```Standards Academy
Day 1
Objectives
• Understand the Critical Areas of our grade
levels.
• Examine the importance of vertical
• What is conceptual understanding?
• Cognitive Rigor Matrix
Who are we?
•
•
•
•
•
Name
School
District
Years spent teaching 3rd or 4th grade
– Keeping those previously mentioned in mind
Norms
Things we all need in order for our time
together to be productive……….
1. .
2. ..
3. …
4. ….
Vertical Alignment
Vertical Alignment
1. Form six groups.
a)
b)
c)
d)
e)
f)
Operations and Algebraic Thinking Grade 3
Operations and Algebraic Thinking Grade 4
Operations and Algebraic Thinking Grade 5
Number and Operation Fractions Grade 3
Number and Operations Fractions Grade 4
Number and Operations Fractions Grade 5
core and discuss it with your group to solidify
3. Re-group so that you are now composed of 3
members one from each grade level.
a)
b)
3, 4, 5 Numbers and Algebraic thinking
3, 4, 5 Numbers and Operations Fractions
5. Combine groups of three, still working within your
domain but you should now have 6 members with
notes.
6. Create a poster displaying the vertical alignment
Reflection
2. If so, why?
3. If not, what would have been more
4. How will this activity change your
teaching next year?
Critical
Areas
Critical Area Graphic
Organizer
• Identify at least one or two important mathematical
concepts within this critical area. What do students
need to learn prior to these concepts?
• What evidence would convince you that a student
understands these concepts?
• What common misconceptions do students have
when studying this critical area? What challenges
have you had in teaching these concepts?
• How do these concepts support learning in later
Reflection
• How do the critical areas help bring focus to the
• How will you use the critical areas to inform your
• What questions do you still have about the
critical areas?
• How has this activity increased your
understanding of the instructional core?
Conceptual
Understanding
What does understand really mean?
1.
2.
3.
4.
5.
6.
7.
8.
Form groups of 5-6 and sit together at a table.
The group discusses the question prompt until time is called
The leader’s role is to record the major points of the conversation that
take place at the table and to then summarize the conversation using
the recorded notes just before rotating to the next table.
The leader stays put; the rest of the group rotates to the next table.
The leader (the one who didn’t move) presents a summary of the
conversation recorded from the former group to the new group.
The new group discusses the new question prompt until time is called.
Again the leader takes notes and summarizes.
Round 1
Discuss the following:
The word "understanding" is used frequently
throughout the document. What do you
think it means and why is it important in a
child's ability to learn math concepts?
Round 2
Reflect on the quote:
"A significant indicator of conceptual
understanding is being able to represent
mathematical situations in different ways,
knowing how different representations can be
useful for different purposes."
Explain why you think it's important for a child
to be familiar with more than one way to solve
a problem.
Round 3
Discuss the following:
How can a teacher help students make
connections between concepts and
representations?
DOK & Cognitive Rigor
1. Develop a shared understanding of the
Cognitive Rigor Matrix.
2. Use the Cognitive Rigor Matrix to:
• Consider rigor expectations in the Common Core
• Examine learning expectations and critical thinking
• Evaluate sample assessments/tasks & rubrics
Before we begin…
Take a couple of minutes to write
“cognitive rigor” as it relates to
instruction, learning, and/or
assessment.
definition
fractions with like denominators.
• What is a basic computational question you might
• What is a more rigorous question you might ask?
Hess Article
Annotate:
• ? On parts of the article that need clarification
• ! For any “ahas” as you read
• Underline or highlight any key terms or
vocabulary
• * next to any key/main ideas from the article
The Hess Cognitive
Rigor Matrix: Integrates
Bloom’s & Webb’s
Blooms Taxonomy
What type of thinking
(verbs) is needed to
Webb’s Depth of
Knowledge
How deeply do you have to
understand the content to
successfully interact with it?
How complex is the
content?
Blooms Taxonomy
Draw
Identify
Define
List
Memorize
Calculate
Illustrate
Who, What, When, Where, Why
Arrange
Design
Tabulate
Repeat
Recall
Connect
Level
Four
Apply Concepts
(Extended
Thinking)
Critique
Analyze
Create
Match
Recognize
Prove
Categorize
Use
Infer
Level One
(Recall)
Synthesize
Webb’s
Depth of
Knowledge
Measure
Name
Graph
Organize
Classify
Describe
Explain
Interpret
Level Two
(Skill/
Concept)
Level Three
(Strategic Thinking)
Modify
Cause/Effect
Relate
Predict
Compare
Interpret
Estimate
Revise
Assess
Summarize
Develop a Logical Argument
Critique
Use Concepts to Solve
Non-Routine Problems
Apprise
Formulate
Investigate
Draw Conclusions
Hypothesize
Construct
Compare
Explain
Differentiate
Show
Webb’s Depth-of-Knowledge
Levels
• DOK 1- Recall & Reproduction-Recall a fact, term, principle,
concept, or perform a routine procedure.
• DOK 2- Basic Application of Skills/Concepts-Use of information,
conceptual knowledge, select appropriate procedures for a task, two
or more steps with decision points along the way, routine problems,
organize/display data, interpret/use simple graphs.
• DOK 3- Strategic Thinking-Requires reasoning, developing a plan
or sequence of steps to approach problem; requires some decision
making and justification; abstract, complex, or non-routine; often
more than one possible answer or approach.
• DOK 4- Extended Thinking-An original investigation or application
to real word; requires time to research, problem solve, and process
multiple conditions of the problem or task; non-routine
manipulations, across disciplines/content area/multiple sources.
difficulty!
The intended student learning outcome determines
the DOK level. What mental processing must occur?
While verbs may appear to point to a DOK level, it is
what comes after the verb that is the best indicator of
the rigor/DOK level.
Let’s see some examples…
It’s what after the verb…
• Describe how two characters are alike and different.
• Describe the information contained in graphics or
data tables in the text; or the rule for rounding of a
number
• Describe the data or text evidence that supports
• Describe varying perspectives on global climate
change using supporting scientific evidence, and
identify the most significant effects it might have on
the planet in 100 years
DOK 1
Recall and Reproduction
DOK 2
Recall, locate basic
facts, definitions,
details, events
Remember
Understand
Apply
Select appropriate
words for use when
intended meaning is
clearly evident.
Explain relationships
Summarize
State central idea
Use language
structure, word
relationships
to determine meaning
Analyze
Use context for word
meanings
Use information using
text features
Identify the kind of
information contained
in a graphic, table,
visual, etc.
Compare literary elements,
facts, terms and events
Analyze format,
organization and text
structures
DOK 4
Reasoning and
Thinking
Extended Thinking
-Explain how concepts
or ideas specifically
relate to other content
domains.
Explain, generalize or
connect ideas using
supporting evidence
(quote, text, evidence)
Devise an approach
among many
alternatives to
research a novel
problem
Use concepts to solve
non-routine problems
and justify
Analyze or interpret
author’s craft (e.g.,
literary devices,
viewpoint, or potential
bias) to critique a text
Analyze multiple
sources or multiple
text. Analyze
complex abstract
themes
Evaluate relevancy,
accuracy and
completeness of
information across
texts or sources
Cite evidence and develop a
logical argument for
conjectures based on one
text or problem
Evaluate
Create
DOK 3
Skills and
Concepts
-Brainstorm ideas,
concepts, problems,
or perspectives
related to a topic or
concept.
Selected Response
Generate conjectures
or hypotheses based
on observations or
prior knowledge
Constructed
Response
Develop a complex model or
approach for a given
situation
Develop an alternative
solution
Synthesize across
multiple sources/ texts
Articulate a new voice,
theme, or perspective
Performance
What DOK Level?
What DOK Level?
What DOK Level?
What DOK Level?
What DOK Level?
Find the next three terms in the pattern
and determine the rule for the
following pattern of numbers:
1, 4, 8, 11, 15, 18, 22, 25, 29, …
Revised Bloom’s
Taxonomy
Remember
Retrieve knowledge from longterm memory, recognize, recall,
locate, identify
Understand
Construct meaning, clarify,
paraphrase, represent, translate,
illustrate, give examples, classify,
categorize, summarize,
generalize, infer logical
conclusion (such as from
examples given), predict,
compare/contrast, match like
ideas, explain, construct models
Apply
Carry out or use a procedure in
a given situation; carry out
(apply to a familiar task), or use
DOK with Multiplication
Webb’s DOK Level 1
Recall & Reproduction
Webb’s DOK Level 2
Skills & Concepts
Draw a model to
represent the problem
5x3
Estimate a reasonable
23 x 8. Explain how you
why it is reasonable.
Find the area of this
shape.
Write a multiplication
statement comparing
brown eyes to blue.
Analyze
Break into constituent parts,
determine how parts relate,
differentiate between relevantirrelevant, distinguish, focus,
select, organize, outline, find,
coherence, deconstruct
Evaluate
Make judgments based on
criteria, check, detect,
inconsistencies or fallacies,
judge, critique
Create
Reorganize elements into new
patterns/structures, generate,
hypothesize, design, plan,
construct, produce
Webb’s DOK Level 3
Strategic Thinking/Reasoning
Compare the 2 strategies used. Explain
the process each student used and
explain who has the correct
Create a table displaying all
the factors of 48.
Webb’s DOK Level 4
Extended Thinking
Can the distributive
property be used with
division? Justify your
conclusions with data
generated from your
investigation.
A
Construct an area model
for the polygon from the
table
with
the
largest
area.
D
Describe
the trend
displayed
in the
data table
to a multiplication
problem called?
B
C
E
Make a conclusion based on
the data presented, use
mathematical relationships
F
DOK
Question
Stems
Questions
3.G.1-2
or
4.G.1-3
Wrap Up & Reflect
Questions or Concerns……..
Complete a 4 point evaluation:
•
•
•
•
What went well today?
What could be improved?
What do you need more support in?
What did you master?
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