1. Strategies for Teaching, Supporting and Assessing Students’ Understanding and Development of Algebra and Function Concepts, Operations and Skills Leading to Conceptual Fluency, Proficiency in varied Applications, and Entry to Algebra (6-12) WEI Math Academy December 6, 2014 Mike Weidner Bridget Schock

2. Learning Objectives Understand the progression of mathematics content focused on algebra and functions Identify instructional strategies that develop students’ mathematical habits of mind that enhance student algebraic and functional competence and their application Engage in activities that model appropriate instructional strategies that support students’ behaviors in mathematical sense-making, conjecturing, reasoning, and communicating

3. Marshmallow Tower The task is simple: in eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. http://www.online- stopwatch.com/countdown-timer/

4. Making Connections As you were working on the marshmallow task, did your team exhibit evidence of "productive struggle"? Was communication important on your team? How so? How does this task fit in the big picture of the Common Core State Standards?

5. CCSSM: Wisconsin Adopted CCSSM on June 2, 2010 Governing member of the Smarter Balanced Assessment Consortium (SBAC), with assessments to be rolled out in the 2014-2015 school year 1.5

6. Make sense of problems Reason quantitatively Viable arguments & critique Model with mathematics Strategic use of tools Attend to precision Look for and use structure Look for regularity in reasoning K–8 Standards by Grade Level High School Standards by Conceptual Categories ________________________ – Domains – Clusters – Standards Standards for Mathematical Practice Standards for Mathematics Content CCSSM New Structure & New Terminology 1.6

7. K-8 Domains & HS Conceptual Categories

8. Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 6. Attend to precision. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Reasoning and Explaining Modeling and Using Tools Seeing Structure and Generalizing William McCallum, The University of Arizona 1.8

9. Focus: Unifying themes and guidance on “ways of knowing” the mathematics. Coherence : Progressions based on mathematics and student learning. Rigor: Deep, genuine understanding of mathematics and ability to use that knowledge in real-world situations. CCSSM Design Principles

10. Productive Struggle http://www.npr.org/blogs/health/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning

11. Task #1: The Bus Problem There are three different busing companies that the Algebra Academy works with. Which company will provide the best deal for the field trips? number of passengers cost 10$125 20$145 30$165 40$185 50$205 60$225 70$245 80$265 90$285 $1.25 per person, plus a $250 administrative fee per trip Carrie’s Cartage Company Best Bus Business Able Transport

12. Task #1: The Bus Problem What were the big math ideas of this task? What standards does this task align to? How did you experience productive struggle?

14. Standards for Mathematical Practice Read the Math Practice Standard that you are least familiar with. What are some student behaviors when engaged in a task with the Math Practice Standard? What are some teacher moves that need to happen in order for the students to become engaged with the standard?

15. Growth Mindset https://www.khanacademy.org/youcanlearnanything

16. Task #2: Toothpick Problem In your group, determine a mathematical model that gives the total number of toothpicks required to construct a square of any size that is subdivided into 1x1 squares of toothpicks. The 1x1 square and the 2x2 square are shown.

17. Task #2: Toothpick Problem What were the big math ideas of this task? What standards does this task align to? How did you experience productive struggle?

18. Making Connections How do you see productive struggle in the Bus and Toothpick problems with your own students? How did you experience the Math Practice Standard when engaged with the tasks?

19. Thank You!!! Survey and Evaluations Resources http://www.nicolet.us/faculty/mweidner/2014weial gfunsworkshop.cfm