1. Sunnyside School District Math Training Conceptual Lessons

2. Good Afternoon 1.Where is your classroom in regards to the year-long fluency expectations? What’s working well and what challenges have come up? 2.Have you tried a performance task with your students? What challenges came up and how did you handle them? 3.What comes to mind when you think about teaching conceptually? What would this look like in a math classroom?

3. Year-long Fluency Standards K---Add/Subtract within 5 1 st —Add/subtract within 10 2 nd —Add/subtract within 20; Add/subtract within 100 (includes regrouping) 3 rd —Multiply/divide within 100; Add/subtract within 1000 4 th —Add/subtract within 1,000,000 5 th —Multi-digit multiplication using standard algorithm 6 th —Multi-digit division; All operations with decimals 7 th —Two-step equations

4. Rigor Measurement Webb’s Depth of Knowledge (DOK) Four Levels Based on the cognitive demand of a task or question Process more important than product Used to write the new standards and assessments Teachers should think about the DOK of: Their questions Student activities Classroom assessments

5. DOK Review Read pages 1 and 2 in the document on Math DOK and come up with a statement about the difference between a DOK 2 and a DOK 3 activity. How can you see the difference in a classroom?

6. DOK Questions Think about the math that you are teaching right now and create a question at each DOK level (1-3).

7. Percentage of questions on AzMERIT at each DOK Level: Level 1: 10-20% Level 2: 60-70% Level 3: 12-30% Level 4: 0% How do these compare to the activities and questions in your classroom? DOK on AZMerit

8. CCSS Math Shifts 1. Focus 2. Coherence 3. Rigor  Procedural Skill and Fluency  Conceptual Understanding  Application of Math Standards

9. Math Practice Standards 1.Make sense of problems and persevere is solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

10. Math Practices 3 and 5 Read Math Practices and discuss: 1.How would these look in a classroom? 2.What are all of the types of tools in MP 5? 3.What are the two parts to MP3? How can you give students an opportunity to practice these?

11. Math Practice 3 Suggestions Critique the reasoning of others: 1.Show two or more solution methods for a problem. 2.Have students identify which is correct and why. 3.Create a common phrase or word to identify the common mistakes we make (oops!, pitfall, misconception, etc.) Joe’s Solution: 2/3 + 1/3 = 3/6 Liz’s Solution: 2/3 + 1/3 = 3/3

12. Initial Instruction BalanceBetween Concepts Procedures 12

13. Concepts and Procedures Doing something correctly, in itself, does not indicate understanding. 13

14. Conceptual Understanding Students can explain HOW the math works. Students can explain why THEY are using a specific strategy. Students can derive formulas and/or shortcuts on their own. Students can explain the meaning of math symbols and numbers.

15. Teaching Conceptually Two Methods: 1.Increase the depth of teacher questioning in your classroom during lessons AND REQUIRE all students to answer them. 2.Create conceptual activities where students discover an understanding.

16. Rigor (DOK) of Teacher Questions Level 1 Questions: 1.Simplify using the order of operations. 2.Solve: 5x + 3 = 168 Level 2 Questions: 1.Represent this word problem with an equation or drawing. 2.Write (in words) your steps to solve the problem. Level 3 Questions: 1.How do you know that your answer is correct? 2.Why can’t you add fractions with unlike denominators?

17. From Teacher Questions Consider this: Did one student answer the question? Did the teacher answer the question? Did ALL of the students answer the question?

18. Reflection What level of questions to you ask most often in your classroom? How can you increase the level of your questions?

19. Create DOK2/3 Question We Do 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

20. Activity For an upcoming standard, identify concepts in the standard and create questions (DOK 2 or 3) that you will ask students to ensure they have the understanding.

21. Closure 1.How can you ensure that all students answer a high level question that you ask? Brainstorm as many strategies as you can.

22. Standards Study K: K.MD.1-3 1 st : 1.MD.1-4 2 nd : 2.MD.1-6 3 rd : 3.MD.1-4 4 th : 4.MD.1-7 5 th : 5.MD.1-5 6 th : 6.G.1-4