Crossing the Bridge to Common Core State Standards for Mathematics Day 4 Dawn Perks Middle School Math Specialist ext

SBAC Smarter Balanced Assessment Consortium North Carolina is a governing state Next generation assessments for implementation in Samples, research, data, and item specifications are available on their website

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 Grade 6 Mathematics Curriculum Overview COMMON CORE STATE STANDARDS-AT-A-GLANCE Unit 1Unit 2Unit 3Unit 4Unit 5Unit 6 Correcting Instruction 4 WEEKS5 WEEKS 4 WEEKS9 WEEKS5 WEEKS4 WEEKS Number System Fluency Rational Number Relationships Rate, Ratio, Fractions, and Proportional Reasoning Statistics & Rational Explorations Expressions, Equations, and Inequalities Area and Volume Adjustment, Remediation & Exhibition 6.NS.1 6.NS.2 6.NS.3 6.NS.4 6.NS.5 6.NS.6a 6.NS.6b 6.NS.6c 6.NS.7a 6.NS.7b 6.NS.7c 6.NS.7d 6.NS.8 6.NS.9 6.RP.1 6.RP.2 6.RP.3a 6.RP.3b 6.RP.3c 6.RP.3d 6.SP.1 6.SP.2 6.SP.3 6.SP.4 6.SP.5a 6.SP.5b 6.SP.5c 6.SP.5d 6.EE.1 6.EE.2a 6.EE.2b 6.EE.2c 6.EE.3 6.EE.4 6.EE.5 6.EE.6 6.EE.7 6.EE.8 6.EE.9 6.G.1 6.G.2 6.G.3 6.G.4 All Standards

Sample Unit… a closer look

Concept Based Instruction KNOW DO UNDERSTAND CONCEPT

Concept Based Unit Planning Process StandardsConceptEnduring UnderstandingsEssential 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

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 OutcomesMaterials & ResourcesInstruction (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

20 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 MathematicsMathScape 21

Inquiry Based Instructional Model 1.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)