Download 3 Types of Questions Carousel Work

The questions that follow below are examples of TMI teachers’ group work on questioning. The
activity began with TMI teachers learning about three types of effective questions: reversibility,
generalization and flexibility. After the initial work time, TMI teachers participated in a carousel
in which they examined each group’s questions and provided feedback. Teachers reconvened
and edited their work based on feedback.
Topic: LCM and GCF
Reversibility:
The LCM of two numbers is 24. Name possible number that could have 24 as the LCM.
Generalization:
2, 4, 6, 8, 10, 12 . . .
8, 16, 24, 32, 40 . . .
13, 26, 39, 52, 65 . . .
Describe a pattern you notice with addition and with multiplication.
Flexibility:
Describe how to find the GCT of the two numbers below:
12 and 36
Topic: Signed Numbers and Temperature
General Question: In Buffalo, New York, the temperature was -11ᵒF in the morning. If the
temperature dropped 9ᵒF, what is the temperature now?
Reversibility:
The temperature was -11ᵒF this morning. If it is -20ᵒF now, what was the degree change
throughout the day?
Generalization: What is the temperature at 9:00 pm? How do you know?
Morning temp
4:00 pm2015
temp
Noon temp(TMI)—PIMSER
Timely Mathematical Interventions
-11ᵒF
-21ᵒF
-16ᵒF
9:00 pm temp
???ᵒF
Page 1
Flexibility:
Create a real-world problem that includes the start temperature, the change in temperature and
the ending temperature. HINT: Rules, Number line, chips and +’s and –‘s.
Topic: Inequalities
General Question: 2x < 14
Reversibility:
Write at least three inequalities that have a solution of x < 7.
Generalization:
Describe a pattern to solve each inequality below:
2x < 14
4x < -20
3x < 18
ax < b
Flexibility:
Ben, Celena and Juan were given the following problem: -2x < 14.
Ben gets x < -7
Celena gets x > -7
Juan gets x < 7
Describe who is correct and why.
Topic: GCF
General Question: What is the GCF for 12 and 15?
Reversibility:
Three is the GCF for what possible numbers other than 3 that are less than 30?
Generalization:
If the GCF of 12 and 15 is 3; 24 and 30 is 6; and 36 and 45 is 9, what pattern could be used to
find the GCF of 120 and 150? Explain.
Flexibility:
What is the relationship between GCF and prime factorization?
Timely Mathematical Interventions (TMI)—PIMSER 2015
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Topic: Laws of Exponents
Reversibility:
X5 * _____ = x12 Explain your reasoning using proper mathematical language.
Generalization: Use of Silent Teaching
X5 * x2 = x7
x__ * x5 = x9
X5 * x7 = x12
24 * ___ = 29
Flexibility:
Write 4 different expressions using multiple properties of exponents that will be equivalent to
x12.
Topic: Solving Equations
General Question:
Solve the following equation for x: 2(x + 3) = 8.
Reversibility:
Write a multi-step equation that equals 8 when x = 1.
Generalization:
Describe the pattern of the following equations:
2(2 + 3) = 10
2(3 + 3) = 10
2(4 + 3) = 10
2(5 + 3) = 10
Using the pattern from above, determine the value of x in the equation below:
2(x + 3) = 8
Flexibility:
In the problem above, Student AJ divided by 2 first, while Student BJ argues that the first step is
to distribute the 2. Which student is correct and why?
Timely Mathematical Interventions (TMI)—PIMSER 2015
Page 3
Topic: Multi-Step Equations
General Question:
10x + 5 = 5x + 25
Reversibility:
Joe Momma’s cell phone bill was $95.00. Each minute used was $0.10. Each text message sent,
cost $0.20. What possible call and text combinations could total $95.00?
Generalization:
Explain the process used to find the value of x.
7x = 3x + 84
-4x = 2x – 24
144 – 12x = 4 – 2x
Flexibility:
The telephone company offers two types of service:
Plan A (per month)
Unlimited call $18.50
Plan B (per month)
Flat rate of $6.50 up to 40 minutes
$0.10 per minute after 40 minutes
How many minutes would you have to use the phone each month to make Plan A the best
option?
Timely Mathematical Interventions (TMI)—PIMSER 2015
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