Crossing the Bridge to Common Core State Standards for Mathematics

Day 4

Dawn PerksMiddle School Math Specialist

919-560-2000 ext. 21315

SBAC

• Smarter Balanced Assessment Consortium• North Carolina is a governing state• Next generation assessments for

implementation in 2014-2015• Samples, research, data, and item

specifications are available on their website

http://www.smarterbalanced.org/

Activity 1-Begin with the end in mind….With your group, complete the 2 sample SBAC problems provided in your participant packet.

Reflect…• What have you learned from this activity?• How will this change your teaching? Planning? The

work in your PLC’s? • What support will you need to make the necessary

changes?

Course Overviews

Standards Included in Units• Italicized standards notate Gap Standards that

are new for North Carolina.• Bold standards notate Power Standards that

are heavily weighted on Standardized Tests.• Italicized and Bold indicates the standard is

both a Gap and a Power Standard.

Durham Public Schools 2012-2013Grade 6 Mathematics Curriculum Overview

COMMON CORE STATE STANDARDS-AT-A-GLANCE

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6Correcting Instruction

4 WEEKS 5 WEEKS 5 WEEKS 4 WEEKS 9 WEEKS 5 WEEKS 4 WEEKS

Number SystemFluency

Rational Number

Relationships

Rate, Ratio, Fractions, and Proportional

Reasoning

Statistics & Rational

Explorations

Expressions, Equations, and

Inequalities

Area and Volume

Adjustment,Remediation& Exhibition

6.NS.16.NS.26.NS.36.NS.4

6.NS.56.NS.6a6.NS.6b6.NS.6c6.NS.7a6.NS.7b6.NS.7c6.NS.7d6.NS.86.NS.9

6.RP.16.RP.2

6.RP.3a6.RP.3b6.RP.3c6.RP.3d

6.SP.16.SP.26.SP.36.SP.46.SP.5a6.SP.5b6.SP.5c6.SP.5d

6.EE.16.EE.2a6.EE.2b6.EE.2c6.EE.36.EE.46.EE.56.EE.66.EE.76.EE.86.EE.9

6.G.16.G.26.G.36.G.4

All Standards

Sample Unit… a closer look

Concept Based Instruction

KNOW DO

UNDERSTAND

CONCEPT

Concept Based Unit Planning Process

Standards

Concept

Enduring Understandings

Essential Questions

• Involves the Big Ideas that give meaning and importance to facts.

• Can transfer to other topics, fields, and adult life.• Is usually not obvious, often counterintuitive, and

easily misunderstood.• May provide a conceptual foundation for basic skills.• Is deliberately framed as a generalization – the

“moral of the story.”

An Enduring Understanding. . .

What do we want students to understand and be able to use several years from

now, after they have forgotten the details?

Adapted from Understanding by Design: Professional Development Workbook by McTighe and Wiggins, p. 115-116.

Example: Enduring Understandings

•Negative numbers can be used to represent quantities less than zero or quantities with an associated direction such as debt, elevations below sea level, low temperatures, moving backward in time, or an object slowing down.•Knowledge of ratios and rates allows sound decision-making in daily life such as determining best values when shopping, creating mixtures, adjusting recipes, calculating car mileage, using speed to determine travel time, or making saving and investing decisions.

Identifying Essential Questions & Enduring Understandings

Essential Questions; Enduring

Understandings

Why study ____?

So what?

What’s the Big Idea implied in

the skill or process of ______?

What larger concept underlies _____?

What couldn’t we do if we didn’t

understand _____?

How is _____ used and applied

in the larger world?

Adapted from Understanding by Design: Professional Development Workbook by McTighe and Wiggins, p. 83.

• Have no simple “right” answer; they are meant to be argued.• Are designed to provoke and sustain student inquiry, while

focusing learning and final performances.• Often address the conceptual or philosophical foundations of

a discipline.• Raise other important questions.• Naturally and appropriately recur.• Stimulate vital, ongoing rethinking of big ideas,

assumptions, and prior lessons.

Essential Questions . . .

Adapted from Understanding by Design: Professional Development Workbook by McTighe and Wiggins, p. 91.

Activity #2-In mathematics, Essential Questions may be considered in terms of the following categories:• Key Concepts – What are the Big Ideas underlying effective

use of the concept?• Purpose/Value – Why is the concept important?• Strategy/Tactics – What strategies do skilled users of the

concept employ? How do users become more efficient and effective?

• Context – When should you use the concept?

Essential Questions

Adapted from Understanding by Design: Professional Development Workbook by McTighe and Wiggins, p. 104.

Example: Essential Questions

Sampling

Key Concepts

What makes an appropriate sample?

Purpose/Value

Why would we want to sample instead of counting

everything?

Context

When is sampling sometimes better than

counting?

Strategy/Tactics

How can we select representative samples?

Adapted from Understanding by Design: Professional Development Workbook by McTighe and Wiggins, p. 104.

Example: Essential Questions

Linear Models

Key Concepts

Why is constant rate of change the key feature of a linear

function? How is it revealed in the different forms of a linear

function?

Purpose/Value

Why is mathematical modeling a valuable process?

Context

When is it appropriate to use a linear model to describe the

relationship between two quantities?

Strategy/Tactics

How do mathematical models help us understand relationships

between quantities?

Concept-Based Unit Planning Process (continued)

Assessment of Student Outcomes

Materials & Resources

Instruction (Differentiation)

Activities & Tasks (Differentiation)

Same materials…Same instruction…Same assessments…Same feedback…

SAME RESULTS!Don’t be this person…

CCSS Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Inquiry Based Learning

• student-centered approach which engages students investigating real world questions

•Research shows that student learning is directly proportional to the quality and quantity of student involvement. (teachers typically consume 70% of classroom conversation)*

•Inquiry-based instruction reverses this trend and places students at the helm of the learning process.

*Cooper and Prescott 198919

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Criteria for a successful inquiry(borrowed from Jeffrey Wilhelm, author of "You Gotta Be The Book" and "Hyperlearning")

1. Start with a guided exploration of a topic as a whole class.2. Proceed to student small group inquiry about an open-ended, debatable, contended issue.3. Encourage students to ask personally relevant and socially significant questions.4. Work in groups to achieve diversity of views.5. Predict, set goals, define outcomes.6. Find or create information...look for patterns.7. Instruction serves as a guide to help students meet their goals.8. Create a tangible artifact that addresses the issue, answers questions, and makes learning visible and accountable.9. Learning is actualized and accountable in the design accomplishment.10. Arrive at a conclusion...take a stand...take action.11. Document, justify, and share conclusion with larger audience.

Inquiry Based Resources available at DPS

Connected Mathematics MathScape

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Inquiry Based Instructional Model1. Launch- (approx. 10 minutes)

-whole class-help students understand the problem setting, mathematical context, and the challenge.

2. Explore- (approx. 30 minutes)-individually, pairs, groups, sometimes whole class-teacher’s role- move about class to observe, encourage, ask questions, provide conformation-time for differentiated learning

3. Summarize- (approx. 10 minutes)-whole group-students provide conjectures, question each other, offer alternatives, refine their strategies, and make connections.

* This model leaves teachers 10 minutes to tackle homework questions.22

Activity 3 -Review CO’s and Unit Plans:

• With your group review the curriculum overviews and sample unit plans.

• Look through the available CMP and MathScape materials

• Be prepared to share with your presenter other resources that could be added.

.

Please find other common core information on Depot or by visiting our common core website.

Next steps:• Unpacking the standards• Professional development on Connected

Mathematics (CMP)