Download Math 4 th Quarter

8th Grade - Math
4th Quarter
Standard 1: Number Sense, Properties, and Operations
Grade Level Expectation:
1. In the real number system, rational and irrational numbers are in one to one correspondence to points on the
number line
Students should know and be Instructional & Assessment
Content Evidence
Resources
Outcomes
able to do:
Planning:
1.1a Define irrational numbers. Define irrational numbers.
1.1b Demonstrate informally
that every number has a
decimal expansion
i. For rational numbers show
that the decimal expansion
repeats eventually.
ii. Convert a decimal expansion
which repeats eventually into a
rational number.
1.1c Use rational
Use rational approximations of
approximations of irrational
irrational numbers to compare
numbers to compare the size of the size of irrational numbers,
irrational numbers, locate them locate them approximately on a
approximately on a number
number line diagram, and
line diagram, and estimate the estimate the value of
value of expressions.
expressions.
1.1d Apply the properties of
Apply the properties of integer
integer exponents to generate
exponents to generate
equivalent numerical
equivalent numerical
expressions.
expressions.
1.1f Evaluate square roots of
Evaluate square roots of small
small perfect squares and cube perfect squares and cube roots
roots of small perfect cubes.
of small perfect cubes.
1.1g Use numbers expressed in Use numbers expressed in the
the form of a single digit times
form of a single digit times a
a whole-number power of 10
whole-number power of 10 to
to estimate very large or very
estimate very large or very small
small quantities, and to express quantities, and to express how
how many times as much one
many times as much one is than
2012-2013
8th Grade - Math
4th Quarter
is than the other.
the other.
1.1h Perform operations with
numbers expressed in scientific
notation, including problems
where both decimal and
scientific notation are used.
i. Use scientific notation and
choose units of appropriate
size for measurements of very
large or very small quantities.
ii. Interpret scientific notation
that has been generated by
technology.
2012-2013
8th Grade - Math
4th Quarter
Standard 2: Patterns, Functions and Algebraic
Grade Level Expectation:
1. Linear functions model situations with a constant rate of change and can be represented numerically,
algebraically, and graphically
Students should know and be Instructional & Assessment
Content Evidence
Resources
Outcomes
able to do:
Planning:
2.1a Describe the connections
Describe the connections
between proportional
between proportional
relationships, lines, and linear
relationships, lines, and linear
equations.
equations.
2.1b Graph proportional
Graph proportional
relationships, interpreting the
relationships, interpreting the
unit rate as the slope of the
unit rate as the slope of the
graph.
graph
2.1c Compare two different
Compare two different
proportional relationships
proportional relationships
represented in different ways.
represented in different ways
2.1d Use similar triangles to
explain why the slope m is the
same between any two distinct
points on a non-vertical line in
the coordinate plane.
2.1e Derive the equation y =
mx for a line through the origin
and the equation y = mx + b for
a line intercepting the vertical
axis at b.
Use similar triangles to explain
why the slope m is the same
between any two distinct points
on a non-vertical line in the
coordinate plane.
Derive the equation y = mx for a
line through the origin and the
equation y = mx + b for a line
intercepting the vertical axis at b
2012-2013
8th Grade - Math
4th Quarter
Standard 2: Patterns, Functions and Algebraic
Grade Level Expectation:
2. Properties of algebra and equality are used to solve linear equations and systems of equations
Students should know and be Instructional & Assessment
Content Evidence
Resources
Outcomes
able to do:
Planning:
2.2a Solve linear equations in
i. Give examples of linear
one variable. (CCSS: 8.EE.7)
equations in one variable with
one solution, infinitely many
solutions, or no solutions.
ii. Solve linear equations with
rational number coefficients,
including equations whose
solutions require expanding
expressions using the
distributive property and
collecting like terms.
2.2b Analyze and solve pairs of i. Explain that solutions to a
simultaneous linear equations.
system of two linear equations
in two variables correspond to
points of intersection of their
graphs, because points of
intersection satisfy both
equations simultaneously.
ii. Solve systems of two linear
equations in two variables
algebraically, and estimate
solutions by graphing the
equations. Solve simple cases
by inspection.
iii. Solve real-world and
mathematical problems
leading to two linear
equations in two variables.
2012-2013
8th Grade - Math
Grade Level Expectation:
3. Graphs, tables and
4th Quarter
equations can be used to distinguish between linear and nonlinear
functions
Standard 2: Patterns, Functions and Algebraic
Content Evidence
Outcomes
2.3a Define, evaluate, and
compare functions. (CCSS: 8.F)
Students should know and be
able to do:
Instructional & Assessment
Planning:
Resources
i. Define a function as a rule that
assigns to each input exactly
one output.
ii. Show that the graph of a
function is the set of ordered
pairs consisting of an input and
the corresponding output.
iii. Compare properties of two
functions each represented in
a different way (algebraically,
graphically, numerically in
tables, or by verbal
descriptions).
iv. Interpret the equation y = mx
+ b as defining a linear
function, whose graph is a
straight line.
v. Give examples of functions
that are not linear.
2012-2013
8th Grade - Math
2.3b Use functions to model
relationships between
quantities.
4th Quarter
i. Construct a function to model
Standard 2: Patterns, Functions and Algebraic
ii.
iii.
iv.
v.
a linear relationship between
two quantities. (
Determine the rate of
change and initial value of the
function from a description of
a relationship or from two (x,
y) values, including reading
these from a table or from a
graph.
Interpret the rate of change
and initial value of a linear
function in terms of the
situation it models, and in
terms of its graph or a table of
values.
Describe qualitatively the
functional relationship
between two quantities by
analyzing a graph. Sketch a
graph that exhibits the
qualitative features of a
function that has been
described verbally.
Sketch a graph that exhibits
the qualitative features of
a function that has been
described verbally.
vi. Analyze how credit and debt
impact personal financial goals
(PFL)
2012-2013
8th Grade - Math
4th Quarter
Standard 3: Data Analysis, Statistics, and Probability
Grade Level Expectation:
1. Visual displays and summary statistics of two-variable data condense the information in data sets into usable
knowledge
Students should know and be Instructional & Assessment
Content Evidence
Resources
Outcomes
able to do:
Planning:
TCAP Standard
2.5a Solve simple linear
equation in problem solving
situations using a variety of
methods (informal and formal)
3.1a Read and construct
displays of data using
appropriate techniques- scatter
plots, box and whisker plots
and stem and leaf plots.
3.2a Display and use measures
of central tendency.
4.2a Describe, analyze and
reason informally about
properties of 2 and 3
dimensional shapes.
4.3a Apply the concept of ratio,
proportion and similarity in
problem solving situations.
2012-2013
8th Grade - Math
4th Quarter
Standard 4: Data Analysis, Statistics, and
Probability
Grade Level Expectation:
1. Direct and indirect measurement can be used to describe and make comparisons
Content Evidence
Outcomes
4.2a Explain a proof of the
Pythagorean Theorem and its
converse.
4.2b Apply the Pythagorean
Theorem to determine
unknown side lengths in right
triangles in real-world and
mathematical problems in two
and three dimensions.
4.2c Apply the Pythagorean
Theorem to find the distance
between two points in a
coordinate system.
4.2d State the formulas for the
volumes of cones, cylinders,
and spheres and use them to
solve real-world and
mathematical problems.
Students should know and be
able to do:
Instructional & Assessment
Planning:
Resources
Explain a proof of the
Pythagorean Theorem and its
converse.
Apply the Pythagorean Theorem
to determine unknown side
lengths in right triangles in realworld and mathematical
problems in two and three
dimensions.
Apply the Pythagorean Theorem
to find the distance between
two points in a coordinate
system.
State the formulas for the
volumes of cones, cylinders, and
spheres and use them to solve
real-world and mathematical
problems.
2012-2013
8th Grade - Math
4th Quarter
Grade Level Expectation:
1. Visual displays
Standard 3: Data Analysis, Statistics, and
Probability
and summary statistics of two-variable data condense the information
in data sets into usable knowledge
Content Evidence
Outcomes
3.1a Construct and interpret
scatter plots for bivariate
measurement data to
investigate patterns of
association between two
quantities
3.1b Describe patterns such as
clustering, outliers, positive or
negative association, linear
association, and nonlinear
association.
Students should know and be
able to do:
3.1c For scatter plots that
suggest a linear association,
informally fit a straight line,
and informally assess the
model fit by judging the
closeness of the data points to
the line.
For scatter plots that suggest a
linear association, informally fit
a straight line, and informally
assess the model fit by judging
the closeness of the data points
to the line.
3.1d Use the equation of a
linear model to solve problems
in the context of bivariate
measurement data,
interpreting the slope and
intercept.
Use the equation of a linear
model to solve problems in the
context of bivariate
measurement data, interpreting
the slope and intercept.
Instructional & Assessment
Planning:
Resources
Construct and interpret scatter
plots for bivariate measurement
data to investigate patterns of
association between two
quantities
Describe patterns such as
clustering, outliers, positive or
negative association, linear
association, and nonlinear
association.
2012-2013
8th Grade - Math
3.1e Explain patterns of
association seen in bivariate
categorical data by displaying
frequencies and relative
frequencies in a two-way table.
4th Quarter
i. Construct and interpret a twoway table summarizing data
on two categorical variables
collected from the same
subjects.
Ii, Use relative frequencies
calculated for rows or columns
to describe possible association
between the two variables.
Standard 4: Shape, Dimension and
Geometric Relationships
Grade Level Expectation:
1. Transformations of objects can be used to define the concepts of congruence and similarity
Students should know and be Instructional & Assessment
Content Evidence
Outcomes
able to do:
Planning:
4.1a Verify experimentally the
Verify experimentally the
properties of rotations,
properties of rotations,
reflections, and translations.
reflections, and translations.
4.1b Describe the effect of
Describe the effect of dilations,
dilations, translations,
translations, rotations, and
rotations, and reflections on
reflections on two-dimensional
two-dimensional figures using
figures using coordinates
coordinates.
4.1c Demonstrate that a twoDemonstrate that a twodimensional figure is congruent dimensional figure is congruent
to another if the second can be to another if the second can be
obtained from the first by a
obtained from the first by a
sequence of rotations,
sequence of rotations,
reflections, and translations.
reflections, and translations.
2012-2013
Resources
8th Grade - Math
4th Quarter
4.1d Given two congruent
figures, describe a sequence of
transformations that exhibits
the congruence between them.
4.1e Demonstrate that a twodimensional 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 congruent figures,
describe a sequence of
transformations that exhibits
the congruence between them.
Demonstrate that a twodimensional figure is similar to
another if the second can be
obtained from the first by a
sequence of rotations,
reflections, translations, and
dilations.
4.1f Given two similar twodimensional figures, describe a
sequence of transformations
that exhibits the similarity
between them.
4.1g 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
Given two similar twodimensional figures, describe a
sequence of transformations
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
2012-2013