Transcript Welcome [mdk12.org]
Welcome
High School Principals’ Session Shifts in Mathematics
Outcome
Principals 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.
6 Shifts in Mathematics
Task
On your chart paper, create a “visual” assigned representation that summarizes your group’s “SHIFT.”
Share Your Shift
Expected Changes in Mathematics Tasks
In addition to the traditional tasks, to complete tasks that: students will be asked
•
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?
Appendix F- ITN 2012-31-PARCC Item Development
The figure 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
35miles 1 gallon
7.5 gallons
1 2 of a 15 gallon tank
1
262.5 miles 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
270
4.9 hours
1 55 miles 55 4 hours 54 minutes+ 30 minutes
5 hours 24 minutes
•
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?
270 miles
09:20 AM
The figure shows a conversation between two friends.
Expected Changes in Mathematics Tasks
In addition to the traditional tasks, to complete tasks that: students will be asked
•
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.
AWAY FROM
Solving equations mechanically Limiting Word problems that invite arithmetic skills Integer Algebra Mechanically simplifying or expanding expressions
TOWARD
Solving equations as a process of reasoning Word problems that invite algebraic approaches Rational Number Algebra 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
Professional Development Module Power Point Enrichment Activity Intervention Activity UDL Activity
Academy at a Glance
Session Audience
Morning School Teams Afternoon Mathematics Teachers by Level Principals Day 1
Time Frame
3
One hour Rotations
1
2 hour and 50 minute block
4
45 minute rotations Session Focus
Literacy Standards compared to the Standards for Mathematical Practice Review
•
Unit Plans
•
Lesson Seeds Shifts in Mathematics
Academy at a Glance
Session
Morning
Audience
Mathematics Teachers by Level Afternoon NA
Day 2
Time Frame
1
3 hour block Session Focus
Review
•
Lesson Plans
•
PARCC Task Types 1
3 hour block
Project Development
Academy at a Glance
Session
Morning Afternoon
Audience
Mathematics Teachers by Level School Teams
Day 3
Time Frame
1
3 hour block Session Focus
•
Project Presentations
•
Shifts in Mathematics 1
3 hour block
Planning Meetings
Exit Ticket
Please share your questions and concerns on the provided Exit Ticket.