Download 2015-2016 8th Grade 4th Quarter Mathematics Scope and Sequence

2015-2016 8th Grade 4th Quarter Mathematics Scope and Sequence
Unifying Concept: Geometry and Bivariate Data
Mathematics Content Focus:
Mathematical Practice Focus
Students apply their knowledge of triangles to various
Mathematically Proficient Students…
2. Reason abstractly and quantitatively.
real-world 2-D and 3-D situations. Students also find the
3. Construct viable arguments and critique the
volume of objects, but also missing dimensions such as
reasoning of others.
the radius or height.
5. Use appropriate tools strategically.
Students recognize special angles and identify missing
6. Attend to precision.
angle measures of parallel lines and transversals.
Students will use transformations on the coordinate plane 8. Look for and express regularity in repeated
reasoning.
to identify similar and congruent figures.
Students will interpret data from two way tables.
8.G.A.1a-c
8.G.A.2
8.G.A.3
8.G.A.4
8.G.A.5
8.SP.A.4
Target Standards
Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
Understand that a two-dimensional figure is congruent to another if the second can be obtained
from the first by a sequence of rotations, reflections, and translations; given two congruent figures,
describe a sequence that exhibits the congruence between them.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures
using coordinates.
Understand that a two-dimensional figure is similar to another if the second can be obtained from
the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them.
Use informal arguments to establish facts about the angle sum and exterior angle of triangles,
about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion
for similarity of triangles. For example, arrange three copies of the same triangle so that the sum
of the three angles appears to form a line, and give an argument in terms of transversals why this
is so.
Understand that patterns of association can also be seen in bivariate categorical data by
displaying frequencies and relative frequencies in a two-way table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use
relative frequencies calculated for rows or columns to describe possible association between the
two variables. For example, collect data from students in your class on whether or not they have a
curfew on school nights and whether or not they have assigned chores at home. Is there evidence
that those who have a curfew also tend to have chores?
Quarter Major Clusters
Arizona considers Major Clusters as groups of related standards that require greater emphasis than some of the
others due to the depth of the ideas and the time it takes to master these groups of related standards.
8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software.
Essential Concepts
Essential Questions
 Translating a point, line, line segment or angle does
 What effect do translating, rotating and reflecting
not change any attributes of that object, it will just
have on a point? Line? Line segment? Angle?
move the object to a new location.
 Why does doing a sequence of rotations,
 When a point is reflected across a line that reflected
reflections, and translations create congruent
point stays the same distance from the line of
figures?
reflection as the original point.
 Why does a dilation create a similar figure as
 When a line segment or angle is rotated, reflected or
opposed to a congruent figure?
translated, the length of that line segment and
 What effect does a dilation, translation, rotation
measure of the angle will not change.
and reflection have on a two-dimensional figure
 A sequence of rotations, reflections, and/or
on the coordinate plane?
8/28/2015 9:49 AM
Curriculum Instruction and Professional Development Math Department
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2015-2016 8th Grade 4th Quarter Mathematics Scope and Sequence
translations to a two-dimensional figure will create a
 How do you determine if two figures are similar?
congruent two-dimensional figure.
 How do determine if a pair of angles created by
 An image is the figure created by doing a
parallel lines cut by a transversal will be
transformation on the pre-image (or original object).
congruent or supplementary?
 A dilation of a two-dimensional figure will create an
 Describe how parallel lines cut by a transversal
image that is a similar figure to the original by a
can be used to prove that the interior angles of a
multiplicative relationship.
triangle will add up to 180o.
 A translated, reflected or rotated two-dimensional
figure will create an image that is a congruent figure to
the original.
 Similar figures are produced by doing a sequence of
rotations, reflections, translations AND dilations. The
sequence of transformation must include dilation in
order to produce a similar figure.
 Similar figures are figures that have the same angles
and proportional side lengths.
 Parallel lines cut by a transversal will create pairs of
angles that are either congruent or supplementary.
 The relationships between the angles made by parallel
lines cut by a transversal can be used to informally
prove that the interior angles of a triangle will add up to
180o.
8.SP.A Investigate patterns of association in bivariate data
Essential Concepts
Essential Questions
 Data that is collected using two variables is called
 What are two ways to represent and/or display
bivariate data.
bivariate data and why would you use one as
opposed to the other?
 Scatterplots and two-way frequency tables are used to
show patterns of association and relationships
 What information will each of the two
between bivariate categorical data.
representations tell us about the bivariate data?
 Scatterplots can suggest a linear
 How do you decide if a line of best fit is a good
association/relationships.
model to determine the relationship of bivariate
data?
 If a scatterplot suggests a linear relationship, then a
 What can a line of best fit tell us about bivariate
line of best fit can be drawn and a linear equation can
be created to model the relationship between the
data?
bivariate data.
 An equation of a line of best fit can be used to interpret
and solve problems in the context of bivariate
measurement data.
8/28/2015 9:49 AM
Curriculum Instruction and Professional Development Math Department
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