Transcript Slide 1

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.
Quiz, Quiz, Trade
Warm-Up
OUTCOME:
The participants will synthesize
their knowledge of the CCSS and
available resources.
Quiz, Quiz, Trade
Project Presentations
OUTCOME:
The participants will
share their projects.
BREAK
Shifts in Mathematics
HERE
THERE
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
Task
On your chart paper, create
a “visual” representation
that summarizes your
group’s assigned “SHIFT.”
Share
Your
Shifts
Locate “Some Important
Elementary Shifts”
Looks
like
this
Some Important
Elementary Shifts
HOW WILL
THESE SHIFTS
IMPACT YOUR
INSTRUCTION??
LET’S LOOK AT A
MATHEMATICS TASK OF THE
FUTURE
270
9:20
AM
• 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?
Appendix F- ITN 2012-31-PARCC Item Development
The figure
below shows a
conversation
between two
friends.
• 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 x 7.5 = 262.5
• 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.
270 ÷ 55 = 4.9
4.9 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.
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.
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 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
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 2012-31-PARCC Item Development
LET’S LOOK AT A
MATHEMATICS TASK OF THE
FUTURE
270
9:20
AM
• 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?
Appendix F- ITN 2012-31-PARCC Item Development
The figure
below shows a
conversation
between two
friends.
“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 costs $4. How much do 3
shirts cost? Show your work.
How is the problem below different from the first?
Each shirt has 6 buttons. How many
buttons are needed to make 7 shirts?
Additional Changes in Mathematics
Straightforward items will still be
important for students to be able
to complete, for example:
 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?
In addition, the new assessments
will include richer, often openended tasks, such as:
 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:
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?
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?
Additional Changes in Mathematics
Away from single answer
questions:
 I have 3 dimes, 3
nickels, and 3 pennies
in my pocket. How
much money do I have?
Toward open-ended problemsolving questions:
 I have 67¢ in my pocket.
How many different
ways can I make 67¢
using coins?
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.
YESTERDAY
TODAY
Engage Me
YESTERDAY
TODAY
Engage Me! - YouTube.wmv