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Math for All: Differentiating Math

Instruction

Lu Ann Weynand

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Differentiated Instruction
Instruction designed to meet differing
learners needs

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Instruction Can be Differentiated

by Focusing on.

Content
Process
Product
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Which number does not

belong? Why?
4, 16, 36, 48, 64, or 81

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4
Its only one number. The rest are two.
Its the only number less than ten; the rest are
between ten and one hundred.
Its only one digit; the rest are two-digit
numbers.
Its the four!
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48
Its the only one that is not a square
number.

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81
Eighty-one is an odd number. All the others
are even numbers.
Eighty-one is not divisible by four. All of the
other numbers are multiples of 4.
You cant get to 81 with just these numbers.
64 16 = 4
64 4 = 16
48 16 + 4 = 36
64 16 = 48
16 x 4 = 64

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4
Its only one number. The rest are
two.

81
Eighty-one is an odd number. All the
others are even numbers.

Its the only number less than ten;

the rest are between ten and one
hundred.

Eighty-one is not divisible by four.

All of the other numbers are
multiples of 4.

Its the four!

You cant get to 81 with just these

numbers.
64 16 = 4
64 4 = 16
48 16 + 4 = 36
64 16 = 48
16 x 4 = 64

48
Its the only one that is not a square
number.

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How is the task Which Does Not Belong? like

your students know and how they solve
problems? How is it different?

What was the purpose of having you draw lines

under your work as we moved through the
processing of the problem? How did your thinking
grow and change as you listened to your peers?

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Scaffolding
Temporary supports that allow students to
would be unable to complete

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Some ways learning can be

scaffolded include:

Teaching Strategies
Questioning Strategies
Student Collaboration
Whole-group Discussions
Making Connections Explicit
Graphic Organizers
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How are a square and cube..

Same

Angle
Cube
Edge
Square

Different

Word Bank
face
degrees
side
vertices

three-dimensional
rectangular prism
two-dimensional
vertex
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Casting a Wider Net

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Ways in Which Tasks Can Cast a

Wider Net
Allow students control over difficulty level

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Ways in Which Tasks Can Cast a

Wider Net
Allow students control over difficulty level

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Billie has won a \$25.00 shopping spree to the

museum and must spend it all. If he doesnt
spend the \$25.00 he does not receive change
back. Use the list below, determine which items
Billy can buy so that he spends all \$25.00.
Find as many different solutions as you can.
\$3.00
Origami Paper
Gem Magnet
Prism
Koosh ball

\$4.00
Kaleidoscope
Magnifying Glass
Inflatable shark
Sunprint Kit

\$5.00
Dinosaur Kit
Inflatable globe
Glow stars
Stuffed animal
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Ways in Which Tasks Can Cast a

Wider Net
Allow students control over difficulty level
Provide students with number story and with
answers -- then have students create the
questions

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Number Story:
Sabina and Mike ran each day this week.
Each day Sabina ran 3 miles in 30
minutes. Mike ran 6 miles in 72 minutes.
Here are the answers: 42, 2, 294, 3 1/2
What could be the questions?

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Ways in Which Tasks Can Cast a

Wider Net
Allow students control over difficulty level
Provide students with number story and with
answers -- then have students create the
questions
Use open-ended probes

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Open-Ended Probes
How do you describe a cube to someone who
has never seen one?
The answer is 87. What could the question
be?
How is measurement used in your home?
How might we write numbers if we didnt have
zeroes?
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Ways in Which Tasks Can Cast a

Wider Net
Allow students control over difficulty level
Provide students with number story and with
answers -- then have students create the
questions
Use open-ended probes
Allow students to show their understanding in
different ways
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Imagine you are trying to help someone

understand what three-tenths means.
What pictures could you draw to be helpful?
You can draw more than one picture. Lets see
how many different pictures we can make.

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Remember, in order to provide for a

wider range of students, teachers
can cast a wider net by:
Allowing students some control over the
difficulty level
Transforming problems so they allow for
more solutions or a wider range of
responses
Encouraging the use of multiple models
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It is important to remember that differentiated

mathematics instruction is most successful when
teachers:
Believe that all students have the capacity to succeed at learning;
Recognize that diverse thinking is an essential and valued resource;
Know and understand mathematics and are confident in their ability
to teach mathematical ideas;
Develop strong learning communities in their classrooms;
Focus assessment; and
Support each other in their efforts
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Planning for Differentiated Instruction

Questions to guide our Thinking
What is the mathematics I want my students
to learn?
What do my students already know? How can
I build on their thinking?
Have I thought about interests, learning
styles, use of language, cultures, and
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Planning for Differentiated Instruction

Questions to guide our Thinking
How can I ensure that each student
experiences challenges?
How can I scaffold learning to increase the
likelihood of success?
In what different ways can my students
demonstrate their new understanding?
Are there choices students can make?
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In the end, all learners

They have that in common
because they are young
humans.
How they need you, however, differs. Unless we
understand and respond to those differences, we fail
many learners.
Carol Ann Tomlinson

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