WELCOME Day 3 EEA Summer 2012

Outcomes for Day 3 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

Quiz, Quiz, Trade

OUTCOME: The participants will share their projects. Project Presentations

BREAK

Shifts in Mathematics HERETHERE

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

Instructional Shifts 1. Focus 2. Coherence 3. Fluency 4. Deep Understanding 5. Application 6. Dual intensity

Locate “Shifts in Mathematics” Looks like this

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

Share Your Shifts

Locate “Some Important Elementary Shifts” Looks like this

HOW WILL THESE SHIFTS IMPACT YOUR INSTRUCTION?? Some Important Elementary Shifts

Will they need to stop for gas? Explain your reasoning. Suppose they decide to stop for gas and the stop lasts 30 minutes. If they continue their trip at the same speed, at what time will they reach LA? The figure below shows a conversation between two friends. Appendix F- ITN PARCC Item Development 270 LET’S LOOK AT A MATHEMATICS TASK OF THE FUTURE 9:20 AM

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. At what time will they arrive in Los Angeles? Driving 270 miles at 55 miles per hour will take 4 hours and 54 minutes. But remember, the stop for gas took an additional 30 minutes. According to the clock the current time is 9:20 a.m. This means they will arrive in Los Angeles at 2:44 p.m. Possible Solution 35 x 7.5 = ÷ 55 = hours equals 4 hour & 54 minutes. 4 hours 54 minutes plus 30 minutes equals 5 hours 24 minutes.

BUT WAIT!!! What about the time they used when they stopped for gas??? We must add the 30 minute gas stop. Soooo…. 4 hours 54 minutes plus 30 minutes equals 5 hours 24 minutes. So they would arrive at 2:44p.m., not 2:14 p.m.

THIS TASK DRAWS ON CONTENT FROM: Grade 7 Cluster: Analyze Proportional relationships and use them to solve real world problems. THE NUMBERS IN THE TASK ARE NOT LIMITED TO INTEGERS. Debriefing the Task

Reflection Construct a viable argument to support whether or not this task is: Practice Forward and/or Integrative

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

Examples of Changes in Expectations AWAY FROMTOWARD Solving equations mechanically Solving equations as a process of reasoning Limiting word problems that invite arithmetic skills Including word problems that invite algebraic approaches Conceiving of fractions as pictures Conceiving of fractions as numbers Mechanically simplifying or expanding expressions Using properties of operations to rewrite expressions Appendix F- ITN PARCC Item Development

Will they need to stop for gas? Explain your reasoning. Suppose they decide to stop for gas and the stop lasts 30 minutes. If they continue their trip at the same speed, at what time will they reach LA? The figure below shows a conversation between two friends. Appendix F- ITN PARCC Item Development 270 9:20 AM Which of the characteristics described in the “Shifts” or “Expected Changes in Tasks” does this task illustrate? LET’S LOOK AT A MATHEMATICS TASK OF THE FUTURE

“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: Duel 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.

Additional Changes in Mathematics Many items will still be important for students to be able to complete, for example: Each shirt has 6 buttons. How many buttons are needed to make 7 shirts? Each shirt costs $4. How much do 3 shirts cost? Show your work. How is the problem below different from the first?

Straightforward items will still be important for students to be able to complete, for example: In addition, the new assessments will include richer, often open- ended tasks, such as: Donna buys 40 apples at 35 cents each. She eats 2 apples and sells the rest for 45 cents each. How much money does she make? Donna buys some apples at 35 cents each. She eats 2 apples and sells the rest for 45 cents each. She makes $4.40. How many apples did she buy? Additional Changes in Mathematics

Assessments still will include 1-point items: BUT students also will need to complete multi-part problems: A bird flies 20 miles in 100 minutes, at a constant speed. At that speed, how long will it take the bird to fly 6 miles? how far will the bird fly in 15 minutes? how fast will the bird be flying in miles per hour? what will be the bird’s pace in minutes per mile? A bird flies 20 miles in 100 minutes, at a constant speed. At that speed, how long will it take the bird to fly 6 miles?

Away from single answer questions: Toward open-ended problem- solving questions: I have 3 dimes, 3 nickels, and 3 pennies in my pocket. How much money do I have? I have 67¢ in my pocket. How many different ways can I make 67¢ using coins? Additional Changes in Mathematics

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

Preparation for School Team Planning 1. Independently prepare discussion points to share with your school team, using ideas from the KEEP-STOP-START activity. 2. Share discussion points with the member of your table group. 3. Share discussion highlights with the large group.

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