1. Leadership Pathway: Rigor in Grades K–5 February 2016
Global Neutral a
Global Warm Neutral
d3d1c8
Global Accent On Dark
ffbf00
Global Accent on Light
ff9800
Global Accent Alt
97c410
ELA - Coral
ff5147
Math
009f93
Leadership
7872bf
Leadership Pathway:
Rigor in Grades K–5
61 minutes for this session
Materials:
Markers (6 colors)
6 sheets of chart paper prepared with the following headings on them
Focus: What is it? (recall)
Focus: Required Leadership Actions (application)
Coherence: What and Why? (recall)
Coherence: Required Leadership Actions (application)
Relationship of Focus, Coherence, Rigor to the Standards (synthesis)
Rigor: What and Why?
Handouts
Find the Rigor (1 page), 1 per participant
February 2016

2. RIGOR IN GRADES K–5 At a Glance
Day
Ideas
Wednesday
8:30-4:00
The Foundation
Components of a Comprehensive Literacy Program
Thursday
Building Knowledge and Vocabulary
The Juicy Language of Text
Organizational Systems and Structures
Friday
Focus, Coherence and Rigor
Saturday
8:30-2:30
Observing the Standards And Shifts
Adaptations for Struggling Learners
L E A R N I N G C O N T E N T
1 min
Speaker Notes:

3. RIGOR IN GRADES K–5 Rigor Session, Part 1
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 and Activator
Rigor: What and Why
Finding Rigor in the Standards
Summary and Reflection
Survey
Tomorrow:
Rigor, Part 2
Observing the Standards and Shifts
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 grades K-5.

4. From the CCSS for Mathematics
RIGOR IN GRADES K–5
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 secs to read - Take a moment to read this quoted section from the CCSS for Mathematics.
30 secs to say: The study of mathematics instruction in this country has identified a number of things we are trying to correct for with the CCSS. 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?

5. Paired Learning Activator
RIGOR IN GRADES K–5
Paired Learning Activator
Is there a time where 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 minutes
Speaker notes:
4 minutes – Stand and to 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 minutes – Still standing with partner, ask the group to share out their experiences
IMAGE CREDITS:

6. Rigor – What and Why?
“Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
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:

7. From “Adding It Up” RIGOR IN GRADES K–5 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

8. From TIMSS Video Study RIGOR IN GRADES K–5
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.

9. From TIMSS Video Study RIGOR IN GRADES K–5 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.

10. Consider this contrast
RIGOR IN GRADES K–5
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:

11. RIGOR IN GRADES K–5
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

12. Find the Rigor Protocol: Do the math.
RIGOR IN GRADES K–5
Find the Rigor
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 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.

13. RIGOR IN GRADES K–5
Task #1
Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend?
Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy?
Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $42, how much did each grandchild get?
1 minute
Speaker Notes:
Answers:
a) Juanita spent $54.
b) Nita bought 6 games.
c) Each grandchild gets $6.
The highlighted aspect of rigor is application because students must use multiplication and division to solve real-world problems. Note the mix of multiplication and division within the task--students must choose different strategies for each problem.
Click to reveal the standard 3.OA.A.3
Source:
3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

14. RIGOR IN GRADES K–5
Task #2
The teacher gives the equation 4 × ___ = 12. Charlie finds the answer by writing and solving 12 ÷ 4 = ___.
Explain why Charlie’s method works.
3.OA.B.6
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
1 minute
Speaker Notes:
Answer: Participants may come up with a variety of responses including verbal descriptions and drawings that relate division to multiplication.
The aspect of rigor is conceptual understanding -- students must have a deep understanding of the meaning of each equation and the relationship between multiplication and division.
Click to reveal the standard 3.OA.B.6.
Source:

15. Task #3 1. Facts for speed and accuracy: a. ____ x 5 = 15
RIGOR IN GRADES K–5
Task #3
1. Facts for speed and accuracy:
a. ____ x 5 = 15
b. 10 ÷ 1 = ___
c. ___ = 6 x 10
d. ___ =20 ÷ 5
e. ___ = 7 x 10
f. 1 x 6 = ___
g. 9 x 2 = ___
h. 0 x 5 = ___
1 min
Speaker Notes:
Answers:
a) 3, b) 10, c) 0, d) 4, e) 70, f) 6, g) 18, h) 0
The highlighted aspect of rigor 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)
Source:
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.

16. Identifying Rigor in the Standards
RIGOR IN GRADES K–5
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.

17. One Final Point: A Balance of Rigor
RIGOR IN GRADES K–5
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 common core 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

18. Carousel Summarizer Carousel Topics
RIGOR IN GRADES K–5
Carousel Summarizer
In small groups, rotate through the chart paper on the walls. Record your learning. Leave room on the paper.
Your facilitators will give you the signal to move. Take your marker with you.
Place a check mark next to any previous recordings to indicate agreement or “ditto.” Add your own learning.
Carousel Topics
Focus: What is it?
Focus: Required Leadership Actions
Coherence: What and Why?
Coherence: Required Leadership Actions
Rigor: What and Why?
Relationship of Focus, Coherence, Rigor to the Standards
20 min
Materials:
Markers (6 colors)
6 sheets of chart paper prepared with the following headings on them
Focus: What is it? (recall)
Focus: Required Leadership Actions (application)
Coherence: What and Why? (recall)
Coherence: Required Leadership Actions (application)
Relationship of Focus, Coherence, Rigor to the Standards (synthesis)
Rigor: What and Why?
Speaker Notes:
We’ve covered a LOT today. Let’s take some time to step back and revisit our learning.
Count off into 6 small groups
Have each group begin at one of the chart papers. Give each group 1 color marker that they will take with them.
Timing: 4 min at 1st chart paper; 4 min at 2nd; 3 min at 2 and 2 min each for last 2.
Transition: We have used this last time to capture your learnings from today. Tomorrow we will first go to a keynote and then come right back here to finish up with Rigor. We’ll leave these charts up to refresh and activate our learning in the morning.

19. RIGOR IN GRADES K–5
Feedback
Please fill out the survey located here:
-Click “ February Institute” on the top right
-Click “Details” on the center of the page
5 min
Speaker Notes:
Please fill out the survey to help us improve!

20. References RIGOR IN GRADES K–5 Slide Source 6 7
8-10 13 14 15 17

21. Image Credits RIGOR IN GRADES K–5
Slide 5:
Slide 6:
Slide 18: