1. Mathematics Common Core Standards and Depth of Knowledge Presented February 8, 2012

2. The “New” Math Increasingly, the computer will do the computation…(but) thinking about the problem, developing the problem, understanding the problem, analyzing it from all sides, deciding what important information is relevant to the problem…is the harder part…You can’t do that without an understanding of the computation. - Achieve (2004)

3. Attributes of the CCSS: Mathematics Engage student in the content through the Mathematical Practices Problem solving Reasoning Modeling Using tools Making arguments Precision Structure

4. – Grade-Level Standards K-8 grade-by-grade standards organized by domain 9-12 high school standards organized by conceptual categories – Standards for Mathematical Practice Describe mathematical “habits of mind” Standards for mathematical proficiency: reasoning, problem solving, modeling, decision making, and engagement Connect with content standards in each grade Common Core State Standards for Mathematics

5. CCSSM Mathematical Practices 1.Make sense of problems and persevere in 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.

6. Norman Webb’s Depth of Knowledge Level 1 - Recall: Recall of a fact, information, or procedure. Level 2 - Skill/Concept: Use information or conceptual knowledge, two or more steps, etc. Level 3 - Strategic Thinking: Requires reasoning, developing plan or a sequence of steps, some complexity, more than one possible answer. Level 4 - Extended Thinking: Requires an investigation, time to think and process multiple conditions of the problem.

8. When assigning the DOK level consider… The level of work students are most commonly required to perform The complexity of the task, rather than its difficulty. The DOK level describes the kind of thinking involved in a task, not the likelihood that the task will be completed correctly. The complete domain of items that would be appropriate for completing the task. Identify the DOK level of the most common of these items. If there is a question regarding which of two levels an objective addresses, it is usually appropriate to select the higher of the two levels.

9. Sample Questions Math, grade 4 – Each day that Jasmine turns in her homework on time, she earns 5points. Jasmine has turned in her homework on time for the last 8 days. How many points has Jasmine earned altogether? a)30 b)35 c)40 d)45 The fact that this is a story problem does not make this more than a level 1 item. The text here quickly reveals that the problem is simple multiplication. However, story problems can often have higher DOK levels even if the computations required are only level 1, as long as there is some skillful or strategic thinking required in determining what computations to perform.

10. Sample Questions Grade 3: The table shows the costs of different numbers of fruit bars. Based on the information in the table, which statement is true? A Each fruit bar costs $4. B Each fruit bar costs $2. C The cost of 6 fruit bars will be $11. D The cost of 6 fruit bars will be $15.

11. Sample Questions GRADE 3:

12. Sample Questions Grade 3

13. Grade 5 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, … How many edges does the figure below have? Mrs. Washington asked her students what fractional part of these 12 circles is shaded. Who is correct – Odessa, Bob, or both? Write how you would explain your answer to part a to Odessa and Bob. Draw your own picture to go with your explanation.

14. Sample Questions Grade 5

15. Sample Questions Grade 7 Boseda is designing a board game. On their turns, players spin a spinner to determine if they will draw a red, blue, green, or yellow card. Boseda draws the spinner so that half the spinner is red and the other half is divided equally between blue, green, and yellow. During a typical game, the spinner is spun 120 times. Based on theoretical probability, how many times will the spinner stop in the “Red” region of the spinner when the spinner is spun 120 times?

16. Sample Questions Grade 8 The price of gasoline was $2.159 per gallon last week. This week the new price is $2.319 per gallon. Determine the percent of increase.

17. Sample Questions Grade 8

19. What Does this Look Like in the Classroom?

20. Questions?