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 3rd or 4th grade Your objective(s) – 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 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) b) 3, 4, 5 Numbers and Algebraic thinking 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 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. 2. 3. 4. 5. 6. 7. 8. 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. 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 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. 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 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 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, … 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 (apply) to an unfamiliar task 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 answer for the problem 23 x 8. Explain how you made your estimate and 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 answer and why. 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 What is the answer to a multiplication problem called? B C E Make a conclusion based on the data presented, use mathematical relationships to justify your response. F 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?