Standards Academy

1. Standards Academy Grades 3 and 4 Day 1

2. 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

3. Who are we? • Name • School • District • Years spent teaching 3rd or 4thgrade • Your objective(s) • Keeping those previously mentioned in mind

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

5. Vertical Alignment

6. Vertical Alignment • Form six groups. • 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 • Spend 10 minutes reading your portion of the core and discuss it with your group to solidify your understanding.

7. Re-group so that you are now composed of 3 members one from each grade level. • 3, 4, 5 Numbers and Algebraic thinking • 3, 4, 5 Numbers and Operations Fractions • Discuss the big ideas from your grade level reading and take notes. • Combine groups of three, still working within your domain but you should now have 6 members with notes. • Create a poster displaying the vertical alignment for grades 3, 4, & 5 within your domain.

8. Reflection Was this activity helpful for you? If so, why? If not, what would have been more helpful? How will this activity change your teaching next year?

9. Critical Areas

10. Major work of 3rd Grade

11. Major work of 4th Grade

12. 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?

13. 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?

14. Conceptual Understanding What does understand really mean? Read the excerpt from Adding it Up. 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.

15. 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?

16. 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.

17. Round 3 Discuss the following: How can a teacher help students make connections between concepts and representations?

18. DOK & Cognitive Rigor • Develop a shared understanding of the Cognitive Rigor Matrix. • Use the Cognitive Rigor Matrix to: • Consider rigor expectations in the Common Core • Examine learning expectations and critical thinking • Evaluate sample assessments/tasks & rubrics

19. 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.

21. 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?

22. 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

23. 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?

24. Blooms Taxonomy

25. Webb’sDepth ofKnowledge • Identify • List • Draw • Define • Memorize • Calculate • Illustrate • Who, What, When, Where, Why • Measure • Arrange • Name • Tabulate • Repeat • Match • Design • Recall • Categorize • Recognize • Use • Connect • Infer • Level One • (Recall) • Graph • Organize • Synthesize • Classify • Level Four • Level Two • (Skill/Concept) • Modify • Describe Explain Interpret • Apply Concepts • Cause/Effect • (Extended Thinking) • Relate • Critique • Predict • Prove • Level Three • (Strategic Thinking) • Compare • Analyze • Interpret • Estimate • Create • Revise • Assess • Summarize • Develop a Logical Argument • Use Concepts to SolveNon-Routine Problems • Show • Critique • Construct • Compare • Apprise • Investigate • Explain • Formulate • Draw Conclusions • Hypothesize • Differentiate

26. 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.

27. 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…

28. 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

29. DOK 2 Skills and Concepts DOK 4 Extended Thinking DOK 3 Reasoning and Thinking DOK 1 Recall and Reproduction Explain relationships Summarize State central idea -Explain how concepts or ideas specifically relate to other content domains. Explain, generalize or connect ideas using supporting evidence (quote, text, evidence) Recall, locate basic facts, definitions, details, events Remember Apply Use language structure, word relationships to determine meaning Use context for word meanings Use information using text features Devise an approach among many alternatives to research a novel problem Use concepts to solve non-routine problems and justify Select appropriate words for use when intended meaning is clearly evident. Understand Analyze multiple sources or multiple text. Analyze complex abstract themes Analyze 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 Analyze or interpret author’s craft (e.g., literary devices, viewpoint, or potential bias) to critique a text 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 -Brainstorm ideas, concepts, problems, or perspectives related to a topic or concept. Generate conjectures or hypotheses based on observations or prior knowledge 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 Selected Response Constructed Response Performance Tasks

30. What DOK Level?

31. What DOK Level?

32. What DOK Level?

33. What DOK Level?

34. 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, …

35. DOK with Multiplication

36. Describe the trend displayed in the data table What is the answer to a multiplication problem called? Can the distributive property be used with division? Justify your conclusions with data generated from your investigation. Construct an area model for the polygon from the table with the largest area. • E • D • A • B • F • C Make a conclusion based on the data presented, use mathematical relationships to justify your response.

37. DOK Question Stems

38. Create Your Own DOK Questions In your tables, create your own DOK grid for: 3.G.1-2 or 4.G.1-3

39. 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?