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’s

Blooms TaxonomyWhat 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 Argument

AssessRevise

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 ResponseConstructed 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?