Download Unit 13

Common Core Curriculum Map 2012-2013
Common Core Math II
Common Core Unit Name: Transformations
Unit Number: 13
Enduring Understanding:
Students will use appropriate tools to represent transformations in the plane using software or transparencies.
Students will look for and express regularity in repeated reasoning when they describe transformations as functions that take points in the plane as inputs & give
other points as outputs.
Students will look for and make use of structure as they compare transformations that preserve distance & angle to those that do not.
Student will use modeling to describe the rotations & reflections that carry a polygon onto itself (rectangle, parallelogram, trapezoid, or regular polygon).
Students will use modeling to define rotations, reflections & translations in terms of angles, circles, perpendicular lines, parallel lines & line segments.
Students will use appropriate tools as they draw the transformed figure given rotation, reflection & translation & specify the sequence used to carry figure onto
another.
Students will reason abstractly and quantitatively as they verify experimentally the properties of dilations given by a center & a scale factor.(a.) Dilation takes a line
not passing through the center of the dilation to a parallel line & leaves line passing through the center unchanged.(b.) Dilation of line segment is longer or shorter in
the ratio given by the scale factor.
Standard
G.CO.2 2. Represent transformations in the plane using, e.g., transparencies and
geometry software; describe transformations as functions that take points in the
plane as inputs and give other points as outputs. Compare transformations that
preserve distance and angle to those that do not (e.g., translation versus horizontal
stretch).
G.CO.3,3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe
the rotations and reflections that carry it onto itself.
G.CO.4 4. Develop definitions of rotations, reflections, and translations in terms of
angles, circles, perpendicular lines, parallel lines, and line segments
Essential Questions
Can I identify the different types
of transformations?
Can I describe how the
transformations of how a figure
is carried onto itself?
Can I compare the different
transformations?
Can I draw the different
transformations given specific
information?
Can I use the properties of
Pacing
Guideline
7 days
Key Academic
Vocabulary
image
preimage
isometry
reflection
line of symmetry
rotation
center of rotation
angle of rotation
rotational symmetry
translation
vector
Common Core Curriculum Map 2012-2013
Common Core Math II
dilations?
G.CO.5 5. Given a geometric figure and a rotation, reflection, or translation, draw the
transformed figure using, e.g., graph paper, tracing paper, or geometry software.
Specify a sequence of transformations that will carry a given figure onto another.
G.SRT.1 1. Verify experimentally the properties of dilations given by a center and a
scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel
line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale
factor.
G.SRT.2 2. Given two figures, use the definition of similarity in terms of similarity
transformations to decide if they are similar; explain using similarity transformations
the meaning of similarity for triangles as the equality of all corresponding pairs of
angles and the proportionality of all corresponding pairs of sides.
F.BF. 3 3. Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally)
as a polynomial function.
Suggested Resources by Unit
Geometry, McDougal Littell, 2004 edition.
Geometry Resources, McDougal Littell, 2004 edition.
http://www.insidemathematics.org/index.php/tools-for-teachers
(Problems of the month are excellent modeling problems.)
http://secmathccss.wordpress.com/secmath1/sec-math-1-year-at-aglance/sec-1-problemassessment-tasks/s1-u5-tasks/
(Culminating activity in which students design Geometric art using
transformations, circles and inscribed figures.)
Location of these resources
initial point
terminal point
component form
glide reflection
composition
frieze pattern
reduction
enlargement
translation
dilation