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Differentiation/Feedback in
Junior Math
Marian Small
February 2015
Primary strategies for DI
•  Open questions
•  Parallel tasks
Basic Principles of DI
-  Focus on big ideas
-  Choice
3
A Big idea
-  Rather than thinking about what we teach
in terms of topics, we can always have big
ideas in the background.
-  They connect ideas across and within
grades.
4
A Big idea
-  These big ideas provide the framework in
which to differentiate.
-  They also help students and teachers
build important connections.
5
An open question
-  List 5 possible fractions that describe this
diagram.
6
For example…
- 
- 
- 
- 
Could []/7 have been used?
Could []/4 have been used?
Could []/2 have been used?
Could 4/3 have been used?
7
For example…
-  3/7 is part of a whole meaning.
-  3/4 is part of a set meaning
-  2/4 as ½ is equivalent fractions.
-  4/3 is a ratio (of top area to
bottom area
- 7/6 is a ratio (full amount compared to
one hexagon) and improper fractions
8
For example…
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You have allowed students to think in:
Parts of sets
Parts of wholes
Changing the whole or using ratios
Improper fractions
Equivalent fractions
9
One more example
-  You want to find out what students
know about measurement formulas.
-  You might ask students to chose two
of these shapes and create those
shapes with an area of 15 square
units:
-  A rectangle
a parallelogram
-  A triangle
A trapezoid
10
Possible solutions
4
4
2
2
-  A rectangle
-  A triangle
A parallelogram
A trapezoid
2
4
2
4
6
11
Providing choice
-  You just saw providing choice by either
using an open enough question that
there is significant choice in how to
respond OR
-  Two different, but parallel, tasks and
the student chooses the one to work
on.
12
•  In open tasks, you pose a single question
that evokes a broad range of responses at
many levels.
•  For parallel tasks, you pose two different
questions at different levels but tied in
terms of the big idea to which they relate
and their context.
13
Grade 3 or 4 (or 5 with
decimals)
•  Use 16 base ten blocks to represent a
number. What could it be?
14
Maybe
• 
• 
• 
• 
• 
88
907
439
547
286
16
52
133
106
313
15
Samples
•  ___ x ___ is ALMOST 400.
•  What are they?
16
Samples
• Choose a denominator.
It has to be the same for both fractions.
Name a fraction between 4/[] and 5/[].
17
Samples
•  When you multiply two numbers, one of
the digits in the answer is the same as one
of the digits you started with (e.g. 4 x 6 =
24).
•  What could the two numbers be if you
don’t use 4?
18
Maybe
•  9 x 10 = 90
•  15 x 5 = 75
•  38 x 6 = 228
19
Samples
•  A shape has a perimeter of 40 cm. What
does it look like and what are some of its
other measurements?
20
Maybe
•  It could be
3
6
17
14
6
10
13
8
8
8
13
14
21
Samples
22
Samples
23
Parallel tasks
•  Example:
•  Choice 1: A blue pattern block is 1/3 of a
whole. What could the whole look like?
•  Choice 2: A blue pattern block is 2/3 of a
whole. What could the whole look like?
Solutions
•  Maybe
•  Choice 1:
Solutions
•  Maybe
•  Choice 1:
Solutions
•  Maybe
•  Choice 1:
Solutions
•  Maybe
•  Choice 2:
Solutions
•  Maybe
•  Choice 2:
Common questions
•  Is the whole bigger or smaller in area than
the blue pattern blocks? Why?
•  Is it more or less than double the area of
the blue pattern blocks? How do you
know?
Common questions
•  Could your whole have actually been
made of a single colour of block? What
colour(s)?
•  What fraction of the whole is not covered
by the blue pattern blocks?
Or maybe
•  Choice 1: Create a rectangular prism with
a volume of 100 cm3.
•  Choice 2: Create a triangular prism with a
surface area of 100 cm3.
Common questions
•  Could your prism be tall?
•  Did it have to be?
•  Once you knew the height, how did you
find the area of the base?
•  Once you knew the area of the base, how
did you get all the missing dimensions?
Or maybe
•  Choice 1: An apartment building has 19
floors. Each floor has 17 windows. How
many windows are there?
•  Choice 2:An apartment building has 9
floors. Each floor has 25 windows. How
many windows are there?
Common questions
•  Are there more than 200 windows? Why?
•  Is the number of windows odd or even?
Why?
•  Do you with there had been another floor?
•  How did you calculate….
Your questions?
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