Learning Outcomes
2.1 Solve systems of linear
equations by graphing.
Chapter Reference 3.1
Differentiated Instructional Activities
An alternative way to approach Lesson 3.1 is to use the Application Lesson Opener. Have students copy the relationship between the graph of a linear system and the system’s number of solutions on a 3X5 index card.
Continue vocabulary file or algebra glossary.
Ask students how a solution to a linear system and a solution to a linear equation are related.
As students review graphing lines, remind them that some lines may be easier to graph using x- and y-intercepts. Other lines may be easier to graph by first converting the equation to slope-intercept form and using the slope and y-intercept. Writing Activity: Have students explain how to use a graph to determine how many solutions there are for a system of linear equations. For additional writing activities see p.145, “Additional Test
Preparation”. Have students do the Using
Technology and/or graphing calculator activities.
Text Book
References*
Examples: 1-4, pp. 139-141
Guided Practice: p. 142, #’s 1-10
Practice: pp. 142-145,
#’s 11-79
(See Assignment
Guide, p. 142)
Using Technology: p. 146
Chapter Resource Book
References
Warm-Up Exercises: p. 11
Lesson Opener (Application): p. 12
Practice A, B, & C: pp. 14-16
Reteaching with Practice: pp. 17-18
Interdisciplinary Application: p. 20
Challenge: p. 21
Graphing Calculator Activity: p. 13
Assessments#
WT: p. 18^ Prerequisite
Skills Review
WT: p. 19^
Checkpoint Exercises: pp. 140-141
HQ: p. 20^
Quiz 1: p. 155, #’s 1-12
RS: Quiz 1: p. 36, #’s 1-3^
* The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
^ These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
# End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
0

Learning Outcomes Differentiated Instructional Activities Text Book
References*
Chapter Resource Book
References
Assessments#
2.2 Solve linear systems (two
variables) of equations
algebraically using:
Substitution
Linear combination (Elimination)
Chapter Reference 3.2
2.3
Graph and solve a system of linear inequalities.
Chapter Reference 3.3
Use the Developing Concepts Activity to introduce
Lesson 3.2. An alternative way to approach Lesson
3.2 is to use the Application Lesson Opener. Have students copy the steps for the substitution method and the linear combination method for solving linear systems on 3X5 index cards. Continue vocabulary file or algebra glossary. Encourage students to think of the common meaning of the words substitute and combining. Stress to students that they should check their solution in both equations to help avoid mistakes. Writing Activity:
Have students write and solve, explaining each step, a system of equations using the substitution method and then the linear combination method.
Have students discuss which method was easier to use and why. Have students do the graphing calculator activity.
Use the Developing Concepts Activity to introduce
Lesson 3.3. An alternative way to approach Lesson
3.3 is to use the Activity Lesson Opener. Have students copy the method for graphing a system of linear inequalities on a 3X5 index card. Continue vocabulary file or algebra glossary. Remind students to test a point in the solution set in each of the inequalities of the system to check their answers. Also, have them double check that dashed and solid lines have been used correctly. Writing
Activity: Have students write a real life problem that can be represented by a system of inequalities.
Have them write the system of inequalities and graph its solution set.
Have students do the graphing calculator activity.
Developing
Concepts: p. 147
Examples: 1-5, pp. 148-151
Guided Practice: p. 152, #’s 1-10
Practice: pp. 152-155,
#’s 11-81
(See Assignment
Guide, p. 152)
Warm-Up Exercises: p. 24
Lesson Opener (Application): p. 25
Practice A, B, & C: pp. 28-30
Reteaching with Practice: pp. 31-32
Real Life Application: p. 34
Challenge: p. 35
Graphing Calculator Activity: pp. 26-27
Developing
Concepts: p. 156
Examples: 1-3, pp. 157-158
Guided Practice: p. 159, #’s 1-11
Practice: pp. 159-162,
#’s 12-78
(See Assignment
Guide, p. 159)
Warm-Up Exercises: p. 39
Lesson Opener (Activity): p. 40
Practice A, B, & C: pp. 42-44
Reteaching with Practice: pp. 45-46
Cooperative Learning Activity: p. 48
Interdisciplinary Application: p. 49
Challenge: p. 50
Graphing Calculator Activity: p. 41
WT: p. 20^
Checkpoint Exercises: pp. 149-150
HQ: p. 21^
Quiz 1: p. 155, #’s 7-19
RS: Quiz 1: p. 36, #’s 2-6^
WT: p. 21^
Checkpoint Exercises: pp. 157-158
HQ: p. 22^
Quiz 2: p. 169, #’s 1-3
RS: Quiz 2: p. 66, #’s 1-2^
* The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
^ These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
# End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
1

Learning Outcomes Differentiated Instructional Activities Text Book
References*
Chapter Resource Book
References
Assessments#
2.4
Solve linear program problems.
Chapter Reference 3.4
Use the Developing Concepts Activity to introduce
Lesson 3.4. An alternative way to approach
Lesson 3.4 is to use the Graphing Calculator
Lesson Opener. Have students copy the optimal solution of a linear programming problem on a
3X5 index card. Continue vocabulary file or algebra glossary. Remind students that the maximum or minimum value of the objective function may occur at a point that lies on an axis.
Writing Activity: Have students explain each step as they proceed to find the maximum value of the function C = 3x – y for the given restraints: x > 0, y > 3/2 x, and x + 2y < 4. Have students do the graphing calculator activity.
Developing
Concepts: p. 163
Examples: 1-3, pp. 164-165
Guided Practice: p. 166, #’s 1-8
Practice: pp. 166-168,
#’s 9-48
(See Assignment
Guide, p. 166)
Warm-Up Exercises: p. 53
Lesson Opener (Graphing
Calculator): p. 54
Practice A, B, & C: pp. 57-59
Reteaching with Practice: pp. 60-61
Real Life & Math and History
Applications: pp. 63-64
Challenge: p. 65
Graphing Calculator Activity: pp. 55-56
WT: p. 22^
Checkpoint Exercises: pp. 164-165
HQ: p. 23^
Quiz 2: p. 169, #’s 4-7
RS: Quiz 2: p. 66, #’s 3-5^
2.5
Solve systems of linear equations in three variables using:
Substitution
Linear Combination (Elimination )
Chapter Reference 3.6
An alternative way to approach Lesson 3.6 is to use the Visual Approach Lesson Opener. Have students copy the steps for the linear combination method to solve a system of linear equations in three variables on a 3X5 index card. Continue vocabulary file or algebra glossary. Have students describe the different types of linear systems in three variables. Remind students that if a false statement occurs when solving a linear system, the system has no solution. If the procedure produces an identity, the system has infinitely many solutions. Writing Activity: Have students write a real life problem that can be solved using a linear system in three variables, solve the system, and interpret their answer.
Examples: 1-4, pp. 178-180
Guided Practice: p. 181, #’s 1-11
Practice: pp. 181-184,
#’s 12-71
(See Assignment
Guide, p. 181)
Warm-Up Exercises: p. 82
Lesson Opener (Visual
Approach): p. 83
Practice A, B, & C: pp. 84-86
Reteaching with Practice: pp. 87-88
Real Life Application: p. 90
Challenge: p. 91
WT: p. 24^
Checkpoint Exercises: pp. 178-180
HQ: p. 26^
Quiz 3: p. 184, #’s 11-14
* The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
^ These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
# End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
2