Facilitators Guide
Common Core State Standards Mathematics Implementation Training
Developed by the Washington State ESD Regional Math Coordinators in collaboration with Washington State Office of Public Instruction
Step 3 – Making the Connections
Time
5 minutes Introduction
Activity
 Intro
 Review of the series & steps
 Instructional Shifts
Resources
Slides 1-6
ESSENTIAL
Review outcomes for current module:
 Determine if the content of instructional materials is deep
enough.
 Compare and contrast the cognitive complexity of tasks and
the Mathematical Practices
 Adjust existing problems/tasks to increase content depth
and support Mathematical Practices.
15 minutes
ESSENTIAL
Common Core Domain and Instructional Materials
 Refer to learning from previous session on the content in the
Common Core Standards and the domain selected for your
grade level
Slide 7-8
See Resource File
Note:
 Other work that needs to be done
in district is pacing and adjusting
materials to the Common Core
Standards
Professional Development Plan – CCSS-M Step 3 Facilitator’s Guide
Activity-protocol on slide
How Deep is the Content in Your Instructional
Materials
 Development of lesson content for students in their current
instructional materials, how it is introduced, developed and
applied (depth vs breadth) compared to the Common Core
domain focus for their grade level
Materials:
 Mathematics Transition Document
for their grade level
 Arizona version Common Core
State Standards for grade
level/band
 Three Year Transition Plan for
CCSS- Mathematics (Domain
Implementation Plan)
Cognitive Complexity and the Standards for Mathematical Practices
Slides 9-22
20 min
Mathematical Tasks that model the Standards for Mathematical
Practice
Materials:
ESSENTIAL
Have participants complete two tasks:

Martha’s Carpeting Task

The Fencing Task
Handout Martha’s Carpeting and Fencing
Tasks
Compare how you would solve the problems.
Participant share solution strategies (if time allows)
Comparing Two Mathematical Tasks
 How are the two tasks the same and how are they different?
Review levels of Cognitive Complexity
5 minutes
ESSENTIAL
Refer to the Carpeting and Fencing Tasks-What are their levels of
cognitive complexity? (Martha’s Carpet Level 1 maybe Level 2
depending on grade level 3-5; Fencing Problem Level 3-4 )
Slides 23-27 Materials:
 Levels of Cognitive Complexity –
Depth of Knowledge(Webb)
2
Professional Development Plan – CCSS-M Step 3 Facilitator’s Guide
60 Minutes
RECOMMENDED
Sorting Activity:
Introduction Setup: Creating, selecting and/or modifying
mathematical tasks is an integral part of a teacher’s work, regardless
of the curriculum. All tasks are not created equal!
Activity:
Use cognitive complexity levels handout to sort tasks.
What criteria do you use to categorize the tasks? What features of
the task do we notice? (Especially difference between 2’s & 3’s)



Does a task presented as a word problem always have a high
level of cognitive demand?
Does using a manipulative indicate a higher level of cognitive
demand?
If a task requires on explanation, does it have a high level of
cognitive demand?
As groups finish sorting, have them record their decisions on a
“master” copy to share group results under the document camera.
Begin with a task that the majority of the groups designated as low
level. Move on to consider other low level tasks, adding and
clarifying the criteria used for sorting as needed (and as possible).
Slides 28- 30
Materials:
 MS Task Cards (1 set per table
group)
 Categorizing Tasks and Scenario
Worksheet one per person
 Categorizing Tasks and Scenario
Worksheet one for a master copy
for total class tallying
To purchase elementary and high school
task materials:
“Perspectives on the Teaching of Mathematics”
copyright 2004 by the National Council of
Teachers of Mathematics. (elementary and HS
tasks are found in this publication)
http://www.nctm.org/catalog/product.aspx?ID
=12709
Note to facilitator:
Answers to Task Sort and Fencing Scenario
Key is on same document – can either
handout after Fencing Scenario activity or
just show under document camera.
Repeat this share/record process for the tasks participants generally
categorized as high level.
Note: Be certain to help participants notice
the distinction and possible
confusion of high math content vs.
high cognitive complexity.
3
Professional Development Plan – CCSS-M Step 3 Facilitator’s Guide
Changing the Cognitive Level of Tasks – Modify task to increase
level:
~ 5 minutes: Each team member picks out a task that was placed in
level 1 or 2. Individually determine how you would modify
your task to be a level 3 task.
~ 5 minutes: Share out with your team & determine which task you
will share with the entire group.
~ 5 minutes: Share out entire group
Which levels of cognitive complexity lead to encouraging the
standards for mathematical practice?
Slides 31-33
15 minutes
ESSENTIAL
What levels of cognitive complexity are in your instructional
materials?
Activity:
Give participants time to review several problems (tasks) from their
instructional materials and determine levels of complexity
Have participants share out at their table.
 What are the prevalent levels of complexity in your
instructional materials?
Whole group share out
Notes:
 Could have participants look for
samples of problems for each
cognitive level in their instructional
materials.
 Sharing after each level.
Optional Examples to determine cognitive
complexity whole group: Math Connects
and Holt see slides 38-42, currently hidden
NOTE: Cognitive complexity can vary based on grade level and opinion. The level
designation is not critical-it is the conversation about the level that is of most
importance.
20 Minutes
Implementing the Common Core Standards through the
Mathematical Practices in the Classroom
ESSENTIAL
Who is doing the thinking?
Slide 34 - 36
See Resource File with links and materials
Turning the responsibility for learning over to the students
(scaffolding awareness)
4
Professional Development Plan – CCSS-M Step 3 Facilitator’s Guide
Dan Meyer Video
Debrief Questions
 How much is too much support, how much is too little?
 How does scaffolding interfere/promote the standards for
mathematical practice?
 How can you apply this to your grade level?
Video Resources
Gas Mileage Activity (without scaffold)
Slide 37
Written Tasks
 Gas Mileage Activity (with and
without scaffolding): Dana Center
http://www.utdanacenter.org/mat
htoolkit/downloads/alg1assess/alg
1_gas.pdf
10 Minutes
ESSENTIAL
Debrief the gas mileage task:
 Compare and contrast the standards for mathematical
practices involved in the scaffold and un-scaffold lesson
 Why is this type of lesson is necessary to be able to allow
students to use the standards for mathematical practice
from the CCSS-M?

Ted Talk: Dan Meyer (12 min) (all
grade levels)
http://blog.ted.com/2010/05/13/
math_class_need/
Optional Articles:
 Teaching Children Mathematics
(elementary grades)
http://www.nctm.org/publications
/article.aspx?id=22158
 Article: Orchestrating Discussionsthe Five Practices (having valuable
discussions with students)
 Never say anything a Kid Can Say?
10 Minutes
Changing the Cognitive Complexity of a task and embedding
application of the mathematical practices
ESSENTIAL
Note – will not need to do if this was done as part of
“recommended” sorting activity earlier
See slides 38-42 with examples from Holt
and Math Connects if you want to practice
whole group.
Note:
Take a text book examples: Task has to be
in critical focus area and fairly easy to
make a subtle shift for the instructional
materials used by your audience
5
Professional Development Plan – CCSS-M Step 3 Facilitator’s Guide
Implementing the Common Core Standards and Mathematical
Practices using your Classroom Instructional Materials
20 Minutes
ESSENTIAL
20 Minutes
RECOMMENDED
Work on the identified Critical Focus area
 Identify standard (within their domain) in your instructional
materials. Find a task in your instructional materials to
practice adjusting-making subtle shifts
 Take a text book-look for an example in their materials and
use it as an example to think about how to adjust the
activity-opening up a task and taking out some of the
scaffolding
 Practice Subtle Adjustments
o Participants take the example task and work in small
groups to make an adjustment to the task
o Participants share out their changes
o How to use a task to address Mathematical
Practices? Which mathematical practices are used to
complete the task?
Activity:
Impact of Teachers: Changing Cognitive Level of Tasks via Teacher
Moves (Hand out Scenarios)
Read case studies of how Fencing Task was used in
four different classrooms. Use worksheet to write
thoughts regarding changes to cognitive level of
activity, if any.
Discussion:
Which teachers(s) helped maintain the cognitive level of the task in
their classroom? Evidence to support your answer?
Which did not? Evidence to support your answer?
Slide 43
Slide 44
Materials:
 Set of scenarios per every 3 to 4
participants
 Categorizing Tasks and Scenario
Worksheet from earlier
Note to facilitator:
Answers to Scenario teacher moves is
found in Stein Scenarios & MS Task Sort
(pdf) – a document of these answers was
created – can make a handout or just show
results on document camera.
Make sure to discuss how questions and
feedback affected cognitive complexity
6
Professional Development Plan – CCSS-M Step 3 Facilitator’s Guide
30 minutes
ESSENTIAL
Brainstorm…….What instructional strategies develop the Standards
for Mathematical Practice?
How to enhance what you already have
 Questioning strategies
 Cognitive complexity of tasks
 Shifts in Classroom Practice
Objectives Revisited
Wrap up – facilitator discussion
Evaluations – two of them
Clock Hours??
Slides 45-47
Hand outs:
PBS questions sheet
Shifts in Classroom practice
Final Reflection
Readiness to Implement Survey
Participants need to bring:
 Instructional materials that relate to domain, as identified in the Three Year Transition Plan for Mathematics
o Grade K Counting and Cardinality (CC); Operations and Algebraic Thinking (OA)
o Grade 1 Operations and Algebraic Thinking (OA); Number and Operations Base Ten (NBT)
o Grade 2 Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT)
o Grade 3 Number and Operations-Fractions (NF)
o Grade 4 Number and Operations-Fractions (NF)
o Grade 5 Number and Operations-Fractions (NF)
o Grade 6 Ratio and Proportion Relationships (RP)
o Grade 7 Ratio and Proportion Relationships (RP)
o Grade 8 Expressions and Equations (EE)
o Algebra 1 Unit 2 Linear and Exponential Relationships
o Geometry Unit 1: Congruence, Proof and Constructions and
Unit 4: Connecting Algebra and Geometry through Coordinates
 Mathematics Transition Documents plan for the grade level
 Arizona version of CCSS for their grade level
 Common Core State Standards for grade level/band (opt)
7