Transcript across grade coherence in grades 3-5

Across Grade Coherence and
Instructional Practice in Grades 3-5
February 2017
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ACROSS GRADE COHERENCE IN GRADES 3-5
Welcome Back!
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ACROSS GRADE COHERENCE IN GRADES 3-5
Thank You for Your Feedback!
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ACROSS GRADE COHERENCE IN GRADES 3-5
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 in which it is “safe to not know”
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ACROSS GRADE COHERENCE IN GRADES 3-5
This Week
Day
Ideas
Monday
Focus and Within Grade Coherence
Tuesday
Wednesday
Rigor and the Mathematical
Practices
Across Grade Coherence and
Instructional Practice
Thursday
Adaptation and Curriculum Study
Friday
Adaptation and Practice
“Do the
math”
Connect
to our
practice
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ACROSS GRADE COHERENCE IN GRADES 3-5
Today
• Morning: Across Grade Coherence in Grades 3-5
• Afternoon: Instructional Practice in Grades 3-5
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ACROSS GRADE COHERENCE IN GRADES 3-5
Morning Objectives
• Participants will understand and apply learning progressions to support
students who are below grade level.
o Participants will be able to identify a sequence of prerequisite
standards necessary in math understanding and learning.
o Participants will be able to identify onramps for teaching major work
to students who are below grade level.
o Participants will be able to adapt a lesson for students below grade
level by adding just-in-time scaffolds based on learning
progressions.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Morning Agenda
I.
Across Grade Coherence
II.
Vertical Coherence Challenge
III.
Mapping the Progressions
IV.
Tools for Understanding the Progressions
V.
Adapting Lessons for Students Below Grade Level
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ACROSS GRADE COHERENCE IN GRADES 3-5
Across Grade Coherence
2
3
4
6
How would a student explain why is equal to ?
4 2 2 2
= × = ×1
6 3 2 3
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ACROSS GRADE COHERENCE IN GRADES 3-5
What Is the Right Order?
Grade 4
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using
visual fraction models, with attention to how the number and size of the
parts differ even though the two fractions themselves are the same size.
Grade 3
Understand two fractions as equivalent (equal) if they are the same size, or
the same point on a number line.
Grade 5
Interpret multiplication as scaling (resizing) by…relating the principle of
fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by
1.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Coherence Is Key
“A focused, coherent progression of mathematics learning, with an
emphasis on proficiency with key topics, should become the norm in
elementary and middle school mathematics curricula. Any approach that
continually revisits topics year after year without closure is to be avoided. By
the term focused, the Panel means that curriculum must include (and engage
with adequate depth) the most important topics underlying success in school
algebra. By the term coherent, the Panel means that the curriculum is
marked by effective, logical progressions from earlier, less sophisticated
topics into later, more sophisticated ones. Improvements like those
suggested in this report promise immediate positive results with minimal
additional cost.”
- National Mathematics Advisory Panel
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ACROSS GRADE COHERENCE IN GRADES 3-5
The Progressions
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Across Grade Coherence:
Learning is carefully
connected across grades
so that students can build
new understanding onto
foundations built in
previous years.
ACROSS GRADE COHERENCE IN GRADES 3-5
Vertical Coherence Challenge
• In your groups, you have 11 standards on pieces of paper. Most standards
come from the Number & Operations—Fractions domains in Grades 3-5.
• The standards are not labeled!
• Determine which standards are prerequisites for other standards.
• Bonus: Can you determine which standards belong in which grade?
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ACROSS GRADE COHERENCE IN GRADES 3-5
A Picture of Coherence
Grade 2
Grade 3
2.G.A.3
3.NF.A.1
A
D
3.NF.A.3
2.MD.B.6
3.NF.A.2
K
F
G
Grade 4
Grade 5
4.NF.A.1
4.NF.A.2
5.NF.A.1
5.NF.A.2
I
E
C
H
4.NF.B.3
4.NF.C.5
B
J
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ACROSS GRADE COHERENCE IN GRADES 3-5
Progressions of Content
How does understanding
the progression of content
support our understanding
of grade-level content?
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ACROSS GRADE COHERENCE IN GRADES 3-5
Standards Mapping
Protocol:
• Identify 3 prerequisite standards – the
standards do not have to be in 3
different grades.
• Identify the aspects of rigor for each
prerequisite.
• Discuss with a partner:
1. How does each prerequisite
support the standard?
2. Why is it important to pay
attention to the rigor of the
prerequisite standard?
The Standards:
Grade 3 – 3.OA.A.2
Grade 4 – 4.OA.A.3
Grade 5 – 5.NBT.B.7
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ACROSS GRADE COHERENCE IN GRADES 3-5
Grade 3 – 3.OA.A.2
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as
the number of objects in each share when 56 objects are partitioned equally
into 8 shares, or as a number of shares when 56 objects are partitioned into
equal shares of 8 objects each. For example, describe a context in which a
number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.A.1
2.OA.C.4
1.OA.D.7
Interpret products of
whole numbers, e.g.,
interpret 5 X 7
as the total number of
objects in 5 groups of
7 objects each.
Use addition to find
the total number of
objects arranged in
rectangular arrays
with up to 5 rows and
up to 5 columns; write
an equation to express
the total as a sum of
equal addends.
Understand the meaning
of the equal sign, and
determine if equations
involving addition and
subtraction are true or
false.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Grade 4 – 4.OA.A.3
Solve multi-step word problems posed with whole numbers and having
whole-number answers using the four operations, including problems in
which remainders must be interpreted. Represent these problems using
equations with a letter standing for the unknown quantity. Assess the
reasonableness of answers using mental computation and estimation
strategies including rounding.
4.OA.A.2
3.OA.D.8
2.OA.A.1
Multiply or divide to solve
word problems involving
multiplicative comparison,
e.g., by using drawings and
equations with a symbol for
the unknown number to
represent the problem,
distinguishing multiplicative
comparison from additive
comparison.
Solve two-step word
problems using the four
operations. Represent these
problems using equations
with a letter standing for the
unknown quantity. Assess the
reasonableness of answers
using mental computation
and estimation strategies
including rounding.
Use addition and subtraction within
100 to solve one- and
two-step word problems involving
situations of adding to, taking
from, putting together, taking apart,
and comparing, with unknowns in
all positions, e.g., by using
drawings and equations
with a symbol for the unknown
number to represent the problem.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Grade 5 – 5.NBT.B.7
Add, subtract, multiply, and divide decimals to hundredths, using concrete
models or drawings and strategies based on place value, properties of
operations, and/or the relationship between addition and subtraction; relate
the strategy to a written method and explain the reasoning used.
4.NBT.A.1
4.NBT.B.4
4.NBT.B.5
Recognize that in a
multi-digit whole
number, a digit in one
place represents ten
times what it
represents in the place
to its right. For
example, recognize
that 700 ÷ 70 = 10 by
applying concepts of
place value and
division.
Fluently add and
subtract multi-digit
whole numbers using
the standard algorithm.
Multiply a whole number
of up to four digits by a
one-digit whole number,
and multiply two two-digit
numbers, using strategies
based on place value and
the properties of
operations. Illustrate and
explain the calculation by
using equations,
rectangular arrays, and/or
area models.
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Break
ACROSS GRADE COHERENCE IN GRADES 3-5
Understanding the Progressions
Content Guides
The Progressions Documents
Wiring Diagram
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ACROSS GRADE COHERENCE IN GRADES 3-5
Understanding the Progressions
How does understanding the progressions support instruction?
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How can we leverage
Leveraging the Progressions
progressions of content to
give students access to
grade-level content?
ACROSS GRADE COHERENCE IN GRADES K-2
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ACROSS GRADE COHERENCE IN GRADES 3-5
Adapting Lessons for Students Below
Grade Level
Protocol:
• Review Lesson 1 and identify the targeted standard.
• Identify the prerequisite standards from prior grades that support the
targeted standard.
o What is the aspect of rigor for each prerequisite?
• Discuss with a partner:
1. How does each prerequisite support the standard?
2. How could you strategically use these prerequisite standards to
support students who are not on grade level?
o Annotate the lesson with specific supports.
• With your table:
o Each pair shares out the specific adaptations you and your
partner made. Explain why you made these adaptations.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Lesson Adaptations
What types of adaptations could you consider at the lesson level?
• Add a warm-up activity that
connects to prior learning.
• Add a section to the concept development
portion to address prerequisite skills.
• Replace one or more of the fluency
activities to support understanding of
prerequisites.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Adapting Lessons for Students Below
Grade Level
Protocol:
• 10 min: Individual
work time
• 15 min: Partner
work
• 10 min: Table share
out
Goals for This Activity:
I. Review Lesson 1 and identify
the targeted standard(s).
II. What are the prerequisite
standards from prior grades
that support this standard(s)?
III. What aspects of rigor are
highlighted in the prerequisite
standards?
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Transition
Transitionto
toPartner
PartnerTime!
Time!
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ACROSS GRADE COHERENCE IN GRADES 3-5
Adapting Lessons for Students Below
Grade Level
Goals for This Activity:
Protocol:
• 10 min: Individual
work time
• 15 min: Partner
work
• 10 min: Table share
out
I.
II.
How do these prerequisite
standards support the grade-level
standard(s)?
How could you strategically use
these prerequisite standards to
support students who are not on
grade level?
o
Annotate the lesson with
specific supports.
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Transition to Table Share!
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ACROSS GRADE COHERENCE IN GRADES 3-5
Adapting Lessons for Students Below
Grade Level
Protocol:
• 10 min: Individual
work time
• 15 min: Partner
work
• 10 min: Table share
out
Goals for This Activity:
o Each pair shares out the specific
adaptations made and explains
why these adaptations were
made.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Adapting Lessons for Students Below
Grade Level
What grade-level
standard does the
lesson address? What
is the evidence of
alignment to this
standard?
What are the
prerequisite
standards from
prior grades
that support
this standard?
Brainstorm ways you could use these
prerequisites to support students below
grade level with accessing the content of
this lesson.
• Annotate the lesson with specific
supports.
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ACROSS GRADE COHERENCE IN GRADES 3-5
Summary
•
What is the shift of coherence?
•
How does coherence help us support students below grade level?
•
How does rigor help us support students below grade level?
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ACROSS GRADE COHERENCE IN GRADES K-2
Lunch 12:00-1:00
Lunch 12:00 – 1:00
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Today
• Morning: Across Grade Coherence in Grades 3-5
• Afternoon: Instructional Practice in Grades 3-5
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Afternoon Objectives
• Participants will be able to use the Instructional Practice Guide (IPG) as a
lesson planning tool and a coaching tool.
• Participants will be able to identify where, in lessons and videos, teachers
engage in Core Actions.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Afternoon Agenda
I.
Intro to the Instructional Practice Guide (IPG).
II.
Core Actions in Action!
III.
Lesson Planning with the IPG.
IV.
Connect to Practice.
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INSTRUCTIONAL PRACTICE IN GRADES K-2
...effective teaching is the non-negotiable core that ensures that all
students learn mathematics at high levels...
Instructional Practice
- Principles to Actions: Ensuring Mathematical Success for All (NCTM)
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Instructional Practice Guide (IPG)
The Instructional Practice Guide
includes coaching and lesson
planning tools to help teachers and
those who support teachers to
make the Key Shifts in instructional
practice required by the Common
Core State Standards (CCSS).
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Core Actions
1.
Ensure the work of the lesson reflects the Shifts required by the CCSS for
Mathematics.
2.
Employ instructional practices that allow all students to learn the
content of the lesson.
3.
Provide all students with opportunities to exhibit mathematical practices
while engaging with the content of the lesson.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Core Action 1
Ensure the work of the lesson reflects the Shifts required by the CCSS for
Mathematics.
Indicators
A. The lesson focuses on the depth of grade-level cluster(s), grade-level
content standard(s), or part(s) thereof.
B.
The lesson intentionally relates new concepts to students’ prior skills
and knowledge.
C.
The lesson intentionally targets the aspect(s) of rigor (conceptual
understanding, procedural skill and fluency, application) called for by
the standard(s) being addressed.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Core Action 2
Employ instructional practices that allow all students to learn the content
of the lesson.
Indicators
A. The teacher makes the mathematics of the lesson explicit by using
explanations, representations, and/or examples.
B. The teacher provides opportunities for students to work with and
practice grade-level problems and exercises.
C. The teacher strengthens all students’ understanding of the content by
sharing a variety of students’ representations and solution methods.
D. The teacher deliberately checks for understanding throughout the
lesson and adapts the lesson according to student understanding.
E. The teacher summarizes the mathematics with references to student
work and discussion in order to reinforce the focus of the lesson.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Core Action 3
Provide all students with opportunities to exhibit mathematical practices
while engaging with the content of the lesson.
Indicators
A. The teacher poses high-quality questions and problems that prompt students to
share their developing thinking about the content of the lesson. Students share
their developing thinking about the content of the lesson.
B. The teacher encourages reasoning and problem solving by posing challenging
problems that offer opportunities for productive struggle. Students persevere in
solving problems in the face of initial difficulty.
C. The teacher establishes a classroom culture in which students explain their
thinking. Students elaborate with a second sentence (spontaneously or
prompted by the teacher or another student) to explain their thinking and
connect it to their first sentence.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Core Action 3 – Indicators (cont’d)
D. The teacher creates the conditions for student conversations where students are
encouraged to talk about each other’s thinking. Students talk about and ask
questions about each other’s thinking, in order to clarify or improve their own
mathematical understanding.
E. The teacher connects and develops students’ informal language to precise
mathematical language appropriate to their grade. Students use precise
mathematical language in their explanations and discussions.
F. The teacher establishes a classroom culture in which students choose and use
appropriate tools when solving a problem. Students use appropriate tools
strategically when solving a problem.
G. The teacher asks students to explain and justify work and provides feedback that
helps students revise initial work. Student work includes revisions, especially
revised explanations and justifications.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Deeper Dive with the IPG
Small Group Protocol
•
Read the indicators of the Core Action for
your group (pp. 5-10).
•
Discuss the following with your small group:
1. How does this Core Action (including the
indicators) support teachers and
coaches in building understanding of
CCSSM-aligned instruction?
2. What are the essential teacher practices
that support the indicators?
3. What resonates with you the most
about this Core Action?
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Deeper Dive with the IPG
Table Discussion Protocol
•
Turn and teach.
•
Discuss the following with your table group:
1.
How does this tool support teachers
and coaches in building understanding
of CCSSM-aligned instruction?
2. What are essential teacher practices
that support each Core Action?
3.
Where does each of the Standards for
Mathematical Practice show up in the
IPG?
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Deeper Dive with the IPG
Whole Group Discussion Protocol
1.
2.
3.
How does this tool support teachers and
coaches in building understanding of
CCSSM-aligned instruction?
Where does each of the Standards for
Mathematical Practice show up in the IPG?
What Core Actions are you most struck by
and why?
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
IPG Summary
• Useful in both planning and coaching
• Evidence for the indicators can come from lesson materials, teacher
actions, student discussion, and student work
• When using as a coaching tool, not all indicators may be evident in a
single class period
• Not to be used as an evaluation instrument
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Core Actions in Action!
What Core
Actions are
visible?
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Break
INSTRUCTIONAL PRACTICE IN GRADES 3-5
Lesson Planning with the IPG
How can we use the Core
Actions and indicators?
• Planning
• Evaluating
• Reflecting
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Lesson Planning
The Core Actions should be evident in planning and observable in
instruction.
•
•
What parts of the lesson plan are vital to show evidence of Core Action
1? Annotate the lesson to show these.
What are some of the things you could do to ensure alignment with the
indicators for Core Actions 2 and 3?
What to Review:
Grade 3, Module 5, Lesson 2
Grade 4, Module 5, Lesson 2
Grade 5, Module 3, Lesson 2
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Example: Grade 3, Module 5, Lesson 5
The lesson
emphasizes
conceptual
understanding, the
aspect of rigor
associated with
3.NF.A.1 (CA.1.C).
Summarize or have students
summarize what it means to
have equal parts (CA.2.E).
Follow by projecting different models to check
for understanding. Reteach as needed (CA.2.D).
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Lesson Planning
Goals for this activity:
Protocol:
• 15 min: Individual
work time
• 10 min: Small
group collaboration
• 15 min: Table share
out
1. Read the lesson.
2. Annotate the lesson for your Core
Action.
•
•
What parts of the lesson plan are
vital to show evidence of Core
Action 1?
What are some of the things you
could do to ensure alignment with
the indicators for Core Actions 2
and 3?
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Transition to Small Group Time!
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Lesson Planning
Protocol:
• 15 min: Individual
work time
• 10 min: Small
group collaboration
• 15 min: Table share
out
Goals for This Activity:
1. Share how you annotated the task
with your group.
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Transition to Table Share!
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Lesson Planning
Protocol:
• 15 min: Individual
work time
• 10 min: Small
group collaboration
• 15 min: Table share
out
Goals for This Activity:
1.
2.
Share your annotations with the people
at your table.
Discuss and record:
• What kinds of evidence supported
the indicators for CA 1?
• What kinds of actions did you add
to support CA 2?
• What kinds of actions did you add
to support CA 3?
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Lesson Planning
Protocol:
Annotate your lesson for each Core Action:
1. What is the evidence of alignment to Core Action 1? How can you
improve alignment to Core Action 1?
2. What are some of the things you could do to ensure alignment
with the indicators for Core Action 2?
3. What are some of the things you could do to ensure alignment
with the indicators for Core Action 3?
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Summary
• How will the Core Actions impact your work with creating and/or
coaching around lesson plans?
• How has your thinking changed about lesson planning?
• How have the Shifts impacted your approach to instruction?
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Feedback
Please fill out the survey located here: www.standardsinstitutes.org
• Click “Winter 2017” on the top of the page.
• Click “Details” on the center of the page.
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Reference List
Slide Source
11
Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education: Washington, DC,
2008. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf
12
http://math.arizona.edu/~ime/progressions/#
13
http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
22
http://math.arizona.edu/~ime/progressions/#
http://achievethecore.org/content/upload/ccssmgraph.pdf
http://achievethecore.org/coherence-map/
https://www.unbounded.org/enhance_instruction?subjects=math
38
Principles to Actions: Ensuring Mathematical Success for All (NCTM)
http://www.nctm.org/PtA/
39-44
http://achievethecore.org/category/1155/printable-versions
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https://www.engageny.org/resource/grade-3-mathematics-module-5-topic-b-lesson-5/file/35276
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INSTRUCTIONAL PRACTICE IN GRADES 3-5
Image References
Slide #
Name and Photographer/Artist
2
"Welcome" by Josh Meek (Flickr)
9
“Students” by Jeff Peterson (Flickr).
13
“Skyscraper” by Japanexperterna.se (Flickr)
16
“Ladder” by Angie Harms (Flickr)
21
“muumuu coffee” by Ken Yamaguchi
24
“Underground” by Sergey Kochkarev (Flickr)
28, 55
"Transitions" by Arjan Almekinders (Flickr)
30, 57
“208/365 - He's got the whole world in his hands.” by Courtney Carmody (Flickr)
34
“Lunch” by MIKI Yoshihito (Flickr)
38
“Clouds” by Alden Chadwick (Flickr)
49
“Binoculars” by Eric (Flickr)
50
“Aunty’s Almonds” by studio tdes (Flickr)
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“mirrors” by Chris (Flickr)
59
“Share” by GotCredit (Flickr)
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