reference
9.M.1.1.5

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Make and evaluate logical arguments (e.g., explain why it is not possible to divide by zero.)

Ch. 7-4

EOC

0813.25 Understand and use positive and negative numbers, fractions, decimals, percentages, and scientific notation.

Standard Reference
9.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Convert decimals (terminating and repeating), fractions, or percents interchangeably.

Ch. 7-5, 7-6

TMA, EOC

02

Convert numbers from scientific notation (including those with negative exponents) to the standard form and vice versa.

Ch. 7-10

TMA, EOC

0813.20 Model real-world phenomena using polynomial, rational, and basic exponential functions, noting restricted domains.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Model real-world phenomena using polynomial, rational, and basic exponential functions.

Ch. 7-4 through 7-8

TMA, EOC

Back to Top

Unit 8

Introduction to Functions

2 weeks

0813.26 Understand the purpose and capabilities or appropriate technology.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Discuss and understand the purpose and capabilities or appropriate technology.

Graphing calculator demonstration

TMA, EOC

0813.27 Understand concepts of the Cartesian Coordinate System.

Standard Reference
9.M.4.3.1, 9.M.4.4.1, 9.M.4.3.3, 9.M.4.3.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the slope of a line using the slope formula, the equation of the line, or the graph of the equation.

Ch. 8-1 through 8-3

TMA, EOC

02

Determine the linear equation of the line using the slope, y-intercept, or coordinates and will compare the slopes of parallel and perpendicular lines.

Ch. 8-4, 8-5

TMA, EOC

03

Determine a linear equation from analyzing the graph of the equation.

Ch. 8-4, 8-5

TMA, EOC

04

Graph a linear equation with two variables.

Ch. 8-4, 8-5

TMA, EOC

0813.28 Represent a set of data in a table, a graph, and as a mathematical relationship.

Standard Reference
9.M.3.5.3, 9.M.3.3.2, 9.M.3.5.2, 9.M.3.5.1, 9.M.4.4.1, 9.M.4.4.2, 9.M.4.4.3

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify whether an expression, ordered pair, or graph does or does not represent a function and justify the conclusion.

Ch. 8-6, Vertical Line Test

TMA, EOC

02

Find the range of a function, given its domain.

Ch. 8-6, 8-7, 8-8

TMA, EOC

Back to Top

Unit 9

Systems of Linear Equations

2 weeks

0813.29 Use graphs, matrices, and sequences to represent and solve problems.

Standard Reference
9.M.3.4.1, 9.M.3.6.2

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use graphs, matrices, and sequences to represent and solve problems.

Ch. 9

TMA, EOC

0813.30 Understand and use appropriate procedures to solve simple linear systems of equations and inequalities such as
x + y = 7
2x + 3y = 21
or
x + y < 7
2x + 3y > 21

Standard Reference
9.M.3.4.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve systems of linear equations in two variables.

Ch. 9-1, 9-2, 9-3, 9-4, 9-5

TMA, EOC

02

Graph a linear equation with two variables.

Ch. 9.1

TMA, EOC

0813.20 Model real-world phenomena using polynomial, rational, and basic exponential functions, noting restricted domains.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Model real-world phenomena using polynomial, rational, and basic exponential functions.

Ch. 9-6, 9-7

TMA, EOC

Back to Top

Unit 10

Inequalities

2 weeks

0813.31 Understand and use variables, expressions, equations, and inequalities.

Standard Reference
9.M.3.1.1

No.

Resource Reference

Assessment Correlation

01

Translate an English phrase or sentence into an algebraic expression and vice versa.

Ch. 10-1, 10-3

TMA, EOC

0813.32 Understand concepts of the Cartesian Coordinate System.

Standard Reference
9.M.4.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Identify inequalities by their representation on a graph.

Ch. 10-1, 10-7, 10-8

TMA, EOC

02

Graph an inequality with one or two variables.

Ch. 10-1, 10-7, 10-8

TMA, EOC

0813.33 Understand and use appropriate procedures to solve linear equations and inequalities such as:
3x – 4 = 2
or
3x – 4 > 2

Standard Reference
9.M.3.3.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve absolute value equations.

Ch. 10-2, 10-3

TMA, EOC

02

Solve inequalities with one variable in computational or word problems

Ch. 10-2, 10-3

TMA, EOC

0813.34 Understand properties of the real number system.

Standard Reference
9.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve inequalities with one variable in computational or word problems.

Ch. 10-2, 10-3, 10-5, 10-6

TMA, EOC

0813.35 Solve problems that involve varying quantities with variables, expressions, equations, inequalities, and absolute values.

Standard Reference
9.M.3.6.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve problems that involve varying quantities variables, expressions, equations, inequalities, and absolute values.

Ch. 10-2, 10-3, 10-5, 10-6

TMA, EOC

0813.36 Understand and use appropriate procedures to solve simple linear systems of equations and inequalities such as
x + y = 7
2x + 3y = 21
or
x + y < 7
2x + 3y > 21

Standard Reference
9.M.3.4.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate an inequality in two variables.

Ch. 10-7, 10-8

TMA, EOC

02

Write an inequality to represent a problem situation or write a possible situation that an inequality could represent.

Ch. 10-3

TMA, EOC

03

Find the solutions set for an inequality.

Ch. 10

TMA, EOC

Back to Top

Unit 11

Rational and Irrational Numbers

2 weeks

0813.37 Understand properties of roots, exponents, and logarithms.

Standard Reference
9.M.1.1.3, 9.M.1.1.4

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Perform operations on numerical expressions containing roots and integral exponents.

Ch. 11-3, 11-4, 11-5, 11-7, 11-8

TMA, EOC

02

Perform basic operations to simplify radical expressions containing variables.

Ch. 11-5, 11-6, 11-10

TMA, EOC

0813.38 Understand properties of the real number system.

Standard Reference
9.M.1.1.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Solve radical equations.

Ch. 11-10

TMA, EOC

0813.39 Know and apply the Pythagorean Theorem to solve real world problems.

Standard Reference
9.M.4.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Find the lengths of the sides or a right triangle using the Pythagorean Theorem, and use the distance formula to find the distance between any two points in a Cartesian plane.

Ch. 11.6

TMA, EOC

Back to Top

Unit 12

Quadratic Functions

1 week

0813.40 Understand and use procedures for operating on algebraic expressions.

Standard Reference
9.M.3.2.1

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Evaluate an algebraic expression using rational numbers.

Ch. 12-1

TMA, EOC

02

Evaluate an expression using exponents.

Ch. 12-1

TMA, EOC

0813.41 Use appropriate procedures to simplify and solve polynomial equations and inequalities such as
x² + 3x = 7
or
x² + 3x < 7

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

State and apply the quadratic formula to simple quadratic equations.

Ch. 12-3

TMA, EOC

Back to Top

Unit Various

Selected Topics

0813.45 Understand the nature and use of mathematical models.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Understand the nature and use of mathematical models.

Throughout Text

TMA, EOC

0813.46 Determine length, area, capacity, weight, time, and temperature with appropriate units.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use US customary and metric units of measurement to calculate perimeter, area, surface area, and volume.

Throughout Text

TMA, EOC

0813.47 Understand equivalent units, comparable units, and conversions

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Understand equivalent units, comparable units, and conversions.

Throughout Text

TMA, EOC

0813.48 Understand units and their relationship to one another and to real world applications.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Use measurement in word problems (e.g., rate, work, distance, power, percent mixture)

Throughout Text and specifically Ch. 8.5, 10.7-10.8

TMA, EOC

0813.49 Understand that error accumulates in a computation when there is rounding at intermediate steps.

Standard Reference

No.

Performance Objective

Resource Reference

Assessment Correlation

01

Determine the reasonableness to computation and word problems, choosing an appropriate method (e.g., using estimation, evaluating according to context).

Throughout Text

TMA, EOC