1. Leadership Pathway: Rigor in Grades 6–8 Winter 2017
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Leadership Pathway:
Rigor in Grades 6–8
95 minutes for this session
1 video, 11 min.
Handouts packets for Day 2
Be sure to load the video prior to participants’ arrival by opening the link and letting it begin to run. This should then have the video ready to view without buffering.
11 min. video:
Winter 2017

2. The Week at a Glance RIGOR IN GRADES 6–8 Day Ideas Monday
8:30–5:00
Focus and Coherence
Tuesday
8:30–4:30
Rigor
Observing the Standards and Shifts
Adaptations for Struggling Learners
Wednesday
The Foundation
Text Complexity
Thursday
Building Knowledge and Vocabulary
The Juicy Language of Text
Friday
8:30–2:30
Organizational Systems and Structures
1 min.
Speaker Notes:

3. Objectives and Agenda Objectives
RIGOR IN GRADES 6–8
Objectives and Agenda
Objectives
Participants will be able to describe the three aspects of rigor and why rigor is important.
Participants will be able to evaluate standards, tasks, and lessons for aspects of rigor.
Participants will be able to observe and coach the rigor shift in teacher practice.
Agenda
Opening
Activator
Rigor: What and Why?
Finding Rigor in the Standards
Observing for Rigor
1 min.
Speaker Notes:
We’ll start by looking carefully at the shift of rigor in math, with an emphasis on why it’s important and what it looks like in in the standards for grades 6–8.

4. Feedback on Feedback RIGOR IN GRADES 6–8 Plus Delta 5 min.
Speaker Notes:
Highlight a couple of pluses and a couple of deltas; choose them based on impact on participant learning and/or so that they feel heard. Tell how we will respond today or what they can expect. For the pluses or deltas that are about group behavior, encourage the group to keep doing the positive and to monitor or minimize those things that could help the learning environment be improved.

5. Norms That Support Our Learning
RIGOR IN GRADES 6–8
Norms That Support Our Learning
Take responsibility for yourself as a learner.
Honor timeframes (start, end, activity).
Be an active and hands-on learner.
Use technology to enhance learning.
Strive for equity of voice.
Contribute to a learning environment where it is “safe to not know.”
1 min.
Speaker Notes:
Choose to remind them of a norm if you think it has been slipping:
Keep an open mind (esp. about what you don't know or thought you knew).
Stay in learning orientation vs. performance orientation—growth mindset.
Be active during video observation by capturing evidence in writing.
Appreciate everyone's perspective and journey.
Share ideas and ask questions, one person at a time (airtime).
Be okay with discomfort and focus on growth.
Be present (monitor multi-tasking, technology, honoring timeframes).

6. Teachable Moments Activator
RIGOR IN GRADES 6–8
Teachable Moments Activator
Step One – Pair
Stand and find a partner. Remain standing.
Step Two – Count
At the facilitator’s direction, count off 1–6.
Step Three – Analyze
Analyze your assigned statement for its misconceptions.
Step Four – Role Play
3 min. – Practice coaching to undo the misconception(s).
3 min. – Provide feedback
3 min. for scenario and protocol
Speaker Notes:
Let’s start the day with an activator that serves 3 purposes:
1. It helps you remember what we learned yesterday about Focus and Coherence.
It helps to surface common misconceptions that educators have when they learn about the shifts.
It gives you a chance to practice a coaching conversation to undo a misconception.
Here’s the scenario: Imagine you have just finished a day of PD back at your school. You loved the Institute session on Focus and Coherence so much that you decided to replicate the experience with your teachers (the materials are free, after all!). After the session, you check-in with individual teachers to hear what they intend to do with their new-found knowledge. Unfortunately, their answers are problematic.
Now here’s the protocol:
<Click > through steps 1 and 2 and have them do them.
<Click> through steps 3 and 4 and explain them. For the coaching role play. This is a one-way coaching practice: 3 min. to coach and 2 min. for the coachee to provide feedback on the effectiveness.
Last Point: Facilitator will monitor time and call out when to switch activities.
IMAGE CREDITS:

7. Teachable Moments Activator
RIGOR IN GRADES 6–8
3. I’m going to make sure I spend at least half my time this year teaching the major work of the grade.
Teachable Moments Activator
1. Ratios and Proportions aren’t relevant in 8th grade because there is no RP domain in 8th—only 6th and 7th. .
2. I decided to skip the Statistics and Probability domain because everything in there is a supporting or additional cluster.
6. I’m going to make sure all the problems/tasks that I assign always align to at least two different standards.
4. My kids can’t do 7.EE so I’m teaching 6.EE first.
5. To strengthen connections, I’ll make sure that my students are solving each problem in as many different ways as possible.
15 min.
Speaker notes:
10 min. to analyze and role play
4 min. analyze statement for misconceptions
6 min. to role play coaching conversation
3 min. role play
3 min. feedback on effectiveness of coach
5 min. to answer any misconceptions questions they might still have
Keep this focused on the content of misconceptions about Focus and Coherence
If any time left, you can ask what an activity like this does for an adult learner or ask if anyone in the room regularly surfaces misconceptions as a part of their professional development activities.
MAIN POINTS: Help build out some of the nuance and inputs to instructional decision-making here
Correct Answers
It is relevant as a prerequisite. From our Ratios: Unbound Content Guide: In Grade 8, there is no separate group of standards for ratios and proportional relationships; these ideas merge completely with the algebra content in the Expressions & Equations domain and the Functions domain. The concept of unit rate evolves into slope, (8.EE.B.5) and students will discover important properties of slope. They explore the connection between proportional relationships (i.e. can be represented by an equation y = mx) and linear equations more generally (y = mx + b).(8.EE.B.6) And after being formally introduced to the concept of a function, students will model linear relationships with functions. (8.F.B.4) Students will rely on these concepts throughout high school and, in many cases, in post-secondary work as well.
Additional clusters are not to be skipped—doing so would put students behind as they move to the next grades where SP is major work. In this case, there is a highly applicable connection to be made between work with lines and scatter plots with linear models.
Major work should comprise the bulk of the learning for the grade level, not “at least half.” But half is not enough, it should be the bulk (at least ⅔ of the learning). Bigger idea is about depth over breadth. Deep learning over fast learning.
Spending a lesson or two on a prerequisite is fine, but students should very quickly be moving into grade level content. Another way of tapping into prerequisites is to spend the beginning of each lesson connecting students to previous learning (vs. devoting entire lessons to reteaching). The math team calls this “coherent content in context”.
This is overkill. Math is intended to be efficient. Solving problems in different ways may make sense some of the time—particularly when the idea is new—but it is poor practice to do it all of the time.
Another example of an overcorrection. Having students learn the content demanded by one standard is fine, especially when the standards ask demonstration of deep conceptual understanding, modeling, and/or application. Rich, quality math tasks help make this happen for students. Within-grade coherence is helpful when the connections are made appropriately and planfully. The Coherence Map can help map these connections out for you. And good curriculum will do that work for you as well.
Final Point - we should not be turning the math shifts into recipes.

8. Rigor: What and Why?
“Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
From the Common Core State Standards
3 min.
Speaker Notes:
Ask: Can I hear from 1–2 people: how would you define rigor?
<Click> for the animation to show the definition
Say:
A common misconception is that rigor just means “hard.” It doesn’t. “Rigor” has a specialized meaning in the context of Common Core math. From CoreStandards.org: “Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
This morning we talked about what mathematical content is important, and what connections exist between standards.
Rigor has everything to do with how students engage with mathematical content: it implies a balance of conceptual understanding, procedural skill and fluency, and application. But why do we care about these aspects of mathematical understanding?
IMAGE CREDITS:

9. From the CCSS for Mathematics
RIGOR IN GRADES 6–8
From the CCSS for Mathematics
“Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like?”
“There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).”
“Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”
1 min.
Speaker Notes:
30 sec. to read—Take a moment to read this quoted section from the CCSS for Mathematics.
30 sec. to say: The study of mathematics instruction in this country has identified a number of things we are trying to correct for with the state standards. One of them is our lack of helping children understand math concepts deeply. I’d like you to think of how this may have impacted mathematical learning for you. Think for a moment: Is there a time where you learned a procedure or a mnemonic or a way of doing the math without understanding what why or what math you were doing? And what impact did that have on your future learning—if any?

10. Paired Learning Activator
RIGOR IN GRADES 6–8
Paired Learning Activator
Is there a time when you learned a procedure or a mnemonic or a way of doing the math without understanding why or what math you were doing?
And what impact did that have on your future learning—if any?
7 min.
Speaker notes:
4 min. – Stand and find someone you have not yet connected deeply with in this Institute. Share your experiences for about 4 minutes.
Note: this is happening in late afternoon, so it is important that people stand for this activity so that it also acts as a mini-energizer.
3 min. – Still standing with partner, ask the group to share out their experiences.
IMAGE CREDITS:

11. From “Adding It Up” RIGOR IN GRADES 6–8 1 min. Speaker Notes:
Researchers in the late 90s identified 5 components (or strands) of mathematical proficiency.
Note particularly these 4: (adaptive reasoning, conceptual understanding, procedural fluency, and strategic competence). These form the basis of what we call “rigor” in the standards. (Adaptive reasoning is also about Rigor. It is the application/modeling portion of it and works hand-in-hand with Strategic Competence)
The other strands make up the mathematical practices
Ask a question: “How well do you think our instruction is currently balanced among these three aspects of rigor?” 1 answer here because of time

12. From TIMSS Video Study RIGOR IN GRADES 6–8
2 min.
Speaker Notes:
TIMSS video study of 7 in the late 1990s compared eighth-grade math instruction in 7 participating countries.
Despite the recognition that a balance of the different strands of mathematical proficiency is necessary (Adding It Up), on average, 75% of “private work time” is spent repeating procedures in the United States.
The point of the slide is not to draw conclusions about what the impact of "repeating procedures" might be but to show the gap between what's happening in the US and what research about the Adding It Up research says. 
NOTE: Repeating procedures in this context means following modeled algorithms/procedures rather than independently applying strategies (without heavy guidance) or time spent demonstrating conceptual understanding by explaining thinking
QUESTION PARTICIPANT MAY ASK:
Might have a leader talk about how our students/culture is different…need to emphasize what the research says what students need, ... and what we control.
Other TIMSS background:
The TIMSS 1999 Video Study was a study of eighth-grade mathematics and science teaching in seven countries. The study involved videotaping and analyzing teaching practices in more than one thousand classrooms. In conjunction with the International Association of the Evaluation of Education Achievement (IEA), the study was conducted by the National Center for Education Statistics, U.S. Department of Education under a contract with LessonLab, Inc. of Los Angeles, California. Although Japan did not participate in the mathematics portion of the study, the Japanese mathematics data collected as part of the TIMSS 1995 Video Study were re-analyzed for the TIMSS 1999 Video Study. U.S. mathematics data collected as part of the TIMSS 1995 Video Study were also re-analyzed.

13. From TIMSS Video Study RIGOR IN GRADES 6–8 2 min. Speaker Notes:
Additionally, the kind of non-routine problem solving implied by the application shift does not seem to be happening either.
Compared to some other high-performing nations, we spend a smaller amount of time on problems that take longer than 45 seconds. (Only 61% of problems are solved in longer than 45 seconds.)
QUESTIONS PARTICIPANTS MAY ASK:
I think a lot of times educators talk about how technology prevents students from spending extended focus time on problem solving...this graphic completely debunks that. Looking at developed nations, have large access to technology, so excuse that students don't have stamina isn't valid.
Note about these slides: While TIMSS is conducted every few years, this "interesting" data (about time spent on different things in classrooms, etc.) comes from the TIMSS Video Study, which has only occurred once, in Otherwise, TIMSS is an assessment system that provides information about what students know and can do around the world. Still interesting, but doesn't give us information about what students and teachers are doing in classrooms.

14. Consider This Contrast
RIGOR IN GRADES 6–8
Consider This Contrast
USA
How can I teach my kids to get the answer to this problem?
Japan
How can I use this problem to teach the mathematics of this unit?
1 min.
Speaker Notes:
Point to the USA question and ask, ”Is this familiar?”
Point to the second question and say, “What differences would we need to see if we approached mathematics instruction this way?”
From:

15. RIGOR IN GRADES 6–8
Three Aspects of 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.
2 min.
Speaker Notes:
The Common Core names and emphasizes three aspects of rigor that are a direct reflection of this research on mathematical understanding.
Procedural skill and fluency shift refers both to “procedural skill” and “fluency”. In some cases, speed with calculations is particularly emphasized. Fluency should be built after conceptual understanding has been achieved.
What does conceptual understanding look like? One way for teachers to get students to understand key concepts is to ask students to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.
Modeling/Application is not “just doing a bunch of real-world problems” but should genuinely require that students know which ideas to apply when and how to “mathematize” real-world situations

16. Finding Rigor in the Standards
RIGOR IN GRADES 6–8
Finding Rigor in the Standards
Protocol:
Do the math.
For each, what aspects of rigor are emphasized and how do you know?
What are the grade-level standards associated with each one?
10 min. to do all three tasks and identify standards
Speaker Notes:
Hand out the tasks sheet.
Say: Rigor is baked into the standards. We’ll start to see what rigor looks like in a task and then and how it is embodied in the standards.
For each task, “do the math” and discuss which aspects of rigor are present.
Determine the grade level standard associated with each one.

17. RIGOR IN GRADES 6–8
Task #1
A mixture of concrete is made up of sand and cement in a ratio of 5:3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix?
6.RP.3.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).
1 min.
Speaker Notes:
Answer: 100 cubic feet of sand and 60 cubic feet of cement
The highlighted aspect of rigor is application because students must use an understanding of ratios to solve real-world problems.
Click to reveal the standard. This is standard 6.RP.3.A.3
Source:

18. RIGOR IN GRADES 6–8
Task #2
Hippos sometimes get to eat pumpkins as a special treat. If 3 hippos eat 5 pumpkins, how many pumpkins per hippo is that?
Lindy made 24 jelly-bread sandwiches with a 16-ounce jar of jelly. How many ounces of jelly per sandwich is that?
Purslane bought 350 rolls of toilet paper for the whole year. How many rolls of toilet paper per month is that?
6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar” or, “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
1 min.
Speaker Notes:
Answers:
5/3 pumpkins per hippo
2/3 ounces of jelly per sandwich
350/12 or 29 rolls per month
NOTE: this IM task has 2 more problems that we skipped for time today.
MAIN POINTS:
The highlighted aspect of rigor is conceptual understanding because students must use the concept of ratio to explain their answer to this problem. Note that computation is not necessary for this example.
In this problem, students may easily get confused with ?? and 5/3—this is where the conceptual understanding comes in. Students must deeply understand the concept of a unit rate. The emphasis is not on computation here.
Click to reveal the standard 6.RP.2.
Source:

19. RIGOR IN GRADES 6–8
Task #3
1 min.
Speaker Notes:
Answers:
15/104
6/35
15/164
The highlighted aspect of rigor FOR THIS TASK is procedural fluency because students must perform computations quickly and accurately.
It’s important to note that there are standards that emphasize procedures, but may not include the word “fluently”—we may emphasize performing procedures accurately with less emphasis on speed for these standards.
Click to reveal the standard.
Transition to next slide by pointing out that Fluency is not the only aspect of rigor required by this standard. Note that many standards may imply more than one aspect of rigor. 3.OA.C.7 is an example (next slide).
6.NS.A.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

20. Identifying Rigor in the Standards
RIGOR IN GRADES 6–8
Identifying Rigor in the Standards
Procedural Skill and Fluency
Conceptual Understanding
3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
1 min.
Speaker Notes:
Point out both aspects of rigor required by this standard.
Transition: In the time we have left today, let’s summarize what we set out to learn and where we are before heading into our reflection and survey.

21. Identifying Rigor in the Standards
RIGOR IN GRADES 6–8
Identifying Rigor in the Standards
Procedural Skill
Application
6.NS.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem).
1 min.
Speaker Notes:
Point out all aspects of rigor required by this standard.
Conceptual Understanding

22. One Final Point: A Balance of Rigor
RIGOR IN GRADES 6–8
One Final Point: A Balance of Rigor
The standards set high expectations for all three components of rigor in the major work of each grade.
(1) The three aspects of rigor are not always separate in materials.
(2) Nor are the three aspects of rigor always together in materials.
1 min.
Speaker Notes:
In the teacher sessions, teachers are examining curricular materials for all aspects of Rigor, including how to look for a balance. We do not have time for that exploration in this session, but you should know:
Criteria were developed to help states, districts, schools faithfully implement the standards through evaluation of curricular materials. “Crosswalking” is not good enough, good curricular must be able to speak to the spirit of the standards.
The Publishers’ Criteria makes clear this balance is important.
“Of course, that makes it necessary that we first follow through on the focus in the Standards” (From Publishers’ Criteria)—We must have a focused curriculum in order for teachers to be able to develop fluencies, conceptual understanding, and application (it’s an issue of time, essentially).
Transition: In the time we have left today, let’s summarize what we set out to learn and where we are before heading into our reflection and survey.
IMAGE CREDITS:

23. Observing for Rigor 1 min. Speaker Notes:
Let’s see what Rigor looks like. In this video, you will see a pretty strong example in a fifth-grade classroom. First, let’s look at what we might see with each of the aspects of Rigor.

24. Key Supervision Questions for Rigor
RIGOR IN GRADES 6–8
Key Supervision Questions for Rigor
What to look for
Opportunities for students
to become more fluent (efficient and accurate) with procedures.
Students practice, many times, with facts and procedures.
Fluency activities build upon conceptual understandings students already have.
to build their conceptual understanding.
Students being asked “why” to rationalize their thinking.
Students working with models to process their thinking.
to model/apply their thinking, particularly in real-world situations.
Students working on rich math problems.
Students use math absent of external prompts (e.g., “use addition to solve this problem”).
1 min.
Speaker Notes:
These are the key questions leaders and coaches ask when engaging classroom observations from a rigor lens. These questions will help you collect the right evidence while in the classroom; they are terrific guiding questions around teacher development as well.

25. Observing for Rigor Standards: 6.RP.A.2, 6.RP.A.3, 7.RP.A.2 Prepare
RIGOR IN GRADES 6–8
Observing for Rigor
Standards: 6.RP.A.2, 6.RP.A.3, 7.RP.A.2
Prepare
Look up the standard(s).
Determine the aspects of rigor embedded
in the standard(s).
Capture Evidence of Rigor Aligned
to the Standard
Procedural skill and fluency.
Conceptual understanding.
Modeling/application.
16 min. (5 min. set-up; 11 min. video)
Speaker Notes:
5 min.:
Look up the standard and identify the aspects of rigor.
6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.
6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
7.RP.A.2 Recognize and represent proportional relationships between quantities.
MAIN POINTS: Rigor in these standards
Conceptual understanding - “Understand the concept of a unit rate a/b…” “...reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.”
Application/Modeling – “Use ratio and rate reasoning to solve real-world and mathematical problems…” “Recognize and represent proportional relationships”
Procedural Skill and Fluency

26. After the Observation Procedural skill and fluency evidence
RIGOR IN GRADES 6–8
After the Observation
Procedural skill and fluency evidence
Students practice, many times, with facts and procedures.
Fluency activities build upon conceptual understandings students already have.
Conceptual understanding evidence
Students being asked “why?” and to rationalize their thinking.
Students working with models to process their thinking.
Modeling/application evidence
Students working on rich math problems.
Students use math absent of external prompts.
10 min.
Speaker Notes:
5 min. – First, you will deconstruct what you just saw in terms of RIGOR. Turn & Talk w/ partner. Make your discussions evidence-based
5 min. – Whole group share.
MAIN POINTS:
Fluency: N/A
Conceptual Understanding: Tape diagrams, unifix cubes, etc, being used to develop an understanding of the problem; students being asked to explain their thinking, “So Jillian, you are saying this is red-to-blue. Why?”
Modeling/Application: students working on rich math problem and using math to solve a real-world applicaton problem

27. RIGOR IN GRADES 6–8
After the Observation
What questions would you now want to ask Ms. Morey?
2 min.
Speaker Notes:
Solicit 1–3 answers (don’t spend much time here).
If they don’t say it, ask why two of the standards were 6th grade standards for this 7th grade class.
On the next slide, we have a couple to suggest that can help unpack her thinking and provide opportunities for her development around rigor.

28. Questions That Develop Rigor
RIGOR IN GRADES 6–8
Questions That Develop Rigor
Procedural Skill and Fluency
Conceptual Understanding
Modeling/Application
If fluency opportunities are not present
Ask where fluency practice is/will be built in upcoming lessons.
If students show fluency as a limiter in their math work
Ask how students’ lack of fluency will be addressed.
Consider curriculum: fluency activities from high-quality lessons for the area that is limiting students.
If conceptual understanding opportunities are not present
Ask how more opportunities may be worked into what the students are thinking when working with math concepts.
If students show conceptual understanding as a limiter in their math work
Consider gaps: re-ask questions in coherence activities.
Consider curriculum: study high-quality lessons aligned to the standard of focus.
If application opportunities are not present
Ask how more application opportunities can be folded into the student math experience.
If students are provided external prompts to complete application problems
Ask how the teacher can adapt opportunities so students can apply math without the prompting.
Consider curriculum: study high-quality tasks aligned to the standard of focus.
4 min.
Speaker notes:
These sets of questions will provide a window into the planning and decision-making that drove the teacher’s lesson. It also leads the discussion into the “what’s next” for these students.
How are these questions the same or different than the way you usually debrief classroom observations? How would these questions help develop your teachers?
Transition: We are now going to do one more culminating video observation of a math lesson and then have an opportunity to practice using these questions while coaching for rigor (and the other shifts).

29. References RIGOR IN GRADES 6–8 Slide Source 8 9
12, 13 14 17 18
25–27

30. Image Credits RIGOR IN GRADES 6–8
Slide 6:
Slide 8:
Slide 10:
Slide 22:
Slides 25–27: