The importance of Coherent Lessons in HIGH school Mathematics

1. COHERENCE The importance of Coherent Lessons in HIGH school Mathematics College and Career Readiness Conference Summer 2014

2. SHIFTS

3. COHERENCE • Coherence comes from the verb to cohere, which means: • To stick together in a way that resists separation; • To be logically linked and naturally related. • Think of Rice Krispies Treats…

4. We want our mathematics curriculum to have coherence… related concepts that stick together in a way that is obvious, understandable, connected, and reliable… for teachers and students alike!

5. COHERENCE A purposeful placement of standards to create logical sequences of content topics that bridge across the grades, as well as across standards within each grade.

6. TODAY’S OUTCOME Participants will: Explore in depth the “shift” of COHERENCE and its impact on mathematics content, instruction, andassessmentof the Maryland CCR Standards in mathematics.

7. Four Corners Teacher, Not HS Math HS Math Teacher, taught Functions HS Math Teacher, hasn’t taught Functions Not a Teacher

8. COHERENCE CONTENT The writers of the CCSS: • Built COHERENCE into the content standards. • Clarified and shared their vision of grade-to-grade and within-grade COHERENCEin the Progressions documents.

9. GRADE-TO-GRADE COHERENCE In the following task from Illustrative Mathematics, complete the following steps: Compute the correct answer. List all of the mathematics concepts/skills you used. Write down the grade at which the concepts/skills are taught and the applicable domain, cluster, or standard. List mathematics concepts/skills in later grades/courses that build upon/expand the information from #2. Reflect on what you just have written. What do you notice about the task’s reliance on COHERENCE? http://www.illustrativemathematics.org/illustrations/1564

10. Parking Lot! A parking lot charges $0.50 for each half hour or fraction thereof, up to a daily maximum of $10. Let C(t) be the cost in dollars of parking for minutes. a. Complete the table below. http://www.illustrativemathematics.org/illustrations/588

11. Do calculations here: DS http://www.illustrativemathematics.org/illustrations/588

12. Sketch graph here DS http://www.illustrativemathematics.org/illustrations/588

13. Questions: Answers http://www.illustrativemathematics.org/illustrations/588

14. GRADE-TO-GRADE INSTRUCTION

15. WITHIN-GRADE COHERENCE In the following task, complete the following steps: Compute the correct answer. List all of the mathematics concepts/skills you used. Write down the grade at which the concepts/skills are taught and the applicable domain, cluster, or standard. List mathematics concepts/skills in later grades/courses that build upon/expand the information from #2. Reflect on what you just have written. What do you notice about the task’s reliance on COHERENCE?

16. INSTRUCTION An equipment rental company has 2 different penalty options for returning a piece of equipment late: Option 1: On day 1, the penalty is $10. On day 𝟐, the penalty is $2𝟎. On day 3, the penalty is $30. On day 4, the penalty is $4𝟎and so on, increasing by $10 each day the equipment is late. Company 2: On day 1, the penalty is $𝟎.𝟎𝟏. On day 𝟐, the penalty is $𝟎.𝟎3. On day 3, the penalty is $𝟎.09. On day 4, the penalty is $𝟎.27 and so on, triplingin amount each additional day late. Jim rented a backhoe using option because he thought it had the better late return policy. The job he was doing with the backhoe took longer than he expected, but it did not concern him because the late penalty seemed so reasonable. When he returned the backhoe 12 days late, he was shocked by the penalty fee. What did he pay, and what would he have paid if he had used Option 1 instead?

17. INSTRUCTION Additional Questions for discussion: Write the formula for the sequence in option 1. Describe the sequence. Write a formula for the sequence in option 2. Describe the sequence. 5. Which of the 2 options grows more quickly? Why?

18. INSTRUCTION Do calculations here: DS

19. INSTRUCTION Do calculations here: DS

20. WITHIN-GRADE COHERENCE INSTRUCTION

21. COHERENCE ASSESSMENT Evidence of Coherencein assessment is not tremendously different from evidence of coherencein classroom instruction.

22. COHERENCE ASSESSMENT High School Content Interpreting Functions (F-IF) • Major- Understand the concept of a function an due function notation • Interpret functions that arise in applications in terms of context • Supporting - Analyze functions using different representations Building Functions(F-BF) • Supporting - Build a function that models a relationship between two quantities • Additional- Build new function from existing functions

23. COHERENCE https://www.parcconline.org/samples/mathematics/high-school-functions ASSESSMENT

24. COHERENCE https://www.parcconline.org/samples/mathematics/high-school-functions ASSESSMENT Do calculations here: DS

25. COHERENCE • Which other Standards for Mathematical Practice are assessed in this task? MP6- Attend to Precision • Content standards F-­‐IF.9. Compare • properties of two functions each represented in a different way(algebraically, graphically, • Numerically in tables, or by verbal • descriptions). • (According to PARCC) ASSESSMENT

26. COHERENCE • Type I-Balance of conceptual understanding, • fluency, and application • Type I- Machine scorable, innovative computer-based formats • Claim A- Major content with connections to • practices • Scoring- Full credit requires selecting correct • answers from drop down menu. Partial credit • can be given for each answer that is correct. • (According to PARCC) ASSESSMENT

27. Shift of Coherence In reality, the “key” to making the Shift of Coherencea success rests on the shoulders of curriculum writers and classroom teachers. Instruction must take advantage of every opportunity to buildconnections between topics both within a grade and from grade to grade.

28. Grade-to-Grade Coherence Activity INSTRUCTION ASSESSMENT COHERENCE

29. What arethe muddiest points? Record any question you still have after today’s presentation on your post-it note. Please provide your name and email address. Stick your post-it on the front wall as you leave today. Thank you!