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Differentiating Math
Using Assessments and Extension Menus
to compact, accelerate, and differentiate
math instruction.
What is today’s objective?
To share with you a strategy for
differentiating instruction in Math using
pre-assessments and extension menus
We will be showing you:
Hardest 5 quizzes
Math Extension Menus
Ideas for Classroom Management and
Environment
What is the Hardest 5 quiz?
 Pre-assessment tool used to check a
student’s mastery of a Math concept
 5 most challenging questions from the lesson
 5-minute quiz time (more time-consuming
concepts such as long division or
multiplication with greater numbers may
require another 1 or 2 minutes)
 To test-out, students must earn 100%
 Two forms: one Hardest 5 quiz given daily or
a set of Hardest 5 quizzes on the next week’s
lessons
How do I use the
Hardest 5 Quiz?
 The Hardest 5 quiz is used to
assess prior knowledge of students.
 Students who show mastery on a
math concept can “test out” for the
day and work on math extension
activities.
 If a whole class passes the hardest
5, this data can be used to compact
or accelerate a lesson (by simply
doing a quick review, for example.)
When do I give the Hardest 5 ?
• Weekly:
• On FRIDAY
– Give the Hardest 5
Quiz that covers the
lessons you will be
teaching the
following week.
• Daily:
• Before the lesson:
– Give the Hardest 5 Quiz
that covers the lesson
you will be teaching that
day.
• After the Lesson:
– Give the Hardest 5 Quiz
that covers the lesson
you will be teaching the
following day.
What does a daily lesson
look like?
• Lesson
– Teach math lesson to class
– All students must listen and take notes
• Structured Practice/Guided Practice
– Students who have tested out will at this time be
excused to work on their Scholar Menu
– Students that have not tested out will continue with
the practice phase of direct instruction.
• Expect classroom transition here!
• Independent Practice
– Students that struggled with the guided practice will
meet with the teacher in small groups for additional
support with the lesson.
– Students who understood the lesson will move on to
independent practice.
– If students finish independent practice quickly they
can move on to Challenge problems that have been
assigned.
– Hardest 5 students will continue to work on their
Scholar Menu in their small groups.
What are Extension Activities?
The purpose of Extension Activities is to provide students who have
shown mastery on a math concept with opportunities to:
Extend Their Learning
Apply Mathematical Knowledge Beyond Procedures
To Connect Mathematical Knowledge to the Real World.
Extension Activities are presented on Extension
Menus, which provide an activity for every lesson in a
Unit, as well as optional activities for student choice.
How do I make Extension Menus?
Look for challenge questions / pages in
your text book.
 Supplemental Challenge activities with your
math program.
 Differentiating Instruction with Menus Math by Laurie E. Westphal
 Find real world applications for the math
concept.

What are some sample


21.2 Multiply Fractions and Whole Numbers
Think Like a Top Chef!

Find or create a recipe that contains at least 3 fractions, no mixed numbers.

Create 3 recipe cards:

First, triple the recipe (multiply every ingredient by 3). Remember, this will triple the amount
of people that the recipe will serve.

Second, rewrite the recipe for a party by multiplying everything by 8.

Third, rewrite the recipe for a banquet by multiplying everything by 24.
What are some sample activities?
Lines and Angles
Map It!

Create a road map for a fictional city. Your map should include examples of each of the following
geometric concepts:
o Point
o Line
o Ray
o Line segment
o Plane
o Right angle
o Acute angle
o Obtuse angle
o Parallel line
o Intersecting line
o Perpendicular line

Create a legend to explain where each geometric concept can be found on your
map.

Your town should be named, colored, locations should be clearly labeled, and your
map should include color where appropriate.
How do I assess Extension Activities?

Rubrics can be created to assess for:

Mathematical Understanding
 Does
the assignment show correct understanding of
the math concept?

Content
 Does
the assignment follow all directions completely
and include all necessary information?

Creativity and Effort
 Is
the assignment neat, attractive, creative, and show
effort and scholarly pride?
Classroom
Environment
How can I organize my
classroom to make Hardest 5
run smoothly?
Where do I keep a list of
Math Groups?
 Math Groups labeled and listed on a
classroom Math board (e.g. Team 1/
Team 2 with students numbers listed
under the appropriate title)
 Location suggestions: whiteboard,
sheet protector with a white paper,
pocket chart
 Other option: Math groups do not have
to be displayed; lists can written down
and kept by the teacher only
Where do I put
Math Extension Menus?
 Pocket files on the Math board or
standing file folder that the students
have access to
 Menu activity resources should be in
the same location
 Other option: Distribute the Menu to all
the students at the beginning of the
week; students keep it in a Math folder
until the end of the Unit
Where do the students who
tested out work while I am
teaching the lesson?
 Work areas should be designated in
the classroom
 Suggestions: classroom library, small
group table, computer table
 Move students in the classroom so
table groups can be made into
Extension Group work areas
 Students understand they are to be
working quietly during your instruction
Troubleshooting! How can I ensure
that Differentiation is a Success?
• Model expectations for Hardest 5 group
• Preview Scholar Menu at beginning of unit or on
Monday when test out students are posted
• Transitions - provide time (when test out students are
excused and students move to empty seats)
• High standards for Extension Menu
– Set expectations at the beginning
– Create a rubric for scholarly work
Presented by:

Bobbi Jo Benedict


Kristine Larson


[email protected]
[email protected]
Cathy Roh

[email protected]
Allen Elementary
Garden Grove Unified School District