Welcome High School Principals’ Session Shifts in Mathematics.
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Transcript of Welcome High School Principals’ Session Shifts in Mathematics.
Shifts in Mathematics
1. Focus
2. Coherence
3. Fluency
4. Deep Understanding
5. Application
6. Dual intensity
TaskOn your chart paper, create a “visual” representation that summarizes your group’s assigned “SHIFT.”
6 Shifts in Mathematics
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