Welcome

Day 3 EEA Summer 2012

High School Mathematics Educators

OutcomesThe 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.

OUTCOMEThe participants will synthesize their knowledge of the CCSS and available resources.

Quiz -Quiz Trade Warm Up

OUTCOMEThe participants will share projects.

Project Presentations

Break Time!!!

Shifts in Mathematics

OutcomeParticipants 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

mathematics 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

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

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 min

1 hour ? h

utes+30 m

ours

55 mile

inutes=5 ho

s 270

urs 24 minute

le

s

mi s

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 taskThis 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

IllustrationsTraditional problems such as the one below will still appear on assessments.

3 1If - 4 , then what is ?

4 2x x

The new assessment will also include much richer problems, often open ended tasks such as:

What are two different equations

with the same solution as

3 1- 4 ?

4 2x

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.

Expand 2 3x x

2

Find a value for and a value for

so that

2 3 .

k n

x x x kx n

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

2 3

3

4Original Tank Volume = π 3 10 + π 3

3

= 90π + 36π = 126πft

3New Tank Volume = 2 126π = 252πft

ft

3 2

2 3

4r +10r - 252 =

4252π = π r 10 + π r

3

r = 4.0459148 4.0459

03

Mathematics Instruction of the

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

KEEP DOING???

STOP DOING???

START DOING???

OUTCOMEThe 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.

C

H

A

N

G

E

Sometimes change may not be what we want.

Sometimes change is what we need!

http://www.change-quotes.net/