Rich Questions to
Support All Learners
Marian Small
October 2016
Suppose I ask
u
There were 24 kids in the class.
u
Each one paid $15 for the field trip.
u
How much was collected?
u
Explain your thinking.
The problem is…
u
For some kids these numbers are too much and
they are excluded.
u
For some kids, this is not much of a problem.
u
So how do we change it up to be more useful to
more kids?
Maybe
u
There were more than 15 kids in a class.
u
Each one paid more than $10 for the field trip.
u
How much are you sure was TOO LOW?
u
How much is TOO HIGH?
u
How much might have been collected?
u
Explain your thinking.
What is great about this is…
u
That kids can pick numbers they can be successful
with, but see that the process is the same no
matter what.
u
Even the too low and too high estimates leave a
lot of latitude for all students.
u
But really strong students are likely to pick
tighter “too low” or “too high” estimates to
challenge themselves.
Agenda
u
Why use open questions?
u
Open questions in number
u
Open questions in measurement
Math is tricky
u
We learned math believing that all kids need to
be doing the same skill on the same day, when we
know this is unrealistic.
u
But we didn’t see options.
Open questions
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Provide a viable option for differentiation.
u
One question can meet the needs of many
learners because the question is not overly tight
and so benefits a broader range of students.
A good open question
u
engenders thinking, not repetition.
u
focuses on important math.
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allows entry to all learners.
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leads to rich mathematical conversation.
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extends strong learners and
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provides LOTS of assessment for learning info.
Where they belong in a lesson
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A minds-on open question is not a long activity,
but engenders discussion that will put students in
the right frame of mind for the action task.
Where they belong in a lesson
u
An open action question can be a “main” activity.
Where they belong in a lesson
u
An open question might suit consolidation if its
focus is to bring out the important math.
Open questions in number
Grade 4 Minds- ON
u
You could ask students to just read numbers like
4002
u
3017
u
2012, OR…
Grade 4 Minds On
u
Whole Numbers
You could ask
u
Which fractions are less than ½?
u
3/10
3/3
1/8
2/3
Or
You could ask
u
Which fraction in each pair is greater?
u
1/8
or 1/10
u
4/5
u
3/5 or 2/3
u
4/7 or 6/11
or 4/9
Or you could ask
You could ask
u
Add these mentally and tell how you did it: 39 +
29.
Or you could ask
You could ask
u
You have 13 quarters, and 5 nickels, 5 dimes and 5
toonies.
u
How much is it worth?
Or you could ask
You could ask
u
What is double 35?
Or you could ask
You could ask
u
A cookie costs 45¢. How much would 9 cookies
cost?
Or you could ask
Action Questions – Grade 5
u
You could ask
u
Order these numbers from least to greatest:
u
4123
51 105
38 612
4313
Or you could ask
You could ask
u
Suppose the hexagon pattern block is 1.
u
Figure out the fraction name for each block.
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Model 11/3 and 7/2.
Or you could ask
You could ask
u
List some fractions equivalent to 7/4.
Or you could ask
You could ask
u
Represent 4.12 in three different ways.
Or you could ask
You could ask
u
You buy 2 shirts that cost $29 each and a pair of
pants that cost $49. Use mental math to get the
total cost.
Or you could ask
You could ask
u
What is the change if you give the clerk $20 to
pay for…..
Or you could ask
Grade 6 consolidation questions
You could ask
You could ask
You could ask
You could ask
You could ask
Starting with a standard question and
opening it up
u
Now you start with a few standard number and/or
operation questions and try to open them up to
work for more students and to create richer
conversations.
Sometimes open questions come from
thinking about what you really care about
u
Suppose I care that students realize that when
you convert from a large unit to a smaller one,
the number of units increases.
I might ask
But suppose the focus is on solving
problems about measurements
Suppose the focus is on area formulas
Suppose the focus is on volume
Suppose the focus is on perimeter
Suppose the focus is on considering both
perimeter and area
Suppose the focus is on considering both
perimeter and area
Suppose the focus is on measuring time
Suppose the focus is on measuring time
Suppose the focus is on measuring
length
Suppose the focus is on measuring mass
or capacity
Strategies You Can Use
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Start with the answer. Students create the
question.
For example..
u
The answer is 200.
u
What might the question have been?
For example..
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The answer is rhombus.
u
What might the question have been?
Alike and Different
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How are adding and multiplying alike? Different?
u
How is adding decimals like adding whole
numbers? How is it different?
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How are fractions and decimals alike? Different?
Choose your own values
u
Choose two different pairs of two-digit numbers.
u
Multiply them different ways.
u
Tell how you multiplied each pair and why you
used different ways.
Choose your own values
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The length of a rectangle is more than double the
width.
u
Choose the length and width and figure out the
area.
Use “soft” words
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You add two decimal numbers and the answer is
slightly less than 7.
u
What might they be?
Use “soft” words
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You divide number A by number B.
u
The answer is a little more than number B.
u
What could the numbers have been?
Choose three expectations in
measurement or pattern and algebra
u
Apply each of the strategies and try to create
open questions that you think suit many students.
So…
u
What are some of the concerns you still have
about using open questions?
u
Let’s talk them over.
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