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CT.CC.EE.8.Expressions and Equations
Expressions and Equations
Analyze and solve linear equations and pairs of simultaneous linear equations. EE.8.7. Solve linear equations in one variable. EE.8.7(a) Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these possibilities is the
case by successively transforming the given equation into simpler forms, until an
equivalent equation of the form x = a, a = a, or a = b results (where a and b are
EE.8.7(b) Solve linear equations with rational number coefficients, including equations
whose solutions require expanding expressions using the distributive property and
collecting like terms.
EE.8.8. Analyze and solve pairs of simultaneous linear equations. EE.8.8(a) Understand that solutions to a system of two linear equations in two
variables correspond to points of intersection of their graphs, because points of
intersection satisfy both equations simultaneously.
EE.8.8(b) Solve systems of two linear equations in two variables algebraically, and
estimate solutions by graphing the equations. Solve simple cases by inspection. For
example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot
simultaneously be 5 and 6.
Understand the connections between proportional relationships, lines, and linear
equations. EE.8.5. Graph proportional relationships, interpreting the unit rate as the slope of the
graph. Compare two different proportional relationships represented in different ways. For
example, compare a distance-time graph to a distance-time equation to determine which of two
moving objects has greater speed.
EE.8.6. 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.
Work with radicals and integer exponents. EE.8.1. Know and apply the properties of integer exponents to generate equivalent
numerical expressions. For example, 3^2 x 3^-5 = 3^-3 = 1/3^3 = 1/27.
EE.8.2. Use square root and cube root symbols to represent solutions to equations of the
form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of
small perfect squares and cube roots of small perfect cubes. Know that square root of 2 is
irrational. Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
EE.8.3. Use numbers expressed in the form of a single digit times a whole-number power of
10 to estimate very large or very small quantities, and to express how many times as much
one is than the other. For example, estimate the population of the United States as 3 times
10^8 and the population of the world as 7 times 10^9, and determine that the world
population is more than 20 times larger.
EE.8.4. Perform operations with numbers expressed in scientific notation, including
problems where both decimal and scientific notation are used. Use scientific notation and
choose units of appropriate size for measurements of very large or very small quantities
(e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that
has been generated by technology.
Use functions to model relationships between quantities. F.8.4. Construct a function to model 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.
Define, evaluate, and compare functions. F.8.1. Understand that a function is a rule that assigns to each input exactly one
output. The graph of a function is the set of ordered pairs consisting of an input and the
corresponding output. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F.8.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a
straight line; give examples of functions that are not linear. For example, the function A =
s^2 giving the area of a square as a function of its side length is not linear because its
graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Solve real-world and mathematical problems involving volume of cylinders, cones, and
spheres. G.8.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them
to solve real-world and mathematical problems.
Understand and apply the Pythagorean Theorem. G.8.7. Apply the Pythagorean Theorem to determine unknown side lengths in right
triangles in real-world and mathematical problems in two and three dimensions.
Understand congruence and similarity using physical models, transparencies, or
geometry software. G.8.1. Verify experimentally the properties of rotations, reflections, and
translations: G.8.1(a) Lines are taken to lines, and line segments to line segments of the same
G.8.1(b) Angles are taken to angles of the same measure.
G.8.1(c) Parallel lines are taken to parallel lines.
G.8.2. 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.
G.8.5. 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.
MP.8.1. Make sense of problems and persevere in solving them.
MP.8.2. Reason abstractly and quantitatively.
CT.CC.NS.8.The Number System
Know that there are numbers that are not rational, and approximate them by rational
numbers. NS.8.1. Know that numbers that are not rational are called irrational. Understand
informally that every number has a decimal expansion; for rational numbers show that the
decimal expansion repeats eventually, and convert a decimal expansion which repeats
eventually into a rational number.
CT.CC.SP.8.Statistics and Probability
Statistics and Probability
Investigate patterns of association in bivariate data. SP.8.1. 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
SP.8.2. Know that straight lines are widely used to model relationships between two
quantitative variables. 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.