Supporting Algebraic Thinking:An Introduction to Common Core

Mathematics

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CCSS Focus: Algebraic Thinking

“The Requirements of an ever-changing workplace dictate that basic skills and routine expertise will

not be sufficient for today’s student as they become tomorrow’s workforce. Instead they will need ‘the levels of knowledge and understanding

that can support transfer to new problems, creativity and innovation’…” (Bill & Jamar, 2010, p. 64)

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The ScenarioCarlos wants to join a gym called FitNation. FitNation offers three membership options:

OPTION 1: Pay as you go – Pay only $6 each time you work out.

OPTION 2: Regular deal – Pay $50 a month and $2 each time you work out.

OPTION 3: All-in-one price! Pay just $100 per month for unlimited use of our great facilities.

Carlos thinks he will go to the gym about 20 times a month.

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The Problem/Task

PART 1:1. How much would each option cost Carlo for one month? 2. Which of the three options is least expensive for Carlo?

PART 2:3. How many visits each month would make the cost of the

Regular deal and the All-in-one price the same? Explain how you figured it out.

Be prepared to share your explanation with the class.

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Extending the Learning: Comparing Gyms

It costs $300 to join the new Superfit Gym. You then pay $15 each month and $2 each time you work out. Carlo thinks he will use the gym about 20 times each month for a year.

1. How much would a membership to Superfit cost for one year?

2. How much will Carlo save during the first year if he uses the Superfit Gym rather than the Regular deal at FitNation? Explain your answer.

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Summing Up

DISCUSS:• What are the various solution paths we came up

with today to solve the gym membership problem?

EXIT TICKET:• Did you modify your own explanation based on

what someone else said or did? Why or why not? Make sure to provide an example.

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Analyze the Architecture of the Lesson

DISCUSS:• How were the various tasks sequenced in this

lesson to build procedural and conceptual understanding?

• In what ways was academic discourse structured and supported by the teacher?

• What role did explanation play in your own learning?

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Analyze the Architecture of the Lesson

Habits of Mathematical Practice – Focus on Standard 3

DISCUSS:1. What does this standard say? What is the purpose of

this standard?

2. What did we do in today’s lesson to meet this standard?

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Analyze the Architecture of the Lesson

Look at the 6-8 grade span algebraic thinking standards

DISCUSS:• How is algebraic thinking described in each

grade level? • How does the standard change from grades 6

through 8?

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The CCSS Requires Three Shifts in Mathematics

1. Focus: Focus strongly where the standards focus.

2. Coherence: Think across grades, and link to major topics

3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

Source: www.achievethecore.org

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Video Viewing & Evidence Collection

DO:• Watch 2 video clips of the DVD plans lesson being

taught.

• Use the evidence collection tool provided to collect and tag evidence of the following TCRP indicators:– 3.2.B: Cognitive level of student learning experiences – 3.3.B: Academic discourse– 3.4.B: Feedback to students

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Video Viewing & Evidence Collection

DISCUSS:1. Share 2 pieces of evidence you collected for

each indicator with a partner.

2. What is the relationship between a rich, problem-solving task and TCRP evidence? What is the relationship between Common Core – aligned curriculum and effective teaching?

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Article DiscussionDISCUSSION QUESTIONS:• What are the features of the new type of math classroom described

in this article? 

• After reading through the classroom example provided here, what will be the most important instructional shift for your school in mathematics?  Why? 

• In what ways do the math problems we explored today compare with what you typically see in algebra or pre-algebra classrooms?

• According to these authors, what are best practices when it comes to orchestrating mathematical explanations (in talk, in writing)?

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Why Math Matters: Creating the Case through CCSS

• Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives

• Students are able to see math as more than a set of mnemonics or discrete procedures

• Conceptual understanding supports the other aspects of rigor (fluency and application)

Source: www.achievethecore.org