Strategic Intervention for Grades 8–12 · Strategic Intervention for Grades 8–12 SUPPORTIVE,...

Strategic Intervention for Grades 8–12

SUPPORTIVE, ENGAGING, and PROVEN to help students succeed in Algebra.

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http://voyagersopris.com/insidealgebra

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A Balanced Approach: What is Inside Algebra?

A student’s performance in algebra has a strong correlation to their success.

Unfortunately, the highest failure rate in high school is Algebra I and this is among the leading indicators of high school drop out.

Inside Algebra provides a solid algebraic foundation designed to help all students, especially those who struggled to master prealgebra skills. Through its intentional, multisensory, hands-on approach, Inside Algebra helps students by working sequentially to build skills necessary to master each concept.

Comprehensive Standards-Based Instruction

From Foundational Skills to Basic Algebra to Advanced Algebra, students experience a consistent and comprehensive approach to master the skills they need to achieve grade-level success.

Inside Algebra is written with a scaffolded instructional approach that supports state standards and standards set forth by the National Council of Teachers of Mathematics (NCTM).

Foundational Skills Basic Algebra Advanced Algebra

Chapters 1–2Prealgebra Skills

• Using operations with rational numbers

• Locating, comparing, and ordering real numbers

• Finding the square root of a number

• Using variables to represent specific values

• Using variables to write general statements

• Using mathematical properties and order of operations

• Using proportions to solve problems

• Graphing ordered pairs and relations

• Finding the domain and range of a relation

Chapters 3–10Basic Algebra Skills

• Writing and solving equations in one and two variables

• Graphing iinear equations

• Identifying functions from a graph, table, or equation

• Writing equations in standard, point-slope, and slope-intercept form, and converting between forms

• Solving and graphing linear inequalities

• Solving systems of linear equations and inequalities

• Adding, subtracting, and multiplying polynomials

• Factoring polynomials

• Solving quadratic polynomial equations using a variety of methods

Chapters 11–12Additional Algebra Skills

• Using operations with rational expressions

• Simplifying rational expressions

• Solving rational equations

• Dividing polynomials

• Simplifying radical expressions

• Using operaions with radical expressions

• Solving equations involving radicals

• Using the Pythagorean theorem to solve problems

• Using coordinate geometry to solve problems

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TEACHER MATERIALS: Teacher Guides (Two-volume set)

Teacher Placement Guide

VPORT® Online Data Management System

Online Resources

Algebra Skill Builders Blackline Masters

Hands-on Manipulatives Class Set

Everything Teachers and Students Need to SucceedSTUDENT MATERIALS: Student Interactive Text

Assessment Book

Student Placement Test

Access to Selected Gizmos® by ExploreLearning®

Larry BradsbyINTERACTIVE TEXT

Larry BradsbySTUDENT PLACEMENT


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Explicit, Objectives-Based Learning

For struggling students, Inside Algebra deconstructs complex algebra skills into smaller, more accessible activities. This is done through an objectives-based approach. Inside Algebra’s 12 chapters are broken into 60 objectives that consist of 500 activities.

The activities allow teachers to provide explicit, scaffolded instruction that clearly defines concepts and skills. They also help students learn to recognize relationships between those concepts and skills.

For an engaging classroom, Inside Algebra provides a variety of instructional models with whole-group, small-group, and individual activities.

Why is the Objectives-based Approach Important?

The objectives-based approach breaks down algebra skills into smaller, accessible components that are more suited to students who have struggled with math. For teachers, this approach maximizes the potential for differentiating instruction and adapting to the needs of students.

Each objective follows a four-step lesson design.

CONCEPT-DEVELOPMENT ACTIVITIES use pictorial representations, hands-on manipulatives, and digital simulations to connect abstract algebra concepts with real-world models.

PRACTICE ACTIVITIES provide more time on task and increased opportunities to master objectives through games, challenges, and small-group collaboration.

PROBLEM-SOLVING ACTIVITIES provide explicit, step-by-step guidance about how to solve multistep problems, justify reasoning skills, and communicate understanding in a teacher-led setting.

PROGRESS-MONITORING ACTIVITIES increase computational fluency, provide informal assessment opportunities, and support data-driven differentiation.

Pro

gress M

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ess

Mon

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Progress Monitoring

Masteryof AlgebraConcepts

Concept Development

PracticeProblemSolving

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A Focus on Differentiation

Every student has unique instructional needs on the path to proficiency. For that reason, Inside Algebra is designed around the most critical instructional component for struggling students—differentiation.

From the objective pretests, teachers can choose between two distinct instructional plans to complete the objective—a streamlined path to move through activities at a faster pace and an intensive path to provide more instruction for students in need. Additional differentiation is embedded in each instructional plan to meet students’ ongoing needs.

Objective 3Instructional Plans9 C

HA

PTER

5-Day Instructional PlanUse the 5-Day Instructional Plan when pretest results indicate that students would benefit from a slower pace. This plan is used when the majority of students need more time or did not demonstrate mastery on the pretest. This plan does not include all activities.

DIFFERENTIATEACCELERATE

Day 1 CD 1 Using Algebra Tiles

★PA 1 Sharing the Factors

Day 2PM 1 Apply Skills 1

★CD 2 Making Area Rugs

Day 3

PM 2 Apply Skills 2

CD 3 Solving the Trinomial Equation

PM 3 Apply Skills 3

Day 4PA 2 Finding the Solution Bingo

PM 4 Apply Skills 4

Day 5

PM 5 Apply Skills 5PM 5 Apply Skills 5

★�PS 1 Paving the Yard

Posttest Objective 3

Pretest Objective 4

CD = Concept Development PM = Progress Monitoring PS = Problem Solving PA = Practice Activity ★�= Includes Problem Solving

4-Day Instructional PlanUse the 4-Day Instructional Plan when pretest results indicate that students can move through the activities at a faster pace. This plan is ideal when the majority of students demonstrate mastery on the pretest.

DIFFERENTIATEACCELERATE

DIFFERENTIATE DIFFERENTIATE

Day 1

CD 1 Using Algebra Tiles

PM 2 Apply Skills 2 PM 1 Apply Skills 1


★PA 1 Sharing the Factors

Day 2

PM 4 Apply Skills 4 PM 2 Apply Skills 2

PA 2 Finding the Solution Bingo


★�CD 2 Making Area Rugs

PM 5 Apply Skills 5 PM 3 Apply Skills 3 CD 3 Solving the Trinomial Equation

Day 3 ★�PS 1 Paving the Yard


PM 3 Apply Skills 3

PM 4 Apply Skills 4 PA 2 Finding the Solution Bingo

Day 4

★�PS 2 Finding Dimensions

★�PS 1 Paving the Yard PM 4 Apply Skills 4

PM 5 Apply Skills 5

Posttest Objective 3

Pretest Objective 4

CD = Concept Development PM = Progress Monitoring PS = Problem Solving PA = Practice Activity ★�= Includes Problem Solving

After each Objective Pretest, teachers use data to SELECT AN APPROPRIATE INSTRUCTIONAL PLAN for the class.

Throughout each instructional plan, teachers use informal assessment data to IDENTIFY GROUPS FOR ACCELERATION OR DIFFERENTIATION.

With results of the Objective Posttest, teachers GROUP STUDENTS BASED ONTHEIR INDIVIDUAL NEEDS.

EXTENDED LEARNING:

Preview new skills

REINFORCEMENT LESSON:

Student-led, small group

RETEACH LESSON:Teacher-led, small group

RETEST:Using Form B Test

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Instructional Walkthrough: Chapter 9 Using Factoring, Objective 3

Objective 3Concept Development Activities

Variation: Gizmos For this activity, use the tiles in the Gizmo Modeling the Factorization of x2 + bx + c to model the factoring of these quadratic expressions.

• Gizmos

Modeling the Factorization of x 2 + bx + c

5. Write several polynomials on the board, and have students use algebra tiles to find the factors. Call on students to give you the factors they found and write them under the appropriate polynomials.

Sample problems:

x 2 + 5x + 6 (x + 2)(x + 3)x 2 + 4x + 4 (x + 2)2

x 2 + x − 6 (x − 2)(x + 3)x 2 + 6x + 5 (x + 1)(x + 5)

6. Demonstrate how to factor x2 + 5x + 6. (x + 2)(x + 3) Discuss the relationship between the numbers (5 and 6) and the factors (2 and 3). Make sure students recognize that 2 + 3 = 5 and 2 • 3 = 6. Use the model to show why the relationship exists. Repeat this process for all polynomials on the board.

7. Ask students to find the factors of x2 + 7x + 10 and x2 + x − 12. Allow students to use the algebra tiles if they need the model to find the factors. x 2 + 7x + 10 = (x + 2)(x + 5), x 2 + x + 12 = (x – 3)(x + 4)

Note: If students need more practice multiplying binomials, refer to Chapter 8, Objective 5.


Use with 5-Day or 4-Day Instructional Plan. In this activity, students factor quadratic trinomials using algebra tiles.

MATERIALS

• Algebratiles,onesetforeverytwostudents

• Variation: Gizmos Modeling the Factorization of x2 + bx + c

DIRECTIONS

1. Review the following term with students: factor A monomial that evenly divides a value 2. Review how to find the product of two binomials using

algebra tiles; for example, write (x + 1)(x + 2) on the board and use the following rectangle to discuss:

x+1

x + 2

x2 x x

x 1 1

Be sure students see that (x + 1)(x + 2) = x 2 + 3x + 2.

3. Discuss the following term with students: quadratic trinomial A polynomial of the

form ax 2 + bx + c 4. Next, show students that to find factors of a

trinomial, they should make a rectangle out of the given trinomial. In other words, work backward from what is shown in Step 2. Write x 2 + 4x + 3 on the board, and use algebra tiles to factor the trinomial. Show students how to determine the dimensions of the overall rectangle. (x + 1)(x + 3)

x+1

x + 3

x2 x x x

x 1 1 1

Objective 3Practice Activities

Copyright 2011 Cambium Learning Sopris West®. All rights reserved. Permission is granted to reproduce this page for student use. Inside Algebra • Blackline Master 38

38Name _______________________________________________________ Date __________________

4 × 4 B I N G O C A R D

4. Continue with other equations. The first student to get four markers in a row should call out, “Bingo!” If the student’s answers are correct, that student is the winner.

5. Alternatively, continue play until a student covers all the squares on his or her card.

NEXT STEPS • Differentiate

5-Day Instructional Plan: PM 4, page 817—All students, to assess progress

4-Day Instructional Plan: PM 5, page 818—Students who are on the accelerated path, to assess progress

PM 4, page 817—Students who are on the differentiated path, to assess progress


Use with 5-Day or 4-Day Instructional Plan. In this activity, students factor quadratic trinomials.

MATERIALS

• BlacklineMaster38

• Gamemarkerstocoversquares

DIREcTIONS

1. Review the following terms with students: factor A monomial that evenly divides a value quadratic trinomial A polynomial of the

form ax 2 + bx + c 2. DistributeonecopyofBlacklineMaster38,4×4

Bingo Card, to each student. Have each student put the numbers −3, −2, −1, 0, 1, 2, 3 at random in the squares of the bingo card. Point out that they will have to repeat some numbers to fill the 16 squares.

3. Write an equation on the board, selected at random from the list below. Tell students to solve the equation and cover the squares that have the solution(s) with their markers. Have students write the equations and solutions on a piece of paper to hand in at the end of the activity.

Equations to Use Solutions Equations to Use Solutions

1. x 2+3x + 2 = 0 –2, –1 14. x 2 – 2x–3=0 –1,32. x 2–4x+3=0 3,1 15. x 2 – x – 2 = 0 2, –13. x 2–4x+4=0 2 16. x 2 – 5x + 6 = 0 3,24. x 2 + x – 6 = 0 –3,2 17. x 2 + 2x–3=0 –3,15. x 2 + x – 2 = 0 –2, 1 18. x 2+4x+3=0 –3,–16. x 2 + 2x + 1 = 0 –1 19. x 2 + 5x + 6 = 0 –3,–27. x 2 + 6x + 9 = 0 –3 20. x 2 + 2x = 0 –2, 08. x 2 – x – 6 = 0 3,–2 21. x 2–4=0 –2, 29. x 2 – 2x = 0 0, 2 22. x 2+3x = 0 0,–3

10. x 2+4x+4=0 –2 23. x 2 – 2x + 1 = 0 111. x 2 + x = 0 0, –1 24. x 2–3x + 2 = 0 1, 212. x 2 – 6x + 9 = 0 3 25. x 2–4x+4=0 213. x 2–3x = 0 0,3

CONCEPT DEVELOPMENT ACTIVITIES use manipulatives to develop algebraic thinking and provide concrete representations of abstract concepts.

CONSISTENT LESSON FORMAT provides explicit direction for teachers to present instruction to support student mastery.

GIZMOS provide alternate presentations of concepts using interactive simulations and virtual manipulatives.

PRACTICE ACTIVITIES use games and small-group interaction to strengthen conceptual understanding.

Important VOCABULARY is highlighted and reviewed at point of use to promote math language development.

NEXT STEPS provide guidance based on student performance along the instructional path.

Objective 3Concept Development Activities

Variation: Gizmos For this activity, use the tiles in the Gizmo Modeling the Factorization of x2 + bx + c to model the factoring of these quadratic expressions.

• Gizmos

Modeling the Factorization of x 2 + bx + c

5. Write several polynomials on the board, and have students use algebra tiles to find the factors. Call on students to give you the factors they found and write them under the appropriate polynomials.

Sample problems:

x 2 + 5x + 6 (x + 2)(x + 3)x 2 + 4x + 4 (x + 2)2

x 2 + x − 6 (x − 2)(x + 3)x 2 + 6x + 5 (x + 1)(x + 5)

6. Demonstrate how to factor x2 + 5x + 6. (x + 2)(x + 3) Discuss the relationship between the numbers (5 and 6) and the factors (2 and 3). Make sure students recognize that 2 + 3 = 5 and 2 • 3 = 6. Use the model to show why the relationship exists. Repeat this process for all polynomials on the board.

7. Ask students to find the factors of x2 + 7x + 10 and x2 + x − 12. Allow students to use the algebra tiles if they need the model to find the factors. x 2 + 7x + 10 = (x + 2)(x + 5), x 2 + x + 12 = (x – 3)(x + 4)

Note: If students need more practice multiplying binomials, refer to Chapter 8, Objective 5.


Use with 5-Day or 4-Day Instructional Plan. In this activity, students factor quadratic trinomials using algebra tiles.

MATERIALS

• Algebratiles,onesetforeverytwostudents

• Variation: Gizmos Modeling the Factorization of x2 + bx + c

DIRECTIONS

1. Review the following term with students: factor A monomial that evenly divides a value 2. Review how to find the product of two binomials using

algebra tiles; for example, write (x + 1)(x + 2) on the board and use the following rectangle to discuss:

x+1

x + 2

x2 x x

x 1 1

Be sure students see that (x + 1)(x + 2) = x 2 + 3x + 2.

3. Discuss the following term with students: quadratic trinomial A polynomial of the

form ax 2 + bx + c 4. Next, show students that to find factors of a

trinomial, they should make a rectangle out of the given trinomial. In other words, work backward from what is shown in Step 2. Write x 2 + 4x + 3 on the board, and use algebra tiles to factor the trinomial. Show students how to determine the dimensions of the overall rectangle. (x + 1)(x + 3)

x+1

x + 3

x2 x x x

x 1 1 1



38Name _______________________________________________________ Date __________________

4 × 4 B I N G O C A R D









MATERIALS



DIREcTIONS







10. x 2+4x+4=0 –2 23. x 2 – 2x + 1 = 0 111. x 2 + x = 0 0, –1 24. x 2–3x + 2 = 0 1, 212. x 2 – 6x + 9 = 0 3 25. x 2–4x+4=0 213. x 2–3x = 0 0,3



38Name _______________________________________________________ Date __________________

4 × 4 B I N G O C A R D









MATERIALS



DIREcTIONS







10. x 2+4x+4=0 –2 23. x 2 – 2x + 1 = 0 111. x 2 + x = 0 0, –1 24. x 2–3x + 2 = 0 1, 212. x 2 – 6x + 9 = 0 3 25. x 2–4x+4=0 213. x 2–3x = 0 0,3

Logical, consistent lesson design keeps students moving toward conceptual understanding and mastery.

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Objective 3Progress-Monitoring Activities

Name __________________________________________ Date __________________________

progress m

oNit

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g

346 Chapter 9 • Objective 3 • PM 1 Inside Algebra

Copyright 2011 Cambium

Learning Sopris West ®. All rights reserved.

A p p ly S k i l l S 1

Factor each of the quadratic trinomials.

Example:

x 2 + 6x + 8 = (x + 2)(x + 4)

1. x 2 + 9x + 20 = (x + 4)(x + 5) 2. x 2 + 12x + 20 = (x + 2)(x + 10)

3. x 2 – 4x – 32 = (x + 4)(x – 8) 4. x 2 + 4x + 3 = (x + 1)(x + 3)

5. x 2 + x – 6 = (x – 2)(x + 3) 6. x 2 + 8x + 12 = (x + 2)(x + 6)

7. x 2 + 6x + 5 = (x + 1)(x + 5) 8. x 2 + x – 2 = (x – 1)(x + 2)

9. x 2 – 6x + 8 = (x – 2)(x – 4) 10. x 2 – 3x – 18 = (x + 3)(x – 6)

11. x 2 – 4x + 3 = (x – 1)(x – 3) 12. x 2 + 10x + 21 = (x + 3)(x + 7)

13. x 2 + x – 12 = (x – 3)(x + 4) 14. x 2 – 7x + 12 = (x – 3)(x – 4)

15. x 2 + 9x – 10 = (x + 10)(x – 1) 16. x 2 – 12x + 32 = (x – 4)(x – 8)

17. x 2 – x – 30 = (x + 5)(x – 6) 18. x 2 – 8x – 9 = (x + 1)(x – 9)

19. 2x 2 + 11x + 12 = (2x + 3)(x + 4) 20. 3x 2 + 16x + 5 = (3x + 1)(x + 5)

PM 1 Apply Skills 1

Use with 5-Day or 4-Day Instructional Plan.

MATERIALS

• Interactive Text, page 346

DIRECTIONS

1. Have students turn to Interactive Text, page 346, Apply Skills 1.

2. Remind students of the key terms: quadratic trinomial and factor.

3. Monitor student work, and provide feedback as necessary.

Watch for: • Dostudentsfactorthetrinomialsusingalgebra

tiles to complete the rectangle?

• Doanystudentstryanalgebraicmethod?


5-Day Instructional Plan: CD 2, page 810—All students, for additional concept development and problem solving

4-Day Instructional Plan: PA 1, page 812—All students, for additional practice and problem solving

Objective 3Problem-Solving Activities

5. Read the following scenario to students:

A rectangular garden (16 feet by 21 feet) has a uniform rock path around it. If the total area of the garden and path is 500 square feet, what is the width of the path?

6. Guide students as they write an equation based on the information they know. Remind students to solve the equation to find the actual dimensions of the area. l • w = 500 sq. ft. (21 + x + x )(16 + x + x ) = 500 (21 + 2x )(16 + 2x ) = 500 4x 2 + 74x + 336 = 500 4x 2 + 74x – 164 = 0 2x 2 + 37x – 82 = 0 (2x + 41)(x − 2) = 0 x = –

412 or 2; measurement must be positive so the

width of the path is 2 ft.


4-Day Instructional Plan: Objective 3 Posttest, page 821—All students

Total area = 500 square feet

16 ft.

21 ft.

PS 2 Finding Dimensions

Use with 4-Day Instructional Plan. In this activity, students apply what they know about quadratic equations to solve word problems.

DIRECTIONS

1. Discuss the following term with students: quadratic formula x = –b ± √b 2 – 4ac

2a where ax 2 + bx + c = 0


A small calf needs to be kept away from the herd of cattle because of an infection. The rancher has fences made of tubing that can be put up quickly. The calf will need 280 square feet of grazing land. The tube frame will be six feet longer than it is wide. Find the dimensions of the fence.

3. Guide students as they write an equation based on the information they know. Remind students to solve the equation to find the actual dimensions of the area. x (x + 6) = 280 sq. ft. x 2 + 6x = 280 x 2 + 6x – 280 = 0 (x − 14)(x + 20) = 0 x = 14, −20; dimensions cannot be negative so the fence is 14 ft. by 20 ft.

4. Tell students to find the dimensions if the calf only needs 160 square feet of grazing land. x (x + 6) = 160 sq. ft. x 2 + 6x = 160 x 2 + 6x – 160 = 0 (x − 10)(x + 16) = 0 x = 10, −16; dimensions cannot be negative so the fence is 10 ft. by 16 ft.

★ = Includes Problem Solving

★

280 square feet

PROGRESS-MONITORING ACTIVITIES determine differentiation through alternate activities as they build fluency with basic algebra skills.

Informal assessment strategies such as ASK FOR, WATCH FOR, and LISTEN FOR provide further insight into student progress.

Modified wraparound Teachers Guide includes ANSWER KEYS.


Name __________________________________________ Date __________________________

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Example:

x 2 + 6x + 8 = (x + 2)(x + 4)

1. x 2 + 9x + 20 = (x + 4)(x + 5) 2. x 2 + 12x + 20 = (x + 2)(x + 10)

3. x 2 – 4x – 32 = (x + 4)(x – 8) 4. x 2 + 4x + 3 = (x + 1)(x + 3)

5. x 2 + x – 6 = (x – 2)(x + 3) 6. x 2 + 8x + 12 = (x + 2)(x + 6)

7. x 2 + 6x + 5 = (x + 1)(x + 5) 8. x 2 + x – 2 = (x – 1)(x + 2)

9. x 2 – 6x + 8 = (x – 2)(x – 4) 10. x 2 – 3x – 18 = (x + 3)(x – 6)

11. x 2 – 4x + 3 = (x – 1)(x – 3) 12. x 2 + 10x + 21 = (x + 3)(x + 7)

13. x 2 + x – 12 = (x – 3)(x + 4) 14. x 2 – 7x + 12 = (x – 3)(x – 4)

15. x 2 + 9x – 10 = (x + 10)(x – 1) 16. x 2 – 12x + 32 = (x – 4)(x – 8)

17. x 2 – x – 30 = (x + 5)(x – 6) 18. x 2 – 8x – 9 = (x + 1)(x – 9)

19. 2x 2 + 11x + 12 = (2x + 3)(x + 4) 20. 3x 2 + 16x + 5 = (3x + 1)(x + 5)

PM 1 Apply Skills 1


MATERIALS


DIRECTIONS











Name __________________________________________ Date __________________________

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Example:

x 2 + 6x + 8 = (x + 2)(x + 4)

1. x 2 + 9x + 20 = (x + 4)(x + 5) 2. x 2 + 12x + 20 = (x + 2)(x + 10)

3. x 2 – 4x – 32 = (x + 4)(x – 8) 4. x 2 + 4x + 3 = (x + 1)(x + 3)

5. x 2 + x – 6 = (x – 2)(x + 3) 6. x 2 + 8x + 12 = (x + 2)(x + 6)

7. x 2 + 6x + 5 = (x + 1)(x + 5) 8. x 2 + x – 2 = (x – 1)(x + 2)

9. x 2 – 6x + 8 = (x – 2)(x – 4) 10. x 2 – 3x – 18 = (x + 3)(x – 6)

11. x 2 – 4x + 3 = (x – 1)(x – 3) 12. x 2 + 10x + 21 = (x + 3)(x + 7)

13. x 2 + x – 12 = (x – 3)(x + 4) 14. x 2 – 7x + 12 = (x – 3)(x – 4)

15. x 2 + 9x – 10 = (x + 10)(x – 1) 16. x 2 – 12x + 32 = (x – 4)(x – 8)

17. x 2 – x – 30 = (x + 5)(x – 6) 18. x 2 – 8x – 9 = (x + 1)(x – 9)

19. 2x 2 + 11x + 12 = (2x + 3)(x + 4) 20. 3x 2 + 16x + 5 = (3x + 1)(x + 5)

PM 1 Apply Skills 1


MATERIALS


DIRECTIONS










EXAMPLES of student solutions showcase one possible strategy that students may use to solve the problem.

PROBLEM-SOLVING ACTIVITIES reinforce strategies and reflective thinking as students synthesize cumulative skills.

Objective 3Problem-Solving Activities


A rectangular garden (16 feet by 21 feet) has a uniform rock path around it. If the total area of the garden and path is 500 square feet, what is the width of the path?

6. Guide students as they write an equation based on the information they know. Remind students to solve the equation to find the actual dimensions of the area. l • w = 500 sq. ft. (21 + x + x )(16 + x + x ) = 500 (21 + 2x )(16 + 2x ) = 500 4x 2 + 74x + 336 = 500 4x 2 + 74x – 164 = 0 2x 2 + 37x – 82 = 0 (2x + 41)(x − 2) = 0 x = –

412 or 2; measurement must be positive so the

width of the path is 2 ft.


4-Day Instructional Plan: Objective 3 Posttest, page 821—All students

Total area = 500 square feet

16 ft.

21 ft.

PS 2 Finding Dimensions

Use with 4-Day Instructional Plan. In this activity, students apply what they know about quadratic equations to solve word problems.

DIRECTIONS

1. Discuss the following term with students: quadratic formula x = –b ± √b 2 – 4ac

2a where ax 2 + bx + c = 0


A small calf needs to be kept away from the herd of cattle because of an infection. The rancher has fences made of tubing that can be put up quickly. The calf will need 280 square feet of grazing land. The tube frame will be six feet longer than it is wide. Find the dimensions of the fence.

3. Guide students as they write an equation based on the information they know. Remind students to solve the equation to find the actual dimensions of the area. x (x + 6) = 280 sq. ft. x 2 + 6x = 280 x 2 + 6x – 280 = 0 (x − 14)(x + 20) = 0 x = 14, −20; dimensions cannot be negative so the fence is 14 ft. by 20 ft.

4. Tell students to find the dimensions if the calf only needs 160 square feet of grazing land. x (x + 6) = 160 sq. ft. x 2 + 6x = 160 x 2 + 6x – 160 = 0 (x − 10)(x + 16) = 0 x = 10, −16; dimensions cannot be negative so the fence is 10 ft. by 16 ft.

★ = Includes Problem Solving

★

280 square feet


8

Relevant Technology

Gizmos are interactive simulations students can manipulate to visualize and learn important concepts. As a web-based technology, students have access to Gizmos wherever and whenever they have Internet access.

Gizmos

Gizmos engage and empower students to test and extend their conceptual understanding of complex algebra skills. As students work independently on fun activities, they self-discover connections between algebra and the real world.

9

Hands-on Manipulatives

Students respond well to multisensory learning. Each Inside Algebra kit comes with a class set of hands-on manipulatives used in whole-group, small-group, and independent activities. The manipulatives-based lessons engage students in multisensory learning experiences that can’t be replicated on paper.

Interactive Games and Competition

Many Inside Algebra activities employ small-group games to practice and reinforce instruction. These gaming activities fuel students’ competitive spirits and encourage them to engage, participate, and collaborate with others in a fun learning environment.


10

Comprehensive Assessment SystemThe Comprehensive Assessment System Tracks and Monitors Student Growth from Placement to Mastery

This user-friendly assessment system provides teachers with the measures they need to accurately place students and monitor their progress through the curriculum. It furnishes the teacher with the data necessary to inform instruction to ensure each student meets his or her goals.

ONGOING ASSESSMENTS VPORT

PLACEMENT TEST

Larry BradsbySTUDENT PLACEMENT

Placement

Based on students’ demonstrated understanding of key mathematics concepts and skills, data from the Inside Algebra Placement Test accurately place students at one of the program’s two entry points.

VPORT

This user-friendly data management system allows teachers and administrators to record, track, and report student test results. Reports can be generated at the individual, class, building, and district levels.

Ongoing Assessments

Regular assessment of student mastery of concepts and skills taught in the program ensures teachers can adjust pacing or instruction to meet the needs of individual students.

• Daily application• Objective pretests• Objective posttests• Chapter tests• Extension activities• Reinforcement activities

rein

force instruct

assess

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Actionable Data & Reports: Data Drives Instruction

Inside Algebra includes VPORT, an online data management system that incorporates benchmark and progress-monitoring assessments with real-time data to:

Identify individual instructional needs and goals

Adjust instruction based on skill need

Monitor progress against goals

Communicate progress to the instructional team

Generate parent reports in English and Spanish

Real-time reporting

The key to effective instruction is real-time data that tracks student progress throughout the year. The Inside Algebra Assessment System uses VPORT data to provide multiple reports to identify student needs, adjust instruction, monitor progress, and evaluate instructional effectiveness.

Inside Algebra IA Demo Inside Algebra Cedarius McGill

Report as of: 07/30/2018Campus Voyager School 1IAClass Inside Algebra IAStudent McGill, Cedarius(ID: IA300137)Teacher Demo Inside AlgebraYear 2017-2018 Academic YearGrade IAProduct Inside Algebra™

Dear Parent/Guardian,Your child is participating in Inside Algebra!, an intervention program designed to ensure yourchild achieves algebra proficiency. The program allows teachers to design instruction aroundstudent need using a multisensory approach and at the same time, engages students inmeaningful lessons that promote mastery. Your child will participate in post-tests to helpmonitor their progress and an end of chapter test to check for skill mastery. Your child will alsohave access to mBook and Gizmos, online tools to help reinforce understanding of mathconcepts. In reviewing the mastery assessments below, please note that students below 80%will be receiving reinforcement from their teachers. Please review all scores and discuss yourchildʼs progress with his or her teacher. Parents can help bridge the home/school connectionby asking your childʼs teacher which math concepts should be practiced from home.

Ch1Obj1Chapter 1 Obj 1





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Proven Student Achievement Systemwide Quantile Results

Inside Algebra students across the nation show dramatic gains when we compare initial and final assessments. Inside Algebra utilizes the Progress Assessment of Mathematics (PAM) powered by The Quantile® Framework for Mathematics to determine a student’s Quantile score. A Quantile represents that student’s range of skills and readiness for learning new skills. The PAM also is used to assess and track student growth and proficiency change for the school year.

Students show increases in Quantile scores from 238Q to 298Q with an average effect size for all students of 1.03, which is considered large and educationally meaningful.

Beginning-of-Year to End-of-Year Results

QU

AN

TIL

ES

1000

1200

All Students

Beginning of Year End of Year

Intensive Students

400

800

200

600

0

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Inside Algebra is Proven Effective

Each chapter outlines a set of objectives. Students are given a pretest to measure their knowledge prior to instruction and a posttest following instruction to measure mastery of the stated objectives. An example of average growth (or gain) in the percent correct by objective from pretest to postest is shown below, but learning doesn’t end with testing—teachers use this data to differentiate and enrich instruction to accelerate students to mastery.

Chapter 5: Analyzing Linear Equations

The Objective Pretests provides baseline data to determine an appropriate instructional plan for the class. The Objective Posttests measure student growth in mastering the objective and identifies concepts that may need reinforcement.

Objective 1: Determine the slope given a line on a graph or two points on a line

Objective 2: Write the equation of a line in standard form given two points on the line

Objective 3: Draw a best-fit line, and find the equation of the best-fit line for a scatter plot

Objective 4: Write linear equations in slope-intercept form to find the slope, x-intercept, and y-intercept, and sketch the graph

Objective 5: Use the slope of lines to determine if two lines are parallel or perpendicular

Data from the Objective Tests represents students from 15 states and 35 districts. All types of students and implementations are represented.

Inside Algebra Systemwide ResultsChapter 5 Objective Tests

PE

RC

EN

T C

OR

RE

CT

100

Objective 1n=434

Objective 2n=371

Objective 3n=204

Objective 4n=317

Objective 5n=321

Pretest Posttest

40

80

20

60

0

22.013.2 10.6

32.3 30.2

63.4

50.4

69.660.9 58.7


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Let Us Create a Custom Implementation Plan

Visit voyagersopris.com/insidealgebra to review training options and a comprehensive menu of services.

QUALITY OF INSTRUCTION

FIVE KEYS TO SUCCESS

AMOUNT OF INSTRUCTION

DIFFERENTIATION

CLASSROOM MANAGEMENT

USE OF ASSESSMENTS

Key stages of Inside Algebra implementation include:

IMPLEMENTATION PLANNING

ONGOING DATA REVIEWLAUNCH

The highest level of educator support leads to increased student achievement. That’s our primary goal.Service does not come in a box. It must be customized to meet the specific needs of districts, schools, administrators, and teachers. Firmly grounded in research, the Voyager Sopris Learning® approach is built around the Five Keys to Success, which form the foundation for a personalized strategy for planning, training, and ongoing support.Our team specializes in partnering with schools and districts to build custom Inside Algebra implementation support plans to ensure all stakeholders are prepared to implement and sustain Inside Algebra implementation.


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Read what teachers and students are saying...

“I really didn’t understand anything and then I got put in this program and it makes everything a lot easier to understand. I just think it is the way Inside Algebra works the problems out...because it is a lot more hands-on and visual.”

—ColleenStudent, NM

“I think it helps them see that algebra isn’t some unattainable skill; that they can learn it step-by-step without too much difficulty. The pretests and posttests give them verifiable proof that they are, in fact, learning. It has provided them with a level of instruction they wouldn’t otherwise have received through a resource setting.”—Pam O’DayTeacher, TN

“I like the program and the activities it includes. I was able to pull out different activities and augment those activities as needed. The students seemed to like the program as well.”—Ashley C. MattinTeacher, TN

“This program seems to get rid of [math anxiety]...and gets them completely engaged.”

—Danielle NeriTeacher, NM


Inside Algebra complements any core algebra program with key features that deliver:

Concept development to build conceptual understanding through modeling experiences

Practice to support new learning through games and small-group activities

Problem solving to build skills through relevant, real-world connections

Progress monitoring to reinforce computational fluency and student understanding

Flexible grouping and provides multiple modeling activities

Enhanced instruction for English language learners (ELLs)

Support for teachers and students with relevant technology

Flexible implementations to address credit-recovery needs

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