Grade 8 Michigan Standards
Number and Operations
Interactivate Lessons | Objectives |
Practicing Arithmetic
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Understand real number concepts
N.ME.08.01 Understand the meaning of a square root of a number and its connection to the square
whose area is the number; understand the meaning of a cube root and its connection to the volume of a
cube.
N.ME.08.02 Understand meanings for zero and negative integer exponents.
N.ME.08.03 Understand that in decimal form, rational numbers either terminate or eventually
repeat, and that calculators truncate or round repeating decimals; locate rational numbers on the
number line; know fraction forms of common repeating decimals.
N.ME.08.04 Understand that irrational numbers are those that cannot be expressed as the
quotient of two integers, and cannot be represented by terminating or repeating decimals;
approximate the position of familiar irrational numbers, (e.g., √ 2, √ 3
and π) on the number line.
N.FL.08.05 Estimate and solve problems with square roots and cube roots using calculators.
N.FL.08.06 Find square roots of perfect squares and approximate the square roots of non-perfect
squares by locating between consecutive integers, e.g., √ 130 is between 11 and 12.
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Fraction Facts
Expected Value
Statistics and Shopping
Chaos
Fractals and the Chaos Game
Statistics and Shopping
Fire!, Probability, and Chaos
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Solve problems
N.MR.08.07 Understand percent increase and percent decrease in both sum and product form, e.g.,
3% increase of a quanitity x is x + .03x = 1.03x.
N.MR.08.08 Solve problems involving percent increases and decreases.
N.FL.08.09 Solve problems involving compounded interest or multiple discounts.
N.MR.08.10 Calculate weighted averages such as course grades, consumer price indices, and sports
ratings.
N.MR.08.11 Solve problems involving ratio units such as miles per hour, dollars per pound, or
persons per square mile.
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Algebra
Interactivate Lessons | Objectives |
Introduction to Functions
Introduction to Linear Functions
Graphing and the Coordinate Plane
Cartesian Coordinate System
Graphs and Functions
Functions and the Vertical Line Test
Reading Graphs
Impossible Graphs
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Understand the concept of non-linear functions using basic examples
A.RP.08.01 Identify and represent linear functions, quadratic functions, and other simple
functions including inverse functions (y = k/x), cubics (y = ax3) roots, (y = square root of x),
and exponentials (y = ax, a > 0), using tables, graphs, and equations.
A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and
population growth, describe how changes in one variable affect the others.
A.PA.08.03 Recognize basic functions in problem context, e.g., area of a circle
is πr2,volume of a sphere is
4/3 πr3, and represent them using
tables, graphs, and formulas.
A.PA.08.04 Use the vertical line test to determine if a graph represents a function in one
variable.
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Graphs and Functions
Functions and the Vertical Line Test
Reading Graphs
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Understand and represent quadratic functions
A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs and
vice versa; in particular, note that solutions of a quadratic equation are the x-intercepts of the
corresponding quadratic function.
A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x axis
and the coordinates of the vertex; use words "parabola" and "roots"; include functions in vertex form
and those with leading coefficient -1, e.g., y=x2 − 36;
y=(x − 2)2− 9; y=−x2; y=−(x − 3)2.
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Recognize, represent, and apply common formulas
A.FO.08.07 Recognize and apply the common formulas: (a+b)2=a2+2ab+b2
(a − b)2=a2 − 2ab+b2
(a+b)(a − b)=a2 − b2; represent geometrically.
A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g.,
x2+6x+9, x2+2x − 3 and x2 − 4; solve simple quadratic
equations, e.g., x2=16 or x2=5 (by taking square roots);
x2 − x − 6=0, x2 − 2x=15 (by factoring); verify solutions by
evaluation.
A.FO.08.09 Solve applied problems involving simple quadratic equations.
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Understand solutions and solve equations, simultaneous equations, and linear inequalities
A.FO.08.10 Understand that to solve the equation F(x)=g(x) means to find all values of x for
which the equation is true, e.g., determine whether a given value, or values from a given set, is a
solution of an equation (0 is a solution of 3x2+2=4x+2, but 1 is not a solution).
A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution,
and by linear combination; estimate solutions using graphs; include examples with no solutions and
infinitely many solutions.
A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets.
A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and
linear inequalities.
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Geometry
Interactivate Lessons | Objectives |
Pythagorean Theorem
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Understand and use the Pythagorean Theorem
G.GS.08.01 Understand at least one proof of the Pythagorean Theorem; use the Pythagorean
Theorem and its converse to solve applied problems including perimeter, area, and volume problems.
G.LO.08.02 Find the distance between two points on the coordinate plane using the distance
formula; recognize that the distance formula is an application of the Pythagorean Theorem.
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Perimeter
Area
Length, Perimeter, and Area
Quadrilaterals
Pythagorean Theorem
Geometry in Tessellations
Visual Patterns in Tessellations
Introduction to Fractals: Infinity, Self-Similarity and Recursion
Geometric Fractals
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Solve problems about geometric figures
G.SR.08.03 Understand the definition of a circle; know and use the formulas for circumference
and area of a circle to solve problems.
G.SR.08.04 Find area and perimeter of complex figures by sub-dividing them into basic
shapes (quadrilaterals, triangles, circles).
G.SR.08.05 Solve applied problems involving areas of triangles, quadrilaterals, and circles.
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Surface Area and Volume
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Understand concepts of volume and surface area, and apply formulas
G.SR.08.06 Know the volume formulas for generalized cylinders ((area of base) x height),
generalized cones and pyramids and spheres and
apply them to solve problems.
G.SR.08.07 Understand the concept of surface area, and find the surface area of prisms, cones,
spheres, pyramids, and cylinders.
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Surface Area and Volume
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Visualize solids
G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids
including orthogonal views (top, front, and side), picture views (projective or isometric), and
nets, use such two-dimensional representations to help solve problems.
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Translations, Reflections, and Rotations
Symmetry in Tessellations
Geometric Fractals
Introduction to Fractals: Infinity, Self-Similarity and Recursion
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Understand and apply concepts of transformations and symmetry
G.TR.08.09 Understand the definition of a dilation from a point in the plane, and relate it
to the definition of similar polygons.
G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes,
and relate them to transformations to solve problems.
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Data and Probability
Interactivate Lessons | Objectives |
Mean, Median and Mode
Statistics and Shopping
Probability and Sports
Fire!, Probability, and Chaos
Stem-and-Leaf Plots
Box Plots
The Bell Curve
Histograms and Bar Graphs
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Draw, explain, and justify conclusions based on data
D.AN.08.01 Determine which measure of central tendency (mean, median, mode) best represents a
data set, e.g., salaries, home prices for answering certain questions; justify the choice made.
D.AN.08.02 Recognize practices of collecting and displaying data that may bias the
presentation or analysis.
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Tree Diagrams Probability
Probability and Sports
Ideas that Lead to Probability
Introduction to the Concept of Probability
Conditional Probability and Probability of Simultaneous Events
Replacement and Probability
From Probability to Combinatorics and Number Theory
Probability and Geometry
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Understand probability concepts for simple and compound events
D.PR.08.03 Compute relative frequencies from a table of experimental results for a repeated
event, and be able to answer questions about the result, using relationship of probability to
relative frequency.
D.PR.08.04 Apply the Basic Counting Principle to find total number of outcomes possible for
independent and dependent events, and calculate the probabilities using organized lists or tree
diagrams.
D.PR.08.05 Understand the relationship of probability to relative frequency.
D.PR.08.06 Understand the difference between independent and dependent events, and recognize
common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times in a row;
she is just as likely to roll a 6 on the fourth roll as she was on any previous roll.
D.AN.08.07 Compute relative frequencies from a table of experimental results for a repeated
event; understand the relationship of experimental probability to relative frequency; answer
questions regarding the results.
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