Common Core High School Mathematics:Transforming Instructional Practice for a New Era

School Year Session 9: January 22, 2014

A New PTR Cycle: Starting at the End

1.1

Agenda

• Reflections on the first cycle & planning for the next

• Starting at the End: An Assessment Task• Break• Analyzing assessment rubrics and work• Picking a focus unit for the spring inquiry• Homework and closing remarks

1.2

Learning Intentions & Success Criteria

Learning Intentions:

We are learning to anchor a unit of instruction in a rich student assessment task.

Success Criteria:

We will be successful when we can identify features of an assessment task and rubric that provide meaningful opportunities to learn about student thinking.

1.3

1.4

Reflecting on the FallActivity 1:

Some things we noticed:• Exceptional thought, energy, and detail went

into your projects and presentations• Identifying good tasks and linking them to the

Standards for Mathematical Practice was strong• Articulating specific student thinking, including

solution paths and misconceptions, was challenging

1.5

Reflecting on the FallActivity 1:

Some things others noticed:• The thoughtful, meaningful ways in which you

designed and implemented tasks• The rich and deep student thinking that

emerged• Your enthusiasm in sharing the outcomes of

your project

1.6

Reflecting on the FallActivity 1:

Some things you wondered:• How can I find (or design in a time-efficient way)

more of these tasks?• How might we reasonably string together a set

of rich student experiences across a unit?• How can we assess in ways that are more

CCSS-compatible and still satisfy district policies and practices?

1.7

Reflecting on the FallActivity 1:

Our plans for the springWhat’s Old• Select a task for a

lesson/series of lessons with CCSSM focus

• Teach the lesson• Collect evidence about

what students learned

What’s New• Consider how the task

fits into the unit• Choose CCSSM-related

unit learning intentions• Design an assessment

that measures the unit’s success criteria

1.8

Reflecting on the FallActivity 1:

An approximate timeline

Select a focus unit

Specify a set of

learning intentions

Design or modify an

assessment

Design a task for a

focus lesson(s)

within the unit

Teach the unit &

lesson and collect

evidence

Plan, Teach, Reflect

project with lesson &

assessment evidenceJanuary 22

February 19March 5

March 5-19By April 5

May 7

1.9

The Cycle ShopActivity 2:

The task we are about to solve is designed as an assessment task for an Algebra I class.

As you solve the task, consider the following:• What standards do you think this task might

assess?• In what ways might you be able to score student

work relative to those standards?

1.10

The Cycle ShopActivity 2:

You work for a small business that sells bicycles, tricycles, and tandem bikes.

1. On Monday, you counted 48 tricycle wheels. How many tricycles were in the shop?Write a rule that shows the relationship between the number of wheels and the number of tricycles.

2. On Wednesday, there were no tandem bikes in the shop. There were a total of 24 seats and 61 wheels in the shop. How many bicycles and tricycles were in the shop? Explain how you know.

3. A month later, there are a different number of bicycles, tricycles, and tandem bikes in the shop. There are a total of 144 front steering handlebars, 378 pedals, and 320 wheels.How many bicycles, tricycles, and tandems are in the shop? Explain how you know.

1.11

The Cycle ShopActivity 2:

Discuss with your groups:• What standards do you think this task might

assess?• In what ways might you be able to score student

work relative to those standards?

Break

1.12

1.13

Analyzing the AssessmentActivity 3:

Consider the set of student work for The Cycle Shop.

• How might you create a rubric to measure the standards we identified as relative to the task?

• How will you distinguish between different levels of performance in assessing students’ written work on the task?

1.14

Analyzing the AssessmentActivity 3:

Consider the rubric and annotated student work for The Cycle Shop. In relation to the set of standards we identified:

• What aspects of student performance does the rubric measure well?

• What aspects of student performance does the rubric measure poorly or not measure at all?

• How might you edit the rubric to capture a wider range of performance?

1.15

So far tonight, we’ve considered as assessment task that might anchor a unit of instruction and the standards that the assessment might measure.

Your packet also contains an initial task and a lesson that might be embedded in a unit for which this assessment would be one measure of success.

How might you use these concepts of task, lesson, standards, and assessment to reconceptualize the process of planning for a new unit?

Picking a Focus UnitActivity 4:

1.16

Picking a Focus UnitActivity 4:

Using your district’s materials (curriculum or pacing guides, curriculum materials, course standards), identify a focus unit that you will be teaching in one of your courses between early March and mid-April. For that unit, identify a set of the CCSSM standards (content standards and Standards for Mathematical Practice) that you will teach and assess in that unit.

Learning Intentions & Success Criteria

Learning Intentions:

We are learning to anchor a unit of instruction in a rich student assessment task.

Success Criteria:

We will be successful when we can identify features of an assessment task and rubric that provide meaningful opportunities to learn about student thinking.

1.17

1.18

Homework & Closing Remarks

Homework:

• Complete your work in identifying standards for your focus unit. Bring the set of standards, along with any relevant assessments for the unit that are already designed, to our next session.

• Begin thinking about a lesson (one or more days) that might be anchored by a high cognitive demand task within the unit.

Activity 5: