Welcome Day 3 EEA Summer 2012 High School Mathematics Educators

Outcomes The participants will: synthesize their knowledge of the CCSS and available resources. share projects. become aware of expected shifts in Mathematics instruction. formulate a plan for training teachers at their school.

OUTCOME The participants will synthesize their knowledge of the CCSS and available resources. Quiz -Quiz Trade Warm Up

OUTCOME The participants will share projects. Project Presentations

Shifts in Mathematics Outcome Participants will become aware of expected shifts in mathematics instruction.

Shifts in Mathematics 1. Focus 2. Coherence 3. Fluency 4. Deep Understanding 5. Application 6. Dual Intensity

Shifts in Mathematics Locate this document.

Task On your chart paper, create a “visual” representation that summarizes your group’s assigned “SHIFT.” 6 Shifts in Mathematics

Share Your Shift

Expected Changes in Mathematics Tasks In addition to the traditional tasks, students will be asked to complete tasks that: assess more than one standard. assess both content and practice standards simultaneously. are not scaffolded. take an extended period of time to complete.

270 miles 09:20 AM Do they have to stop for gas? Explain your reasoning. Suppose they decide to stop for gas and the stop takes 30 minutes. If they continue their trip at the same speed, what time will they reach LA? The figure shows a conversation between two friends. Let’s look at a mathematics task of the future. Appendix F- ITN PARCC Item Development

Will they need to stop for gas? Yes, they will need to stop for gas. They have enough gas to travel miles but according to the road sign, the distance to Los Angeles is 270 miles Solution

What time will they arrive in Los Angeles? Driving 270 miles at 55 miles per hour will take 4 hours and 54 minutes. According to the clock the current time is 9:20 a.m.. This means that they will arrive in Los Angeles at 2:44 p.m. Solution

270 miles 09:20 AM Do they have to stop for gas? Explain your reasoning. Suppose they decide to stop for gas and the stop takes 30 minutes. If they continue their trip at the same speed, what time will they reach LA? The figure shows a conversation between two friends. Which of the characteristics described in the “Shifts” or “Expected Changes in Tasks” does this task illustrate?

Expected Changes in Mathematics Tasks In addition to the traditional tasks, students will be asked to complete tasks that: assess more than one standard. assess both content and practice standards simultaneously. are not scaffolded. take an extended period of time to complete.

Debriefing the Task This task draws on content from: Grade 7. Cluster :Analyze proportional relationships and use them to solve real world problems. “Expected Changes” illustrated by this task This task: is not scaffolded. takes an extended amount of time to solve. assesses both content and practice standards. assesses more than one standard.

“Shifts” illustrated by this task Shift 1 :Focus This task focuses on analyzing proportional relationships and using them to solve real world problems which is a critical concept in grade 7. Shift 2 :Coherence What students need to know and be able to do to complete this task connects to their learning of measurement, multiplication and division in the elementary grades.

“Shifts” illustrated by this task Shift 3 :Procedural Fluency Students are able to efficiently and accurately complete the multiplication and division computations necessary to solve the proportions. Shift 4 :Deep Conceptual Understanding Students who successfully complete this task demonstrate conceptual understanding of proportional reasoning.

“Shifts” illustrated by this task Shift 5: Applications (Modeling) To complete this task, students must choose and use an appropriate mathematical model without being prompted to do so. Shift 6: Dual Intensity By completing this task, students demonstrate that they know that this task requires the use of proportional reasoning and that they are able to successfully carry out the computations required to solve a proportion.

CCSSM Shifts Relating to “Particular Content” AWAY FROMTOWARD Solving equations mechanically Solving equations as a process of reasoning Limiting Word problems that invite arithmetic skills Word problems that invite algebraic approaches Integer AlgebraRational Number Algebra Mechanically simplifying or expanding expressions Using properties of operations to rewrite expressions Appendix F- ITN PARCC Item Development

Illustrations Traditional problems such as the one below will still appear on assessments. The new assessment will also include much richer problems, often open ended tasks such as: Which shifts/changes are illustrated by this problem?

Illustrations Students will still need to demonstrate that they are able to complete problems such as the one below. In addition to this type of problem, assessments of the future will require students to demonstrate deeper conceptual understanding by making it necessary for students to access concepts from a number of perspectives as illustrated by the problem below. Which shifts/changes are illustrated by this problem?

Propane tanks are used to store propane gas. Often these tanks are made in the shape of a cylinder with hemispheres on the ends. The Propane Tank Company makes tanks with this shape in different sizes. The cylinder part of every tank is exactly 10 feet long, but the radius of the hemispheres, r, will be different depending on the size of the tank. A standard tank measures 6 feet in diameter. The company wants to double the capacity of its standard tank. What should the radius of the new tank be? 10 feet Illustration Which shifts/changes are illustrated by this problem?

Solution

Mathematics Instruction of the Future To successfully implement the Common Core Mathematics Curriculum, what must mathematics teachers: KEEP DOING??? STOP DOING??? START DOING???

OUTCOME The participants will formulate a plan for training teachers at their school. Reflection

Independently, use guiding questions to prepare discussion points to share with their school team Share discussion points with members of your table group Share highlights with large group Preparation for Team Planning

Sometimes there are things in life that aren't meant to stay. CHANGECHANGE Sometimes change may not be what we want. Sometimes change is what we need!