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Exploring the Standards for
Mathematical Practice using
the Shell Centre Lessons
Katey Arrington &!
Brian Newsom, Dana Center!
1
Lesson 13:
Sorting Equations and Identities
2!2
Always, Sometimes, or Never
True?
(x + 2)(y + 2) = xy + 4
3!3
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Always, Sometimes, or Never
True?
(x + 2)(y + 2) = xy + 4
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4
4
Always, Sometimes, or Never
True?
(x + 2)(x – 2) = x2 + 4
5!5
Always, Sometimes, or Never
True?
•  In your groups, discuss the placement of each equation card.
Justify your answer to your partner(s).
•  If you think the equation is sometimes true, you will need to
find values of x for which it is true and values of x for which it
is not true.
•  If you think the equation is always true or never true, you will
need to explain how we can be sure that this is the case.
•  Another member of the group should then either explain that
reasoning again in his or her own words, or challenge the
reasons you gave.
•  When the entire group agrees, place the card onto your chart.
Write the reason for your choice of category with the card.
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6
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Lessons Reflect CCSSM
Support for Teachers
•  Tasks are aligned to content standards at the
cluster heading level
•  Tasks are aligned to Standards for Mathematical
Practice
7!7
Design of the Lessons
The lessons include
•  Problems for students to solve
•  Samples of student work so students can
•
analyze and compare different approaches
•
diagnose misconceptions of other students
•  Questions for students to discuss in small
groups or as a class
8!8
Design of the Lessons
Support for Teachers
•  Detailed guidance on
•
ways to interpret student responses
•  providing appropriate interventions
•  Solutions to the tasks
9!9
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Formative Assessment Lessons
Two Kinds
•  Concept-focused lessons - which focuses on
assessing and developing conceptual
understanding
•  Problem-focused lessons - which focuses on
the application of previously learned
mathematics to non-routine problems
10
10!
How to Use These Lessons
Suggestion
Concept-focused lessons should be used:
•  every two weeks over one or two class
periods.
•  in the middle of a unit to gauge and/or
improve students’ understanding.
11
11!
How to Use These Lessons
Suggestion
Problem-focused lessons should be used:
•  from time to time throughout the year to
connect all the mathematics learned.
•  to assist students in understanding
practical situations.
12
12!
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To access Shell Center Lessons
http://udlnonline.ning.com
or
http://map.mathshell.org/materials
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13!
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