Common Core Standards, K – 12 Kentucky Core Academic Standards

1. Common Core Standards, K – 12 Kentucky Core Academic Standards Mathematics

2. What do we mean by: Understanding Mathematics? Jake is a Genius • Each person get 4 post-it notes and silently read pages 3, 4, & 5, and the bottom of page 8. • On the 1st post-it write down a couple of the most important ideas in the Introduction (pg 3), • On the 2nd post-it write down a couple of the most important ideas about Understanding Mathematics (pg 4), • On the 3rd post-it write down a couple of the most important ideas about How to read the grade level standardsand what the standards do and do not mean (pg 5), • On the 4th post-it write down a couple of the most important ideas about Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content (pg 8).

3. What do we mean by: Understanding Mathematics? • When everyone has finished reading & jotting down their ideas, share your ideas from each post-it by having each person read one idea for each topic. Take turns letting a different person be the first to share their ideas for each of the topics: • Introduction • Understanding Mathematics • How to read the grade level standards & what the standards mean • Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content How did this process clarify your thinking about what was read?

4. Standards for Mathematical Practice

5. Standards for Mathematical Practice – pgs 6-8 • Silently read the mathematical practice assigned to your group and highlight your MIPs. • On chart paper, your group will represent your mathematical practice in words and pictures. • Be prepared to share out.

6. Standards for Mathematical Practice – pgs 6-8 • Cut out your foldable and write one mathematical practice on each front flap. • As each group presents their mathematical practice, use your foldable to record ideas about the meaning of each practice. foldable

7. Frontier

8. Middle School Landscape • Using the topics assigned to your group, identify where the topic starts and stops in the CCSS using the Cluster & Domain Progression handout. • Discuss with your group any differences you notice between the progression of your topic in the CCSS and the KY POS. • Be prepared to share your findings.

9. High School Landscape • Use the suggested CCSS Pathway to compare the content of this course to the table of contents of your assigned text. • Discuss with your group any content differences you notice between the two. • Be prepared to share your findings.

10. Existing Curricula Creation Standards

11. In what ways do the differences between the old and new arrangement of content topics impact any two of these areas?

12. Analyzing Cognitive Demand • All mathematical tasks are not created equal. • As we solve two problems dealing with area, we will look for similarities and differences between the two. • Afterwards, we will sort new and different problems into low and high level tasks.

13. Why instructional tasks are important? Comparing Two Mathematical Tasks: 1. Martha’s Carpeting Task 2. The Fencing Task

14. Martha’s Carpeting Task: Solve on your own, then discuss with your table group. Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

15. Martha’s Carpeting TaskSolution Strategies: Using the Area Formula A = l x w A = 15 x 10 A = 150 square feet Drawing a Picture 10 15

16. The Fencing Task:Solve on your own then discuss with your table group. Ms. Brown’s class will raise rabbits for Their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. • If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? • How long would each of the sides of the pen be if they had only 16 feet of fencing? • How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

17. The Fencing Task Solution Strategies: Diagrams on Grid Paper

18. The Fencing Task Solution Strategies: Using a Table

19. The Fencing Task Solution Strategies: Graph of Length and Area Max

20. Comparing Two Mathematical Tasks • How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

21. Similarities and Differences Differences • The amount of thinking and reasoning required • The number of ways the problem can be solved • Way in which the area formula is used • The need to generalize • The range of ways to enter the problem Similarities • Both are “area” problems • Both require prior knowledge of area

22. Reflect back to the original scenario • Would both the Carpet & Fencing tasks likely be assigned by both a teacher who accepted the student claim and a teacher who explored the claim? • Which task, Carpet or Fencing, would help the student who made the claim to actually understand why her claim is not accurate?

23. Mathematical Tasks:A Critical Starting Point for Instruction Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000

24. Mathematical Tasks: The level and kind of thinking in which students engage determines what they will learn. Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997

26. Mathematical Tasks: There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 1995

27. Mathematical Tasks: If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks. Stein & Lane, 1996

28. Task Sort • Being able to sort tasks according to cognitive demand allows teachers to better match tasks with learning targets. • As you sort through these tasks: • Separate them by “cognitive demand” • Map all applicable standards/ practices to these tasks

29. Demonstrating Competency Does this always look the same? When does a teacher need to consider what this looks like? How does this impact teaching and learning, assessment, and interventions?

31. Fortune Cookie • Each team receives an envelope. • One person draws a question, and makes one statement about the topic, then passes it on. • The next person adds their statement or responds to the previous statement. • When everyone has responded to the first statement, another person draws from the envelope and repeats the process.