Download Math 6-8 - Mid-Michigan Consortium

6-8 Mathematics
Power Standards
and
Related Learning Targets
June, 2008
Based on 12.05 Mathematics Grade Level Content Expectations
with MEAP “core” designations
What are Power Standards?
 Power standards are the most important learning targets for a grade, often culminating a learning
progression that started at earlier grades.
 Power standards prepare students for what they will learn in later grades.
 Power standards help focus and simplify teachers’ understanding of the scope of the subject at their
grade.
 Power standards may be big ideas, skills or dispositions.
 Power standards may be rewritten in teacher or student friendly language.
 Power standards may combine more than one GLCE.
 Power standards do not replace the GLCEs.
Related Learning Targets
The related learning targets include the foundational knowledge and skills behind the power standard. If
a power standard is about fluency, then the related learning targets are often the essential concepts and
subskills that are needed by students to perform the fluency standard efficiently and flexibly, with
understanding – and to remember how to perform the standard over time and apply it to new situations.
Traditional teaching where students simply practice an algorithm without understand the reasons why it
works does not produce long-term math proficiency for most students.
Some foundational learning targets for a power standard are found in an earlier grade, so be sure
to check the corresponding power standard and related learning targets in one or two previous grades.
For example, the 7th grade algebra power standards rely considerably on what students have learned in
the corresponding 6th grade algebra topics.
Formative assessments are most often developed from the related learning targets rather than the power
standards. Knowing where they are in their progress toward confident and reliable performance of the
power standard helps students take responsibility for their learning and helps teachers plan the next steps
needed to move students forward.
Note: This is not an assessment document, even though the MEAP codes for “core” GLCEs are included
for 6th – 8th grade (all others are “extended” or “NASL”). No school curriculum should include only the
GLCEs listed by MEAP as core, because the others are essential for learning the core GLCEs, either in
the current grade or in subsequent grades. To focus only on the core GLCEs and ignore the others would
undermine students’ learning in subsequent grades.
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 2
Middle School Power Standards – Mathematics
6
Whole
Number
Operations
7
8
Students should be fluent with
whole number operations by 5th
grade.
M6.1 Understand and use
negative numbers.
M7.1 Solve problems involving
operations with integers,
including solving linear equations
with integer coefficients.
M6.2 Multiply and divide any two
fractions fluently to solve applied
problems.
See Algebra/equations below.
See Algebra/equations below.
Fractions
M6.3 Solve applied problems that
use the four operations with
appropriate decimal numbers.
See Algebra/equations below.
See Algebra/equations below.
Decimals
M6.4 Use ratios and rates in
problem situations.
M7.2 Solve problems involving
proportions.
M8.1 Solve problems involving
everyday arithmetic calculations,
including percent increases and
decreases, weighted averages, and
problems involving ratio units
(e.g. miles per hour, dollars per
pound, etc.)
M6.5 Represent situations using
algebraic expressions and solve
simple equations.
M7.3 From applied situations,
generate and solve linear
equations and interpret solutions.
(Equations may include integers
and/or positive and negative
decimals or fractions.)
M8.2 Set up and solve applied
problems involving linear
inequalities or simultaneous
equations in two variables.
(Equations may include integers
and/or positive and negative
decimals or fractions.)
M6.6 Represent linear
relationships using verbal
descriptions, tables, graphs, and
formulas; be able to translate
among the representations.
M7.4 Represent directly
proportional and linear
relationships using verbal
descriptions, tables, graphs, and
formulas, and translate among
these representations.
M8.3 Identify and represent
families of functions (linear,
quadratic and exponential) using
tables, graphs, and equations;
describe how changes in one
variable affect the other.
M6.7 Understand and apply
properties of lines, angles, and
triangles.
M7.5 Solve problems about
similar figures and scale drawings
(using concepts of proportionality
related to M7.2).
M8.4 Solve problems involving
area of triangles, quadrilaterals
and complex figures; area and
circumference of circles; surface
area and volume.
Integers
Rates, Ratios,
and
Proportions
Algebra
(Equations)
Algebra
(Functions)
Geometry and
Measurement
Data and
Probability
M6.8 Compute the volume and
surface area of cubes and
rectangular prisms given the
lengths of their sides using
formulas.
M7.6 Represent and interpret data
using appropriate graphs.
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 3
Grade 6 Power Standards
M6.1 – Understand and use negative numbers.
Related Learning Targets:
 Measure and compare integer temperatures in degrees, both Celsius and Fahrenheit. (M.UN.04.03)
 Understand that 0 is an integer that is neither negative nor positive. (N.ME.06.19)
 Locate negative rational numbers (including integers) on the number line; know that numbers and
their negatives add to 0 and are on opposites sides and at equal distance from 0 on a number line.
(N.ME.06.17)
 Know that the absolute value of a number is the value of the number, ignoring the sign, or is the
distance of the number from 0. (N.ME.06.20)
 Understand integer subtraction as the inverse of integer addition. Understand integer division as the
inverse of integer multiplication. (N.MR.06.08)
 Add and multiply integers between -10 and 10; subtract and divide integers using the related facts.
Use the number line and chip models for addition and subtraction. (N.FL.06.09 core)
M6.2 – Multiply and divide any two fractions fluently to solve applied problems. (N.FL.06.04 core)
Related Learning Targets:
 Understand that a fraction or a negative fraction is a quotient of two integers, e.g., - 8/3 is -8 divided
by 3. (N.ME.06.07)
 Find the product of two unit fractions with small denominators using an area model. (N.ME.05.12)
 Solve for the unknown in equations such as:¼ ÷ _ = 1, ¾ ÷ _ = ¼ and ½ = 1 • _ . (N.MR.06.03 core)
 Divide a fraction by a whole number and a whole number by a fraction, using simple unit fractions.
(N.MR.05.13)
 Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = _, then 2/3 • _ =
4/5 , so _ = 4/5 • 3/2 = 12/10. (N.MR.06.01 core)
 Given an applied situation involving dividing fractions, write a mathematical statement to represent
the situation. (N.FL.06.02 core)
 Multiply and divide any two fractions fluently. (N.FL.06.04 core)
M6.3 – Solve applied problems that use the four operations with appropriate decimal numbers
and percentages. (N.FL.06.15 core, N.FL.06.10 core)
Related Learning Targets:
 Represent rational numbers as fractions or terminating decimals when possible and translate
between these representations. Order rational numbers and place them on the number line.
(N.ME.06.06, N.ME.06.05)
 Multiply one- and two-digit whole numbers by decimals up to two decimal places. For applied
situations, estimate the answers to calculations involving operations with rational numbers.
(N.MR.05.17, N.FL.06.14 core)
 Understand percentages as parts out of 100, use % notation, and express a part of a whole as a
percentage. (N.ME.05.09)
 Express fractions and decimals as percentages and vice versa. (N.MR.05.22)
 Calculate part of a number given the percentage and the number. (N.FL.06.12 core)
 Solve contextual problems involving percentages such as sales taxes and tips. (N.MR.06.13)
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 4
M6.4 – Use ratios and rates in problem situations. (A.PA.06.01)
Related Learning Targets:
 Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3:5, 3/5 cups per
person; recognize and find equivalent ratios. (N.ME.05.23)
 Find equivalent ratios by scaling up or scaling down. (N.ME.06.11 core)
 Solve applied problems involving rates including speed, e.g., if a car is going 50 mph, how far will
it go in 3 ½ hours? (A.PA.06.01 core)
M6.5 – Represent situations using algebraic expressions and solve simple equations. (A.FO.06.06
core, A.FO.06.14)
Related Learning Targets:
(Students have represented addition and subtraction situations using equations for many years, both
with whole numbers and with fractions, equations such as 13 - __ = 7 or 1/4 + x = 7/12.)
 Use letters, with units, to represent quantities in a variety of contexts, e.g., y lbs., k minutes, x
cookies. (A.FO.06.03 core)
 Use standard conventions for writing algebraic expressions, e.g., 2x + 1 means “two times x, plus 1”
and 2(x + 1) means “two times the quantity (x + 1).” (A.FO.06.05)
 Represent information given in words using algebraic expressions and equations. (A.FO.06.06 core)
 Distinguish between an algebraic expression and an equation. (A.FO.06.04 core)
 Simplify expressions of the first degree by combining like terms, and evaluate using specific values.
(A.FO.06.07)
 Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 = 10, to particular
contexts and solve. (A.FO.06.11 core)
 Understand that adding or subtracting the same number to both sides of an equation creates a new
equation that has the same solution. (A.FO.06.12 core)
 Understand that multiplying or dividing both sides of an equation by the same non-zero number
creates a new equation that has the same solutions. (A.FO.06.13 core)
 Solve equations of the form ax + b = c, e.g., 3x + 8 = 15 by hand for positive integer coefficients
less than 20, using calculators otherwise, and interpret the results. (A.FO.06.14)
M6.6 – Represent linear relationships using verbal descriptions, tables, graphs, and formulas; be
able to translate among the representations. (A.RP.06.10)
Related Learning Targets:
 Plot ordered pair of integers and use ordered pairs of integers to identify points in all four quadrants
of the coordinate plane. (A.RP.06.02)
 Understand that relationships between quantities can be suggested by graphs and tables.
(A.RP.06.08)
 Solve problems involving linear functions whose input values are integers; write the equation; graph
the resulting ordered pairs of integers, e.g., given c chairs, the “leg function” is 4c; if you have 5
chairs, how many legs?; if you have 12 legs, how many chairs? (A.PA.06.09)
 Represent simple relationships between quantities using verbal descriptions, formulas or equations,
tables, and graphs, e.g., perimeter-side relationship for a square, distance-time graphs, conversions
such as feet to inches. (A.RP.06.10)
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 5
M6.7 – Understand and apply properties of lines, angles, and triangles.
Related Learning Targets:
 Use paper folding to perform basic geometric constructions of perpendicular lines, midpoints of line
segments and angle bisectors; justify informally. (G.SR.06.05)
 Understand and apply basic properties of lines, angles, and triangles, including:
 triangle inequality
 relationships of vertical angles, complementary angles, supplementary angles
 congruence of corresponding and alternate interior angles when parallel lines
 are cut by a transversal, and that such congruences imply parallel lines
 locate interior and exterior angles of any triangle, and use the property that an exterior
 angle of a triangle is equal to the sum of the remote (opposite) interior angles
 know that the sum of the exterior angles of a convex polygon is 360º. (G.GS.06.01)
 Understand that for polygons, congruence means corresponding sides and angles have equal
measures. (G.GS.06.02)
M6.8 – Compute the volume and surface area of cubes and rectangular prisms given the lengths of
their sides using formulas. (M.TE.06.03 core)
Related Learning Targets
 Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid
exactly (nets). (M.PS.06.02 core)
Also in 6th grade:
 Integer exponents, N.ME.06.16. Students studied the use of exponents in 5th grade for representing
the prime factorization of composite numbers. They should learn about scientific notation when
they study the decimal place value system. This can be their first introduction to negative
exponents, to represent 0.1, 0.01, etc. This is an abstract representation with little meaning for 6th
graders, and therefore not directly related to any power standard.
 Convert between basic units of measurement within a single measurement system, e.g., square
inches to square feet. M.UN.06.01 – this is a continuation of work on units of measurement from
earlier grades.
 Express probabilities as fractions, decimals or percentages between 0 and 1; know that 0
probability means an event will not occur and that probability 1 means an event will occur.
Compute probabilities of events from simple experiments with equally likely outcomes, e.g.,
tossing dice, flipping coins, spinning spinners, by listing all possibilities and finding the fraction
that meets given conditions. (D.PR.06.01, D.PR.06.02)
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 6
Grade 7 Power Standards
M7.1 – Solve problems involving operations with integers, including solving linear equations.
Related Learning Targets:
 Understand that 0 is an integer that is neither negative nor positive. (N.ME.06.19)
 Locate negative rational numbers (including integers) on the number line; know that numbers and
their negatives add to 0 and are on opposites sides and at equal distance from 0 on a number line.
(N.ME.06.17)
 Add and multiply integers between -10 and 10; subtract and divide integers using the related facts.
Use the number line and chip models for addition and subtraction. (N.FL.06.09)
 Understand integer subtraction as the inverse of integer addition. Understand integer division as the
inverse of integer multiplication. (N.MR.06.08)
 Understand and use basic properties of real numbers: additive and multiplicative identities, additive
and multiplicative inverses, commutativity, associativity, and the distributive property of
multiplication over addition. (A.PA.07.11 core)
 Solve problems involving operations with integers. (N.FL.07.07 core)
M7.2 – Solve problems involving rates, ratios, and proportions using various methods.
Related Learning Targets:
 Express ratios in several ways given applied situations, e.g., 3 cups to 5 people, 3:5, 3/5 (cups per
person); recognize and find equivalent ratios. (N.ME.05.23)
 Find equivalent ratios by scaling up or scaling down. (N.ME.06.11)
 Solve applied problems involving rates including speed, e.g., if a car is going 50 mph, how far will
it go in 3 ½ hours? (A.PA.06.01)
 Solve problems involving derived quantities such as density, velocity, and weighted averages.
(N.MR.07.02)
 Calculate rates of change including speed. (N.FL.07.03 core)
 Convert ratio quantities between different systems of units such as feet per second to miles per hour.
(N.MR.07.04 core)
 Solve proportion problems using such methods as unit rate, scaling, finding equivalent fractions,
and solving the proportion equation a/b = c/d; know how to see patterns about proportional
situations in tables. (N.FL.07.05 core)
 Solve problems about similar figures and scale drawings. (G.TR.07.04)
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 7
M7.3 – From applied situations, generate and solve linear equations of the form ax + b = c and
ax + b = cx + d, and interpret solutions. A.FO.07.13 (Equations may include integers and/or positive
and negative decimals or fractions.)
Related Learning Targets:
 Relate simple linear equations with integer coefficients, e.g., 3x = 8, x + 5 = 10, or 3x + 8 = 15 to
particular contexts and solve. (A.FO.06.11, A.FO.06.14)
 Understand and use basic properties of real numbers: additive and multiplicative identities, additive
and multiplicative inverses, commutativity, associativity, and the distributive property. (A.PA.07.11
core)
 Add, subtract, and multiply simple algebraic expressions of the first degree and justify using
properties of real numbers. Be able to add, subtract, multiply, and divide positive and negative
rational numbers fluently in algebraic expressions. (A.FO.07.12 core, N.FL.07.08 core)
M7.4 – Represent directly proportional and linear relationships using verbal descriptions, tables,
graphs, and formulas, and translate among these representations.
Related Learning Targets:
 Recognize when information given in a table, graph, or formula suggests a directly proportional or
linear relationship. (A.PA.07.01 core)
 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs,
and formulas and translate among these representations. (A.RP.07.02 core)
 Given a directly proportional or other linear situation, graph and interpret the slope and intercept(s)
in terms of the original situation; evaluate y = mx + b for specific x values. (A.PA.07.03 core)
 For directly proportional or linear situations, solve applied problems using graphs and equations.
(A.PA.07.04 core)
 Recognize and use directly proportional relationships of the form y = mx, and distinguish from
linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional
relationship between two quantities, one quantity is a constant multiple of the other quantity.
(A.PA.07.05 core)
 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points
on the graph, and express the answer as a fraction and a decimal; understand that linear functions
have slope that is a constant rate of change. (A.PA.07.06 core)
 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting
slope and y-intercept. (A.PA.07.07)
 Find and interpret the x and/or y-intercepts of a linear equation or function. Know that the solution
to a linear equation of the form ax + b = 0 corresponds to the point at which the graph of y = ax + b
crosses the x-axis. (A.FO.07.08)
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 8
M7.5 – Solve problems about similar figures and scale drawings (using concepts of proportionality
related to M7.2). (G.TR.07.04 core)
Related Learning Targets:
 Understand that in similar polygons, corresponding angles are congruent and the ratios of
corresponding sides are equal; understand the concepts of similar figures and scale factor.
(G.TR.07.03 core)
 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA
similarity); the ratios of two pairs of corresponding sides are equal and the included angles are
congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use
these criteria to solve problems and to justify arguments. (G.TR.07.05 core)
 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are
related by a factor of r2. (G.TR.07.06 core)
M7.6 – Represent and interpret data using appropriate graphs.
Related Learning Targets:
 Represent and interpret data using circle graphs, stem and leaf plots, histograms, and box-andwhisker plots and select appropriate representation to address specific questions. (D.RE.07.01 core)
 Create and interpret scatter plots and use an estimated line of best fit to answer questions about the
data. (D.AN.07.02 core)
 Calculate and interpret relative frequencies and cumulative frequencies for given data sets.
(D.AN.07.03)
 Find and interpret the median, quartiles, and interquartile range of a given set of data. (D.AN.07.04)
Also in 7th grade:
 The concept of square root and cube root, and estimation with calculators, N.MR.07.06. Square
roots are used extensively in 8th grade with the Pythagorean Theorem.
 Estimate results of computations with rational numbers, N.FL.07.09 (core). This notion of number
sense when using decimals and fractions is taught at all grades where decimals and fractions are
studied, and emphasized in 6th grade. Students continue to work with decimals and fractions as
coefficients of variable and unknowns in functions and equations (see M7.1). As you review
decimals and fractions, make sure to emphasize estimation as a technique for knowing whether an
answer is reasonable. This GLCE is tested on the 8th grade MEAP.
 Inversely proportional relationships, A.PA.07.09 and A.RP.07.10. This is a nice extension of other
relationships that students study in 7th grade. Inversely proportional relationships are not as central
to continued study of algebra as directly proportional and linear relationships, which is why they
were not included in the power standards.
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 9
Grade 8 Power Standards
M8.1 – Solve problems involving everyday arithmetic calculations, including percent increases
and decreases, weighted averages, and problems involving ratio units (e.g. miles per hour, dollars
per pound, etc.) (N.MR.08.08, N.MR.08.10, N.FL.08.11)
Related Learning Targets:
 Understand percent increase and percent decrease in both sum and product form, e.g., 3% increase
of a quantity x is x + .03x = 1.03x. (N.MR.08.07)
 Solve problems involving compounded interest or multiple discounts. (N.FL.08.09) This is an
extension of percent increase or decrease
M8.2 – Set up and solve applied problems involving linear inequalities, linear equations, quadratic
equations, and simultaneous equations (system of equations) in two variables.
Related Learning Targets:
 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the
equation is true. (A.FO.08.10) –In solving equations that result in rational numbers, students also
need to understand rational numbers either terminate or eventually repeat and that calculators
truncate or round repeating decimals; they need to locate rational numbers on the number line; and
know fraction forms of common repeating decimals, e.g., 0.111… = 1/9; 0.333…= 1/3.
(N.ME.08.03)
 Set up and solve applied problems involving 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.08.11, A.FO.08.13)
 Set up and solve applied problems involving linear inequalities in one and two variables, and graph
the solution sets. (A.FO.08.12, A.FO.08.13)
 Recognize and apply the common formulas: (a + b)2 = a2 + 2ab + b2, (a-b)2 = a2 – 2ab + b2, (a + b)
(a – b) = a2 – b2, and represent these geometrically. (A.FO.08.07)
 Factor simple quadratic expressions with integer coefficients; solve simple quadratic equations;
verify solutions by evaluation. (A.FO.08.08)
 Solve applied problems involving simple quadratic equations. (A.FO.08.09)
M8.3 – Identify and represent families of functions using tables, graphs, and equations; describe
how changes in one variable affect the other.
Related Learning Targets:
 Identify and represent linear functions, quadratic functions, and other simple functions including
inversely proportional relationships; cubics; roots; and exponentials; using tables, graphs, and
equations. (A.RP.08.01)
 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.08.02)
 Recognize basic functions in problem context; e.g., area of a circle is r2, volume of a sphere is
4/3r3, and represent them using tables, graphs, and formulas. (A.PA.08.03)
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 10
 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.08.05)
 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. (A.RP.08.06)
M8.4 – Solve problems involving area of triangles, quadrilaterals and complex figures; area and
circumference of circles; surface area and volume.
Related Learning Targets:
 Use the Pythagorean Theorem and its converse to solve applied problems including perimeter, area,
and volume problems. (G.GS.08.01) –In solving these problems, students need to 1. understand at
least one proof of the Pythagorean Theorem (G.GS.08.01); 2. understand the meaning of a square
root of a number and its connection to the square whose area is the number; 3. understand the
meaning of a cube root and its connection to the volume of a cube (N.ME.08.01); 4. estimate and
solve problems with square roots and cube roots using calculators (N.FL.08.05); 5. find square roots
of perfect squares and approximate the square roots of non-perfect squares by locating between
consecutive integers, e.g., is between 11 and 12 (N.FL.08.06); and 6. 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 , π on the number line. (N.ME.08.04)
 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. (G.LO.08.02)
 Understand the definition of a circle; know and use the formulas for circumference and area of a
circle to solve problems. (G.SR.08.03)
 Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals,
triangles, circles). (G.SR.08.04)
 Solve applied problems involving areas of triangles, quadrilaterals, and circles. (G.SR.08.05)
 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. (G.SR.08.08)
 Know the volume formulas for generalized cylinders (bh), generalized cones and pyramids (1/3bh)
and spheres (4/3r3) and apply them to solve problems. (G.SR.08.06)
 Understand the concept of surface area, and find the surface area of prisms, cones, spheres,
pyramids, and cylinders. (G.SR.08.07)
Also in 8th grade:
 meanings for zero and negative integer exponents (N.ME.08.02) – used primarily to express
scientific notation
 the vertical line test (A.RP.08.04) – part of the theory of functions that is addressed more
completely in high school
 dilations from a point in the plane (G.TR.08.09) – an extension of the 7th grade power standard
about similar figures and proportions
 reflective and rotational symmetries of two-dimensional shapes, and how they relate to
transformations (G.TR.08.10) – extensions of work done in earlier grades
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 11
 measures of central tendency (mean, median, mode) that best represent a data set, e.g., salaries,
home prices; justify the choice made (D.AN.08.01); practices of collecting and displaying data
which may bias the presentation or analysis (D.AN.08.02) – these are extensions of the 7th grade
power standard on representing and interpreting data
 relative frequencies from a table of experimental results for a repeated event; theoretical probability
(D.PR.08.03, D.PR.08.05); the Basic Counting Principle (D.PR.08.04); the difference between
independent and dependent events; and common misconceptions involving probability
(D.PR.08.06) – these are extensions of the 6th grade power standard on probability
6-8 Mathematics Power Standards and Related Learning Targets, Mid-Michigan Consortium, 6/28/09
p. 12