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Distinguish between conceptual and procedural CFUs in order to increase the rigor of the classroom without increasing the amount of paper to pen work for the students.
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Do Now:
Make sure you have an objective and example problem you want to focus on.
This should be an objective you will teach within the next week.
Wednesday, November 27, 2012
Middle School Math Learning Team
Student Outcome: Students will be able to understand and explain math processes throughout the
math lesson cycle.
CM Strategy: CMs will plan effective CFUs and create spaces where students can justify their
answers.
CFUs and Follow-through
Today we are learning to grow brains …
1Definitions and Examples
2Methods of
Questioning
3Scaffolding
Two Kinds of CFUs
Conceptual
Relationships
“Why can’t I multiply across right from the beginning?”
Procedural
Rules and Procedures
“How do I make an improper fraction from a mixed number?”
Guided Practice = multiple opportunities to practice + a focus on key points + teacher guidance/feedback
Two Kinds of CFUs
Procedural: Rules and Procedures
“What will happen if I just divide across right now?”
“How do I make an improper fraction from a mixed number?”
“In order to solve this problem, how should I change this problem?”
Conceptual: Relationships
“When can I just divide across?”
“Why can’t I multiply across right from the beginning?”
“Will I always have to have
regular fractions to solve?”
Task: Write THREE procedural and THREE conceptual questions for a problem you have.
How do you CFU?
1. Asking the what– Procedural: “How did we make an improper fraction?”– Conceptual: “Why did we make an improper fraction?”
2. Asking for a repeat– Procedural: “How did we make it into a multiplication problem?”
– Conceptual: “Why did we make flip the sign and the fraction behind?”
3. Asking to clarify– Procedural: “How did we get 36 as a numerator?”– Conceptual: “Why is our denominator still 7?”
How do you CFU?Task: Label each step with a procedural and a conceptual question.
What should we do first in this problem?
How did we make 1 2/7 into 9/7?
How did we get 36 as a numerator?
How did we get 5 as a whole number?
How did we make it into a multiplication problem?
Why did we make the mixed number into a improper fraction?
Why did we flip the sign and the fraction behind?
Why can’t this be our final answer?
Why is the denominator still 7?
Why can’t we just divide across?
I DO to WE DO to YOU DO
I DO: problem one
• Think aloud the conceptual and the procedural at every step
WE DO: problem two
• First conceptual questions, then procedural questions
• 50% teacher led
WE DO: problem three
• First procedural questions, then conceptual questions
• 25% teacher led
I DO: Problem 11. Write the problem: ME2. Change mixed numbers to improper
fractions: ME3. Identify whether it can be divided across:
ME4. Flip the operation: THEM5. Flip the second fraction: THEM6. Operate across: THEM
WE DO: Problem 21. Write the problem: ME2. Change mixed numbers to improper
fractions: THEM3. Identify whether it can be divided across:
ME4. Flip the operation: THEM5. Flip the second fraction: THEM6. Operate across: THEM
WE DO: Problem 31. Write the problem: ME2. Change mixed numbers to improper
fractions: THEM3. Identify whether it can be divided across:
THEM4. Flip the operation: THEM5. Flip the second fraction: THEM6. Operate across: THEM
I DO to WE DO to YOU DO
I DO: problem one
• Think aloud the conceptual and the procedural at every step
WE DO: problem two
• First conceptual questions, then procedural questions
• 50% teacher led
WE DO: problem three
• First procedural questions, then conceptual questions
• 25% teacher led
Task: Role play with Real Time Coaching cards.
