NYS COMMON CORE MATHEMATICS CURRICULUM A Story of

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Coherence Across the Grades in Number and Operations—Base Ten © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives • Examine the sequence of standards that comprise the Number and Operations—Base Ten domain. • Examine the sequence of base ten models employed in A Story of Units. • Examine and practice the algorithms employed in A Story of Units. 2 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda NBT ACROSS THE GRADES: A Progression of Standards A Progression of Visual Models A Progression of Algorithms The Progressions Document for Number and Operations—Base Ten 3 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards Card Sort! 4 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards • Compose and decompose numbers 11– 19 into 10 ones and some further ones… (K. NBT. 1) • Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. (1. NBT. 5) • Mentally add 10 or 100 to a given number 100– 900, and mentally subtract 10 or 100 from a given number 100– 900. (2. NBT. 8) 5 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards • Use place value understanding to round whole numbers to the nearest 10 or 100. (3. NBT. 1) • Use place value understanding to round multi-digit whole numbers to any place. (4. NBT. 3) • Use place value understanding to round decimals to any place. (5. NBT. 4) 6 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 7 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units NBT Standards Across PK-5 Take a moment to reflect on the curriculum map. • What role does your grade play in the development of Number and Operations—Base Ten? • How does it rely on the previous grade and prepare students for the subsequent grade? 8 © 2012 Common Core, Inc. All rights reserved. commoncore. org

A Story of Units NYS COMMON CORE MATHEMATICS CURRICULUM A Progression of Standards A Story of Units A Story of Ratios A Story of Functions The Number System Algebra 6 -8 9 -12 Number and Operations— Base Ten Number and Operations— Fractions K-5 9 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards 10 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA NBT ACROSS THE GRADES: A Progression of Standards A Progression of Visual Models A Progression of Algorithms The Progressions Document for Number and Operations—Base Ten 11 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Visual Models 12 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 13 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Visual Models • What did you notice about the sequence of visual models? • In what ways will students benefit from this sequence? • How does it compare with other models that you currently use? 14 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA NBT ACROSS THE GRADES: A Progression of Standards A Progression of Visual Models A Progression of Algorithms The Progressions Document for Number and Operations—Base Ten 15 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Demonstration – A Progression of Algorithms 16 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Algorithms • What did you notice about the sequence of algorithms? • In what ways will students benefit from this sequence? • How does it compare with other algorithms that you currently use? 17 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units AGENDA NBT ACROSS THE GRADES: A Progression of Standards A Progression of Concrete and Pictorial Models A Progression of Algorithms The Progressions Document for Number and Operations—Base Ten 18 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Study of the Progression • Pick a grade and read the appropriate section of the Progressions document, highlighting evidence in support of this morning’s demonstrations. • Do the same with the previous and subsequent grades. 19 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Study of the Progression • What connections did you find between the Progressions document and this morning’s demonstrations? • Think about the modules that you explored yesterday. How are they relevant in the coherence of the NBT domain? 20 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units A Progression of Standards Card Sort! 21 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Next Steps • How will this information impact instruction in your classroom/school/district? • How will you continue to use the Progressions documents as you implement A Story of Units? • How can you initiate a study of the Progressions with your colleagues? 22 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points • • • While work in NBT is dependent on understanding of the meanings and properties of operations, it also fosters a deeper understanding of them. The NBT standards include a deliberate trajectory from reasoning about quantities, the base-ten system, and the meanings of operations to mastery of standard algorithms. The Standards and Progressions provide valuable insight that enables educators to meet their students’ needs in a way that also maintains coherence across the curriculum. 23 © 2012 Common Core, Inc. All rights reserved. commoncore. org