Sample tasks from:
Geometry Assessments
Through the Common Core
(Grades 6-12)
A resource from
The Charles A Dana Center at
The University of Texas at Austin
2011
About the Dana Center Assessments
More than a decade ago, the Charles A. Dana Center began work on collections of assessment tasks
that could be used by teachers at many grade levels to enable them to assess student learning
continually as they enacted mathematics instruction. These assessments, developed in collaboration
with mathematics educators, are designed to make clear to teachers, students, and parents what is
being taught and learned about the most central mathematical concepts at each grade or in each
course. Published by the Dana Center as a series of books (available for order here:
http://www.utdanacenter.org/products/math.php), these collections of assessments eventually
encompassed tasks for middle school, Algebra I, Geometry, and Algebra II.
These tasks have been used and tested by tens of thousands of educators and their students. Now
the Dana Center has published a selection of these tasks in new editions: 118 tasks in Algebra
Assessments Through the Common Core (Grades 6-12) and 57 tasks in Geometry Assessments
Through the Common Core (Grades 6-12).
The alignment to the Common Core State Standards for Mathematics of 164 existing Dana Center
mathematics assessment tasks, and the development of 11 new tasks aligned to the standards, was
made possible by a grant from Carnegie Corporation of New York and from the Bill and Melinda
Gates Foundation. (Gates Foundation grant number OPP-48458 and Carnegie Corporation of New
York grant number B 8312.) The statements made and views expressed are solely the responsibility
of the authors.
We thank the Gates Foundation and Carnegie Corporation of New York for their support of
Improving Mathematics and Literacy Instruction at Scale, a collaboration between the Aspen
Institute (literacy) and the Dana Center (mathematics). We used funds from this grant to align
mathematics assessments to the "Standards for Mathematical Content" and "Standards for
Mathematical Practice" of the Common Core State Standards for Mathematics and to publish these
assessments to this UDLN website. We thank these funders for their generous support of this work.
To support the adoption of the Common Core State Standards for Mathematics, the Dana Center is
pleased to make available here two sample tasks from Geometry Assessments Through the
Common Core (Grades 6-12): “Whitebeard’s Treasure” and “Walking the Archimedean Walk.”
About Whitebeard’s Treasure
Standard for Mathematical Practice #3 calls for students to construct viable arguments. Students
should be able to use definitions in constructing arguments and justify their conclusions. In this
task, students explore a context involving two quadrilaterals in a coordinate plane. Students
construct the second quadrilateral from the first following specific directions, and are asked to
describe the new quadrilateral. Students must use the definitions of special quadrilaterals to
identify the type of quadrilateral they have created, and justify their answer using two different
mathematical arguments.
About Walking the Archimedean Walk
Standard for Mathematical Practice #7 calls for students to look for and make use of structure.
Specifically, students are expected to look closely for patterns and to make use of those patterns. In
this task, students recreate Archimedes’s approach to using patterns to investigate the value of !
using a series of polygons inscribed in circles without using measurement. Students describe how
patterns they see in the relationships between the diameter and the perimeter/circumference
approach the value of !.
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the Common Core (grades 6-12), 2011
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at The University of Texas at Austin
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the Common Core (grades 6-12), 2011
*OHW[LY!*VVYKPUH[L.LVTL[Y`
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at The University of Texas at Austin
*OHW[LY!*VVYKPUH[L.LVTL[Y`
Ch 1–43
Geometry Assessments Through
the Common Core (grades 6-12), 2011
1
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at The University of Texas at Austin
Ch 1–44
Geometry Assessments Through
the Common Core (grades 6-12), 2011
*OHW[LY!*VVYKPUH[L.LVTL[Y`
1
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at The University of Texas at Austin
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Geometry Assessments Through
the Common Core (grades 6-12), 2011
*OHW[LY!*VVYKPUH[L.LVTL[Y`
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The Charles A. Dana Center
at The University of Texas at Austin
*OHW[LY!*VVYKPUH[L.LVTL[Y`
Ch 1–47
Coordinate
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Geometry Assessments Through
the Common Core (grades 6-12), 2011