the teacher might say, “That’s a good
answer. Can you think of anything else?”
Parallel tasks focus on the same big
ideas but have different levels of difficulty,
Creating Open Questions
Teachers create open questions by
allowing for a certain level of ambiguity.
2 For example, rather than asking
for two numbers that add up to 37,
a teacher could ask for two numbers
that add up to about 40. Or instead of
asking for the third angle size in a triangle with one angle of 20° and another
of 38°, a teacher could ask for three
possible angle sizes in a triangle with at
least one narrow (or sharp) angle.
Students may initially be
uncomfortable with ambiguity in a
subject that has, until now, seemed so
clear-cut. However, they almost always
warm up to and appreciate the latitude
that this ambiguity allows. Four strategies for creating open questions follow.
Strategy 1: Start with the answer. A
teacher can take a straightforward
question and present it backward. For
example, instead of asking, “What is
23 + 38?” a teacher could say, “I added
two numbers. The sum is 61. What
numbers might I have added?”
Students can provide multiple
responses, including 60 + 1, a simple
and straightforward answer that might
be accessible to students who have
struggled with more closed questions.
Teachers can use Strategy 1 to probe
student thinking in computation or
measurement. They might ask,
n The area of a rectangle is 20 square
inches. What might be its length and width?
thus taking into account the variation
in student readiness.
Strategy 2: Ask for similarities and
differences. Asking students how two
things are alike and how they are
different can provide teachers with
valuable assessment for learning information. A teacher might ask,
n How are the numbers 4 and 9 (or 350
and 550 or 100 and 1,000, and so on)
alike? How are they different? (Students
might point out whether the numbers are
even or odd or divisible by numbers other
than themselves.)
n How is the formula for the perimeter
of a rectangle like the formula for its
area? How is it different? (Students might
indicate that both formulas involve using
values for the length and width of the
rectangle, but that one involves addition
and the other doesn’t.)
n A pattern starts at £, and you add D
each time. Choose values for £ and D.
Will 40 be in your pattern? Explain.
Strategy 4: Ask students to create a
sentence. Asking students to create a sentence using specific mathematics vocabulary is a good way to assess student
understanding of the vocabulary and to
foster creativity. A teacher might ask,
n Use the words even, more, and always,
and the number 10 in a sentence. (
Students might say, “If you add 10 to an
even number more than 10, the answer
is always even and always has at least two
digits.” )
n Use the words length, width, formula,
and the number 10 in a sentence.
n Use the words increasing, decreasing,
pattern, and the number 18 in a sentence.
n A 3D shape has 8 vertices. What might
it look like? (Students might suggest a
cube.)
n How are these two patterns alike? How
are they different?
4, 8, 12, 16, 20, . . .
4, 7, 10, 13, 16, . . .
Strategy 3: Allow choice in the data
provided. Students are empowered by
the opportunity to choose one or more
numbers with which to work. For
example, teachers might ask,
n Choose a number for the box on the
left. What is the length of the hypotenuse
of this right triangle?
n The 10th term in a pattern is 36. What
might the 8th and 9th terms be? Describe
the pattern. [Students might think
36 = 26 + 10, so the pattern might start
27 ( 26 + 1), 28 ( 26 + 2), and so on, with
the students realizing that the 8th and 9th
terms are 34 ( 26 + 8) and 35 ( 26 + 9).]
12
n Choose a value for the fourth number
in the series that follows and calculate the
mean: 4, 5, 6, ___.
Parallel Tasks
Another approach to differentiation is
using parallel tasks. Although test creators think of parallel tasks as having
similar levels of difficulty, in this
context parallel tasks focus on the same
big ideas but have different levels of
difficulty, thus taking into account the
variation in student readiness.
For example, using multiplication to
simplify the counting of equal groups is
useful no matter the size of the numbers
involved in the computation. Parallel
tasks might allow students who are
ready to deal with only simpler values to
use those simpler values, whereas students who are ready for more complex
work could use more challenging
values. Common questions that focus
