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 Years spent teaching 3 rd or 4 th grade Your objective(s) –Keeping those previously mentioned in mind

Norms Things we all need in order for our time together to be productive……… … 4.….

Vertical Alignment

1.Form six groups. a)Operations and Algebraic Thinking Grade 3 b)Operations and Algebraic Thinking Grade 4 c)Operations and Algebraic Thinking Grade 5 d)Number and Operation Fractions Grade 3 e)Number and Operations Fractions Grade 4 f)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.

Reflection 1.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 3 rd Grade

Major work of 4 th 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 called 4.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 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 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 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 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’s Depth of Knowledge 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 Recall Match Graph Classify Cause/Effect Estimate Compare Relate Infer Categorize Organize Interpret Predict Modify Summarize Show Construct Develop a Logical Argument AssessRevise Apprise Hypothesize Investigate Critique Compare Formulate Draw Conclusions Explain Differentiate Use Concepts to Solve Non-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 1 Recall and Reproduction Remember Understand DOK 2 Skills and Concepts Apply Use language structure, word relationships to determine meaning Explain relationships Summarize State central idea Use context for word meanings Use information using text features DOK 3 Reasoning 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 events Analyze 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 4 Extended Thinking Synthesize across multiple sources/ texts Articulate 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 situation Develop 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?

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 Multiplication Revised Bloom’s Taxonomy Webb’s DOK Level 1 Recall & Reproduction Webb’s DOK Level 2 Skills & Concepts Webb’s DOK Level 3 Strategic Thinking/Reasoning Webb’s DOK Level 4 Extended Thinking Remember Retrieve knowledge from long- term 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 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. Apply Carry 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. Analyze Break 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. Evaluate Make 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. Create Reorganize elements into new patterns/structures, generate, hypothesize, design, plan, construct, produce Create a table displaying all the factors of 48.

D D F F Can the distributive property be used with division? Justify your conclusions with data generated from your investigation. A A B B C 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 largest area. Make a conclusion based on the data presented, use mathematical relationships to justify your response. E E

DOK Question Stems

Create Your Own DOK Questions In your tables, create your own DOK grid for: 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?