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Standards Academy. Grades 3 and 4 Day 1. Objectives. Understand the Critical Areas of our grade levels. Examine the importance of vertical alignment across our grade levels. What is conceptual understanding? Cognitive Rigor Matrix. Who are we?. Name School District - PowerPoint PPT PresentationTRANSCRIPT
Standards Academy
Grades 3 and 4Day 1
Objectives• Understand the Critical Areas of our
grade levels.• Examine the importance of vertical
alignment across our grade levels.• What is conceptual understanding?• Cognitive Rigor Matrix
Who are we?• Name• School• District• Years spent teaching 3rd or 4th grade• Your objective(s)– Keeping those previously mentioned in
mind
NormsThings we all need in order for our time together to be productive……….1. .2. ..3. …4. ….
Vertical Alignment
Vertical Alignment1. Form six groups.
a) Operations and Algebraic Thinking Grade 3b) Operations and Algebraic Thinking Grade 4c) Operations and Algebraic Thinking Grade 5d) Number and Operation Fractions Grade 3e) Number and Operations Fractions Grade 4f) Number and Operations Fractions Grade 5
2. Spend 10 minutes reading your portion of the core and discuss it with your group to solidify your understanding.
3. Re-group so that you are now composed of 3 members one from each grade level.
a) 3, 4, 5 Numbers and Algebraic thinking b) 3, 4, 5 Numbers and Operations Fractions
4. Discuss the big ideas from your grade level reading and take notes.
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 for grades 3, 4, & 5 within your domain.
Reflection1. Was this activity helpful for you? 2. If so, why? 3. If not, what would have been more
helpful? 4. How will this activity change your
teaching next year?
Critical Areas
Major work of 3rd Grade
Major work of 4th Grade
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 grades?
Reflection• How do the critical areas help bring focus to the
standards at your grade level?• How will you use the critical areas to inform your
curriculum and guide your instruction?• 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. Read the excerpt from Adding it Up.2. Form groups of 5-6 and sit together at a table.3. The group discusses the question prompt until time is called4. 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.
5. The leader stays put; the rest of the group rotates to the next table.6. The leader (the one who didn’t move) presents a summary of the
conversation recorded from the former group to the new group.7. The new group discusses the new question prompt until time is called.8. 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 2Reflect 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 3Discuss 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 your personal definition of “cognitive rigor” as it
relates to instruction, learning, and/or assessment.
Let’s apply your rigor definition
Your class is studying addition of fractions with like denominators.
• What is a basic computational question you might ask?
• What is a more rigorous question you might ask?
Hess ArticleAnnotate:• ? 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’sBlooms Taxonomy
What type of thinking (verbs) is needed to
complete a task?
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
Webb’sDepth ofKnowledge
Describe Explain
Interpret
Level One(Recall)
Level Three(Strategic Thinking)
(Extended Thinking)
Level Two(Skill/
Concept)
Design
Synthesize
Connect
Apply Concepts
Critique
Analyze
Create
Prove
Arrange
Calculate
Draw
Repeat Tabulate
Recognize
Memorize
Identify
Who, What, When, Where, Why
List
Name
Use
Illustrate
Measure
Define
RecallMatch
Graph
Classify
Cause/Effect
Estimate
Compare
Relate
Infer
Categorize
Organize
Interpret
Predict
Modify
Summarize
ShowConstruct
Develop a Logical ArgumentAssessRevise
Apprise
Hypothesize
InvestigateCritique
Compare
Formulate Draw ConclusionsExplain
Differentiate
Use Concepts to SolveNon-Routine Problems
Level Four
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.
DOK is about complexity—not 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 your solution, reasoning, or conclusions
• 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
Recall, locate basic facts, definitions, details, events
Select appropriate words for use when intended meaning is clearly evident.
DOK 1Recall and Reproduction
Remember
Understand
DOK 2Skills and Concepts
ApplyUse language structure, word relationships to determine meaning
Explain relationshipsSummarizeState central idea
Use context for word meaningsUse information using text features
DOK 3Reasoning and
Thinking
Analyze
Analyze or interpret author’s craft (e.g., literary devices, viewpoint, or potential bias) to critique a text
Explain, generalize or connect ideas using supporting evidence (quote, text, evidence)
Compare literary elements, facts, terms and eventsAnalyze format, organization and text structures
Identify the kind of information contained in a graphic, table, visual, etc.
Cite evidence and develop a logical argument for conjectures based on one text or problem
Evaluate
Use concepts to solve non-routine problems and justify
DOK 4Extended Thinking
Synthesize across multiple sources/ textsArticulate a new voice, theme, or perspective
Evaluate relevancy, accuracy and completeness of information across texts or sources
Analyze multiple sources or multiple text. Analyze complex abstract themes
Devise an approach among many alternatives to research a novel problem
-Explain how concepts or ideas specifically relate to other content domains.
Develop a complex model or approach for a given situationDevelop an alternative solution
Generate conjectures or hypotheses based on observations or prior knowledge
-Brainstorm ideas, concepts, problems, or perspectives related to a topic or concept.
Create
Selected Response Constructed Response
Performance Tasks
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, …
DOK with MultiplicationRevised Bloom’s
TaxonomyWebb’s DOK Level 1
Recall & ReproductionWebb’s DOK Level 2
Skills & ConceptsWebb’s DOK Level 3
Strategic Thinking/Reasoning
Webb’s DOK Level 4Extended Thinking
RememberRetrieve knowledge from long-term memory, recognize, recall, locate, identify
UnderstandConstruct 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
Draw a model to represent the problem
5 x 3
Estimate a reasonable answer for the problem 23 x 8. Explain how you made your estimate and
why it is reasonable.
ApplyCarry out or use a procedure in a given situation; carry out (apply to a familiar task), or use (apply) to an unfamiliar task
Find the area of this shape.
AnalyzeBreak into constituent parts, determine how parts relate, differentiate between relevant-irrelevant, distinguish, focus, select, organize, outline, find, coherence, deconstruct
Write a multiplication statement comparing brown eyes to blue.
EvaluateMake judgments based on criteria, check, detect, inconsistencies or fallacies, judge, critique
Compare the 2 strategies used. Explain the process each student used and explain who has the correct answer and why.
CreateReorganize elements into new patterns/structures, generate, hypothesize, design, plan, construct, produce
Create a table displaying all
the factors of 48.
D F
Can the distributive property be used with division? Justify your conclusions with data generated from your
investigation.
A B C
Describe the trend displayed in the data table
What is the answer to a multiplication problem called?
Construct an area model for the polygon from the table with the largestarea. Make a conclusion based on
the data presented, use mathematical relationships
to justify your response.
E
DOK Question Stems
Create Your Own DOK Questions
In your tables, create your own DOK grid for:
3.G.1-2or
4.G.1-3
Wrap Up & ReflectQuestions 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?