Enduring Understandings
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Principles of similarity are an integral part of the world
around us, especially in the areas of architecture, art and design
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Scaling makes things bigger or smaller, but it maintains
the relationship between parts
·
Geometric figures can change position and maintain the same
attributes in a plane (transformations)
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Essential Questions
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What
does twice as big mean? What are we talking about?
·
When figures are similar, how are the lengths, area and
scale factors related?
·
How does the transformation of a geometric figure affect
its attributes?
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GLEs: 1, 4, 5, 9, 10, 11, 12, 13, 20, 21, 22,
24, 25, 27, 28, 29, 30, 39, 40, 41
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Students will know…
·
Similarity (when two objects are identical except for
proportional differences in lengths and areas.)
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Enlargement (a copy of a given figure that is
proportionately larger)
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Image (the resulting figure when a given figure is enlarged
/stretched or shrunk)
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Correspondence (given a figure and an image of it, knowing
which segments or vertices in the original figure correspond to segments or
vertices in the image)
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Transformation (changing a figure in a consistent way)
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Transformation rule (defines how a figure is to be
transformed, often given in (x,y) coordinate form)
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Scale factor (number multiplied by the dimensions of the
original figure to transform it into an image similar to the original figure)
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Reptiles (figures made with copies of a given figure)
·
Map scales (linear scales given on maps that can be used to
find distances and areas)
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Similar triangles (triangles which have congruent
corresponding angles)
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Ratio (comparison of two quantities that gives the scale
factor between them)
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Students will be able
to…
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Enlarge and shrink plane figures (with rubber-band
stretcher and scale factors)
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Subdivide figures (to determine scale factors)
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Use scale maps, diagrams, and figures (use scale factors to
find actual distances/areas with scale maps, diagrams, and similar figures)
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Solve problems using properties of similar triangles
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Compute applications of similarity
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Identify and draw angles, circles, diameters, radii,
attitudes and two-dimensional figures with given specifications, including
their reflections and translations on a coordinate grid
·
Locate and plot coordinates in all four quadrants
(including missing vertex in a parallelogram)
·
Recognize and compute equivalent representations (fractions,
decimals, and percents)
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Compute fractions and decimals (four basic operations)
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Compare, order, and convert measurements and area using
common reference points (within and between US and metric systems)
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Recognize that pi is the ratio between the circumference
and diameter of any circle
·
Apply of circle attributes in real life problems (i.e.
radius, diameter, circumference, and area)
·
Apply knowledge of triangles (measures of interior angles
add up to 180°)
·
Model and explain how scale change in linear dimensions
affects perimeter/circumference and area of a two dimensional figure
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