Download College Board Geometry Statement

Geometry on the SAT
Prepared by College Board Assessment Design and Development (April 28, 2016)
On the SAT Math test, questions that require geometry-based skills and
abilities take many forms: questions may provide a figure and ask test
takers to use geometric properties to find missing information, or they
may provide given information and ask the test-taker to identify
another statement that must be true. Teachers prepare test takers for
these questions by including a rich, coherent set of geometry
experiences in their instruction. Secondary school educators build upon
the foundation of concepts, definitions, and theorems related to lines,
angles, circles, and triangles (and other polygons) which begins in
elementary school. Advanced geometry experiences build conceptual
understanding of geometry content while highlighting connections
between geometric concepts with content outside of geometry (e.g.
algebra and functions). Geometry, and indeed mathematics in general,
is a very connected subject and test takers who grasp these connections
have very powerful understandings that create a deep, flexible type of
knowledge that gives them multiple entry points to solve problems in
unfamiliar situations.
In the following two SAT examples, there are several different geometry
theorems that a test taker may utilize while formulating a problem
solving strategy.
Example 1:
Connections
There is no prescribed process to solve
Example 1. Instead, students draw from
prior knowledge and experience to apply
theorems such as:
 Vertical angles have the same
measure.
 When parallel lines are cut by a
transversal, the alternate interior
angles have the same measure.
 If two angles of a triangle are
congruent to (have the same
measure as) two angles of another
triangle, the two triangles are similar.
 The Pythagorean Theorem.
 If two triangles are similar, then all
ratios of lengths of corresponding
sides are equal.
 If point E lies on line segment AC,
then AC = AE + EC.
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Example 2:
Foundations
Problem solving in geometry-based items
requires foundation knowledge of concepts
and definitions. To solve this problem,
students must understand the terms: area,
square, regular hexagon, and side length.
Geometry experiences also help test takers enhance existing skills and
abilities. For example, when graphing geometric figures on the xy-plane,
test takers revisit algebra concepts like points, lines, slopes, and
intercepts. Geometry concepts like translations and rotations also
reinforce connections of parallel and perpendicular lines. Therefore,
geometry experiences provide additional benefits, such as multiple
entry points into items, for SAT test takers. Another example of an SAT
question that shows how geometry experiences enhance existing skills
and abilities is shown in Example 3.
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Example 3:
Multiple Entry Points
Making connections between geometry
and algebra deepens student
understanding and provides multiple
points of entry into a problem.
A student may choose to identify two
coordinates on line, shift each of the points
over 5 and up 7, and then calculate the
slope.
However, realizing that a translated line is
parallel to the original line and therefore
retains its original slope will save time and
reduce the chance for error.
The Official SAT Study GuideTM contains four SAT practice tests. To
illustrate the benefits of a rich, coherent set of geometry experiences,
some questions on the first two practice tests are classified below as (1)
geometry-based questions or (2) questions in which geometry
experiences enhance test-takers’ skills and abilities on non-geometry
questions.


Practice Test 1 geometry-based questions include No Calculator
#17 and Calculator #3, #24, and #35. Additionally, an
understanding of underlying geometric structure will benefit
test takers on No Calculator questions #8, #12, and #19 and
Calculator questions #2, #4, #26, and #27. Therefore, geometry
experiences will aid test takers on 11 questions, or 19% of this
practice test.
Practice Test 2 geometry-based questions include No Calculator
#8, #18, and #19 and Calculator #24, #30, and #36. Additionally,
an understanding of underlying geometric structure will benefit
test takers on No Calculator questions #6 and #9 and Calculator
questions #3, #6, #22, #23, #28, #31, and #33.
Therefore, geometry experiences will aid test takers on
14 questions, or 24% of this practice test.
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As shown, there are many questions on which a test taker will benefit
from geometry experiences. Not only are geometry concepts part of the
math that matters most on the SAT, but they also help test takers
improve their depth of understanding of additional math that matters
most. Although there are only a few geometry-based questions on the
SAT, test-takers can expect that 19%–24% of the test will utilize skills
they learned or developed through geometry experiences. Test takers
who have invested time by developing geometry skills related to
procedural skill and fluency, conceptual understanding, and ability to
apply and model what was learned will increase their chance of success
on the SAT and in future coursework.
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