Welcome High School Principals’ Session Shifts in Mathematics.

WelcomeHigh School Principals’ Session

Shifts in Mathematics

OutcomePrincipals 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.

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

6 Shifts in Mathematics

ShareYour 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 math

task of the future.

Appendix F- ITN 2012-31-PARCC Item Development

Will they need to stop for gas?

Yes they will need to stop for gas. They have enough gas to travel 262.5 miles but according to the road sign, the distance to Los Angeles is 270 miles

17.5 gallons of a 15 gallon tank

35miles 235 7.5 262.5 miles

1 gallon 1

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.

270 miles 1 hour 2704.9 hours

1 55 miles 554 hours 54 minutes+ 30 minutes 5 hours 24 minutes

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.

•The numbers in the task are not limited to integers.

•The 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 FROM TOWARD

Solving equations mechanically

Solving equations as a process of reasoning

Limiting Word problems that invite arithmetic skills

Word problems that invite algebraic approaches

Integer Algebra Rational Number Algebra

Mechanically simplifying or expanding expressions

Using properties of operations to rewrite expressions

Appendix F- ITN 2012-31-PARCC Item Development

Mathematics Instruction of the

Future

To successfully implement the Common Core Mathematics Curriculum, what must mathematics teachers:

KEEP DOING???

STOP DOING???

START DOING???

Project Choices

Power Point

Professional Developmen

tModule

InterventionActivity

EnrichmentActivity

UDLActivity

Academy at a Glance

Day 1Session Audience Time Frame Session Focus

MorningSchool Teams

3 One hour Rotations

Literacy Standards compared to the

Standards for Mathematical

Practice

Afternoon

Mathematics Teachers by Level

12 hour and 50 minute block

Review • Unit Plans• Lesson Seeds

Principals4

45 minute rotations

Shifts in Mathematics

Academy at a Glance

Day 2Session Audience Time

FrameSession Focus

MorningMathematics Teachers by Level

13 hour block

Review• Lesson Plans • PARCC Task Types

Afternoon NA1

3 hour block Project Development

Academy at a Glance

Day 3Session Audience Time Frame Session Focus

Morning

Mathematics Teachers by Level

13 hour block

•Project Presentations•Shifts in Mathematics

AfternoonSchool Teams

13 hour block Planning Meetings

Exit Ticket

Please share your questions and concerns on the provided Exit Ticket.