1. Fractions
A Vertical Look 3-8

2. What fraction of the design is colored?
Which has the most color?
Warm up:
Stand and talk
Fractiontalks.com
What fraction of the design in colored? Which has the most color?

3. We will:
Examine the Number and Operations Fractions domain in the TN Math Standards and analyze the content progressions.
Apply content progressions to instructional tasks.
Summarize new learning so we can plan effective lessons and create aligned tasks and assessments.

4. How?
Read, build, draw
Talk
Write and Record

5. The Learning Progressions
The progression of the Domains
Talking Points:
The progressions are very important throughout the grades.
The standards build on one another and especially so in the earlier grades.
Note how some domains are more broken up than others (geometry is solid all the way across but algebraic thinking is not).
This is an indication of an emphasis in the progressions for those domains. In other words, there is greater stress laid on those domains in the early grades because they are so vital to the foundation for Algebra and mathematical success for college and career ready students.

6. Instructional Shifts Focus
The standards are focused on fewer topics so that students can dig deeper within the mathematics.
Coherence
Topics within a grade are connected to support focus. Additionally, standards are linked across grades to ensure vertical coherence.
Rigor
The standards set expectations for a balanced approach to pursuing conceptual understanding, procedural fluency, application, and modeling.

7. Expectation Three: Rigor
Procedural Skill and Fluency: The standards call for speed and accuracy in calculation.
Conceptual Understanding: The standards call for conceptual understanding of key concepts, such as place value and ratios. 
Modeling/Application: The standards call for students to use math in situations that require mathematical knowledge.

8. Nomenclature and Coding
4.OA.A.1
Grade
Cluster
Domain
Standard
Talking Points:
In K-8 the standards are coded with the grade level, conceptual category/domain, cluster, and content standard.
Let’s take a look at an example (click to animate)
4 is the grade level.
OA Operations and Algebraic Thinking is the domain.
A is the cluster which are ordered by A, B, C, etc. for first cluster, second cluster, etc..
1 is the standard number (the standards are numbered consecutively throughout each domain regardless of cluster)

9. Clusters for Grade Levels
Group
Cluster Progression 1
3.NF.A
4.NF.A
5.NF.A 2
4.NF.B
5.NF.B.3
5.NF.B.7
6.NS.A 3
5.NF.B.4
5.NF.B.5
5.NF.B.6
7.NS.A.2
8.NS.A.1 4
4.NF.C
5.NF.B
Participants will write their assigned clusters in the Instructional Alignment Chart and find them in their standards.
6th
7th convert frac to decimals using long division
8th apply to irrational numbers

10. Step 1: Focus Thinking Around One Big Idea
Review the assigned clusters.
Discuss the big idea that each cluster is asking the students to know and be able to do.

11. Step 2: Collaborate & Discuss Changes
How is the cluster different from the previous grade level?
Are there new concepts introduced or added?
Are any concepts dropped?
How does the demand of the cluster change?
Does an idea or skill get more complex? How?
(Analyze the verbs)

12. Step 3: Consider Rigor when Planning Instruction
Is this a new concept that has never been taught?
What content knowledge should be developed or shared?
What resources or support might we need to teach this concept?
What types of assessment might we need to measure this learning?

13. Expectation Three: Rigor
Procedural Skill and Fluency: The standards call for speed and accuracy in calculation.
Conceptual Understanding: The standards call for conceptual understanding of key concepts, such as place value and ratios. 
Modeling/Application: The standards call for students to use math in situations that require mathematical knowledge.

14. Summarize Instructional Shifts
Focus: what is the focus of each grade level
Coherence: what changes from grade to grade
Rigor: Where do you see the 3 aspects of rigor
Create a visual as a class: class anchor chart. Can add to throughout session (Concept map)
Each group creates own, instructors grab elements from across the room as participants work to create a whole-group chart. (Don’t waste time creating work in front of class.)

15. Break

16. Graham Fletcher Video Fractions Progression Pull it all together
Stop and Chat

17. Norms Provide explanations and justifications with all answers
Make sense of each others’ solutions
Say when you don’t understand or don’t agree
For your classroom: YouCubed.org Norms for Math class
Post: Mistakes are…Expected, Inspected, Respected

18. Developing Understanding of Fractions as Numbers
Justify each students thinking.
Michael says the image represents 2.
Sophie says the image represents 2/3.
Kate says the image represents 2/6.
*Defining Meaning 3.NF.A.1 (Illustrative Math) Trios sharing: “Form a trio with two people not sitting at your table. Together, brainstorm ways that this model could represent 2/6, 2/3, and 2.”
Michael says this image represents 2/6.
Kate says this image represents 2/3.
Sophie says this image represents 2.
Justify each students’ thinking.

19. Understanding Equivalence
Compare 2/3 and 8/10. Show how you arrived at this conclusion.
Equivalence and Comparing: With your group, choose one method that was interesting and talk about how you approached it.
Highlight Common Den, Common Num, Benchmark fractions, missing part
How can strategies such as common denominators and common numerators, missing parts, and benchmarks help students compare fractions without using the “butterfly method”?

20. Add and Subtract Make sense of the problem:
Two fifths of the cross-country team arrived at the weight room at 7 am. Ten minutes later, 3/10 of them showed up. The rest of the team stayed home.
5.nf.a.2- illustrative math (What fraction of the team made it to the weight room that day?)
Think-share-compare routine
(Make sense of the problem-Solve and Support Your Thinking-Discuss-Compare-Connect and Reflect)

21. 3 Act Task
The Apple
Graham Fletcher 3 act task: 6.NS.A.1

22. Planning Reflect on this session: What did you come to understand?
What did you discuss?
What groupings/ format did you use to discuss?
What scaffolds were provided? When were they provided?
How did you record and share your thinking?