1. Coherence with Fractions
2017 K-8 Math Standards Implementation Summer Professional Development
Coherence with Fractions
Denise Schulz
Mathematics and Science Section
Standards, Curriculum, and Instruction Division

2. Agenda
Please go to the following bit.ly to find today’s agenda: This room is Charter Schools: Alpha Academy-NC Leadership Academy Public School Districts: Chapel Hill-New Hanover Once the bit.ly is open, please complete the electronic sign-in for Day 2.

3. Who’s in the room?

4. Purpose
Purpose: Building from the Spring Regional sessions, teachers and teacher leaders will expand on their understanding of the coherence of the K-8 mathematics standards. Throughout these sessions, participants will be introduced to tools and protocols to assist in the roll-out and implementation of the K-8 revised mathematics standards.

5. Essential Questions Why are all standards essential?
How do we build capacity of our staff?
Take a few moments to think on these questions and record your thoughts on the essential questions handout.

6. Coherence with Fractions

7. We’ve had a tendency in our traditional scope and sequence of math that you teach all this whole-number stuff…and then, all of a sudden, you get to fractions, and it’s a whole new world of what to do—everything they learned in whole numbers has nothing to do with how you do fractions. Linda Gojak

8. Fractions are a rich part of mathematics, but we tend to manipulate fractions by rote rather than try to make sense of the concepts and procedures. Researchers have concluded that this complex topic causes more trouble for students than any other area of mathematics.
Bezuk and Bieck 1993
Emphasize the bold in the sentence!

9. Fraction Coherence Through Vertical Alignment

10. Vertical Alignment Connection to the Essential Questions:
How can a vertical study of the standards support and deepen teacher understanding?
How can using a vertical alignment process build professional capacity?

11. Vertical Alignment Process

12. Investigating vertical alignment in the NC Mathematics Standards
As a group…
Select a big idea for your group to investigate.
Using unit fractions to reason about numbers.
Determine what your big idea means.
What is a unit fraction? Why are unit fractions powerful for understanding fractions?
Study one standard at a time. Consider all parts of the standards.
For each standard, determine what the student should know and be able to do.
What is a unit fraction? Why are unit fractions powerful for understanding fractions?
They represent a unit — an amount or a distance.
They behave much like whole numbers for counting.
Properties of operations apply to fraction computations.
As with whole numbers, fractional amounts can be composed and decomposed in various ways.

13. Investigating vertical alignment in the NC Mathematics Standards
As a group, discuss and come to consensus on what order you think these standards should be taught in based on the language and expectations of each standard.
Use the standards strips to build a learning trajectory, starting with Kindergarten as the foundation at the bottom and moving up through 6th grade on the top.
Check your standards order and make adjustments as necessary, then glue or tape your learning trajectory on chart paper.

14. Investigating vertical alignment in the NC Mathematics Standards
As a group, analyze the trajectory, considering the following questions:
What changes occur from grade to grade?
Where are concepts introduced, developed, and finalized?
Does an idea or skill get more complex, and if so, how?

15. Reflection
What does the classroom teacher gain from studying a vertical learning trajectory of the standards?
How does studying the standards in this way support students who have gaps in their learning?

16. Connection to the Essential Questions:
How can a vertical study of the standards support and deepen teacher understanding?
How can using a vertical alignment process build professional capacity?

17. Exploring Fractions Through Tasks and Models

18. Learning Stations

19. Learning Stations 4 stations (1-4 or 5-8)
Partitioning
Equivalence, Addition and Subtraction
Multiplication
Division
Exploration using manipulatives and/or games
Tasks to solve with visual models (purple handout)

20. Reflection
Why is it important for teachers to know and understand how to create visual models of fractions and operations?
How does problem solving in this way support student understanding of fractions?

21. Questions

22. DPI Mathematics Section
Lisa Ashe
Secondary Mathematics Consultant
Denise Schulz
Elementary Mathematics Consultant
Joseph Reaper
Beverly Vance
Math and Science Section Chief 22