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The Effects of Kentucky Virtual High School’s Algebra I Hybrid Course on Teaching Practices,

Classroom Quality, and Student Learning

ACT 5 ON-LINE DISCUSSION

JUNE 24, 2009COHORT III, 2009-2010

REGIONAL EDUCATIONAL LAB REGIONAL EDUCATIONAL LAB ~ APPALACHIA~ APPALACHIA

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Agenda for ACT 5 On-line Discussion

• Welcome and Introductions• Equipment check-in• Updates• “Linking Formative Assessment to

Scaffolding”• ACT 5 Discussion• Mini-Lesson on Polynomials• Next Steps – ACT 6

Wednesday, July 1, 2009

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“Linking Formative Assessment to Scaffolding”

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Breakout Rooms

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ACT 5- Solving Linear Inequalities

HIGHLIGHTS REGARDING:• Content • Instructional Strategies

• Reflections

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SCENE 1 – How Do I Teach This?

Critical use of the NUMBER LINE for:• modeling solution(s),• representing Real Numbers in multiple

ways, • increasing number sense or

numeracy.

-2 -1 0 1 2 3 4

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Instructional Strategies

• Modeling using the number line with a geometric approach using Transformations

• Inequality Applets to support KYVS:– http://www.ronblond.com/M11/LinIne/

index.html – http://joemath.com/applets/abs/

• Other Applets to investigate:– http://www.decimalsquares.com/dsGames/

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Where in Scene 1:

Accessing Prior Knowledge, ReflectionsInstructional Strategies for Promoting

Mathematical Literacy: Developing Vocabulary Reading Mathematics Texts/Materials (Reading to

Learn) Writing to Learn Writing to Demonstrate Learning Engaging in Meaningful Conversations (Academic

Dialogue) Modeling (Multiple representations)

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Where in Scene 2:

Accessing Prior Knowledge, ReflectionsInstructional Strategies for Promoting

Mathematical Literacy: Developing Vocabulary Reading Mathematics Texts/Materials (Reading to

Learn) Writing to Learn Writing to Demonstrate Learning Engaging in Meaningful Conversations (Academic

Dialogue) Modeling (Multiple representations)

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Where in Scene 3:

Accessing Prior Knowledge, ReflectionsInstructional Strategies for Promoting

Mathematical Literacy: Developing Vocabulary Reading Mathematics Texts/Materials (Reading to

Learn) Writing to Learn Writing to Demonstrate Learning Engaging in Meaningful Conversations (Academic

Dialogue) Modeling (Multiple representations)

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Connections: KYVS Algebra to SpotLight on Algebra

SPOTLIGHT ON ALGEBRA: ACT 5, Solving Linear InequalitiesKYVS ALGEBRA I COURSE: Unit 2 & 3

• Lesson 5 – Sets, Intersections, Unions• Lesson 6 - Inequalities & their graphs • Lesson 7 - Using Inequalities • Lesson 8 - Solving equations using absolute value • Lesson 9 - More solving equations using absolute

value

• Lesson 14 – Parallel & Perpendicular Lines & linear inequalities

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Key Components For The Algebra I Blended Lessons

• Learning Goals: Verbalizing these goals with students and connecting to the Program of Studies

• Learning Cycle: Activating Prior Knowledge, New Learning, Reflections

• Vocabulary: Critical to communicating understanding

• Multiple Representations: NAGS where Numbers within the table of values, Algebra within the equation, Graph of the algebraic equation, Sentence to describe the mathematics

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(cont.) Key Components For The Algebra I Blended Lessons

• How will students track key concepts and critical understandings in both the face-to-face instruction and the KYVS Algebra I Lessons?[Look at various tracking tools for Lesson 5-9 & 14. Is there a variety of scaffolded and open-ended questions?]

• How will students transition from the face-to-face instruction to the virtual environment?

• Are there check points along the way? What are they?

• What kind(s) of closure will you use?

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Exponential Rules

• Show examples of using exponents with numbers23 = 2 x 2 x 234 = 3 x 3 x 3 x 3

• Since the exponent is the number of times the base is used as a factor, then:(a + b)2 = (a + b)·(a + b) by using the FOIL method(a + b)·(a + b) = a2       STEP 1(a + b)·(a + b) = a2 + ab        STEP 2(a + b)·(a + b) = a2 + ab + ba STEP 3(a + b)·(a + b) = a2 + ab + ba + b2 STEP 4(NOTE: ab is the same as ba by the Commutative Property)a2 + ab + ab + b2 = a2 + 2ab + b2

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Discussion: Multiplying Binomials

1. Use a matrix array to support/model the use of the Distributive Property.

2. Use tiles to create the area model display.

3. Make Connections amongst the approaches.

4. Take students through a numerical approach and discussion: (5 + 3)2 = 82 = 64 as compared to 52 + 32 = 25 + 9 = 34.

A B

A A2 AB

B BA B2

A2 + AB + BA + B2 = A2 + 2AB + B2 is the simplified form.

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Websites to Remember

• KYVS for SpotLight on Algebra and the KYVS Algebra I Course: http://www.kyvs.org

• Horizon Wimba: http://67.202.209.114/

• Hybrid Algebra Wiki for sharing: http://hybridalgebra.wikispaces.com/

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Next Steps – ACT 6

• Wednesday, July 1, 2009, 9-11am EST• ACT 6 assignments:

► Investigate ACT 6, note findings in preparation for discussion. ► Investigate Content and Pedagogy Quizzes for ACT 6 – COURSE MATERIALS QUIZZES; work some of the questions that relate to Pedagogy and come prepared to discuss. Try at least five questions that interest you.► Have graphing calculators and notes from ACT 6 ready► Open Spotlight on Algebra and the KYVS Algebra I Course in separate tabs

THANKS FOR JOINING IN TODAY’S DISCUSSION!