Shifts in Mathematics Session

Welcome Principals!

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

Shifts in Mathematics Instruction

1. Focus2. Coherence3. Fluency4. Deep

Understanding5. Application6. Dual intensity

Shifts in Mathematics

Locate this document.

Task:Create a representation on your chart paper that summarizes your group’s assigned “SHIFT”.

Group Sharing

• Will they need 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, at what time will they reach LA?

The figure below shows a conversation between two friends.

Appendix F- ITN 2012-31-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 262.5 miles but according to the road sign, the distance to Los Angeles is 270 miles

35 miles ? miles

1 gallon 7.5 gall

1 of a 15 gallon tank = 7.5 gallons

2

35miles 7.5 gallons 35 7.5 262.5 miles

1 gall

o

on 1

ns

Solution

At 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 4 hours 54 minutes

1 55 m

1 hour ? hours

55 miles 270

iles 5

m l

5

i es

Solution

4 hours 54 minutes plus 30 minutes ≈ 5 hours 24 minutes

Expected Format Changes in

Mathematics Tasks

In addition to traditional tasks, students also will be asked to complete tasks that:

• assess more than one content

standard.• simultaneously assess content and practice standards.

• are not scaffolded.• take an extended period of time to complete.

Some Content ShiftsAWAY FROM TOWARD

Solving equations mechanically

Solving equations as a process of reasoning

Limiting word problems that invite arithmetic skills

Including word problems that invite algebraic approaches

Limiting integer algebra

Including rational number algebra

Mechanically simplifying or expanding expressions

Using properties of operations to rewrite expressions

Appendix F- ITN 2012-31-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 2012-31-PARCC Item Development

270

9:20 AM

• Which “Shifts” and “Changes”

are represented by this task?

• Why do you think so?

LET’S LOOK AT A MATHEMATICS TASK OF THE

FUTURE

Debriefing the Task

• This task draws on content from: • Cluster 7.RP.1-3. 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 content standard.

Mathematics Instruction of the

Future

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

• KEEP DOING???

• STOP DOING???

• START DOING???

Academy at a Glance

Day 1Session Audience Time

FrameSession Focus

MorningSchool Teams

Three 1-hour

Rotations

Comparison between the Literacy Standards and the Standards for Mathematical Practice

Afternoon

Mathematics

Teachers by Level

One2-hour and 50 minute

block

Review • Unit Plans• Lesson Seeds

PrincipalsFour

45-minute rotations

Shifts in Mathematics

Academy at a Glance

Day 2Session Audience Time

FrameSession Focus

Morning

Mathematics Teachers by Level

One3-hour block

Review• Lesson Plans • PARCC Task Types

Afternoon N/A

One3-hour block

Project Development

Academy at a Glance

Day 3Session Audience Time Frame Session Focus

Morning

Mathematics Teachers by Level

One3-hour block

Project Presentationsand

Shifts in Mathematics

Afternoon

School Teams

One3-hour block

Planning Meetings

Project Choices

Professional Development

Module

Enrichment

Activity

Intervention

Activity

UDLActivity

Preparing for Tuesday Afternoon’s Project

Exit Ticket

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