Version 2.0
B. Number Operations and Relationships
Grade 8
MPS Learning Target #1
(Grade 8)
Explain comparisons and operations on real numbers and use proportional reasoning (including ratios and
percents) to solve problems with and without contexts.
Descriptors
Concepts: 1, 2, 3
Computation: 4, 6
Grade of
Wisconsin Sub-skill Descriptors (Beginning of Grade 10)
Emphasis
Sub-skill B.a: Concepts
Grade 8
1) Compare and order real numbers.
Grade 8
2) Analyze and solve problems using percents.
Grades 8-10
3) Apply proportional reasoning and ratios in mathematical and real world contexts.
Sub-skill B.b: Computation
Grades 8-9
4) Compare, perform, and explain operations on real numbers with and without context (e.g.,
transitivity, rate of change, exponential functions, scientific notation, roots, powers,
reciprocals, absolute value, ratios, proportions, percents).
Grade 9
5) Select and use appropriate properties, computational procedures, and modes of
representation with and without context (e.g., simple and compound interest, commission,
percents, proportions).
Grades 8-10
6) Determine reasonableness of answer.
Note: Teachers in Grade 8 and Grade 9 grade share the Beginning of Grade 10 Descriptors.
Some Descriptors are more relevant to one grade than the other.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
C. Geometry
Grade 8
MPS Learning Target #2
(Grade 8)
Analyze relationships among figures and their parts, including the Pythagorean Theorem, using properties of
plane and coordinate geometry, and use proportional reasoning, transformations, and spatial visualization in
problem-solving situations.
Descriptors
Describing figures: 1, 3
Spatial relationships and transformations: 4, 5, 6
Coordinate systems: 7
Grade of
Wisconsin Sub-skill Descriptors (Beginning of Grade 10)
Emphasis
Sub-skill C.a: Describing figures
Grade 8
1) Identify, describe and analyze properties of figures, relationships among figures and
relationships among their parts (e.g., parallel, perpendicular and congruent sides, various types
of angles and triangles, complementary and supplementary angles, sum of angles in a triangle).
Grade 9-10
2) Present convincing geometric arguments by means of informal proof, counter-examples or
other logical means.
Grades 8-9
3) Model problems using the Pythagorean Theorem and right triangle trigonometry.
Note: Grade 8 emphasize Pythagorean. Grade 9 emphasize right triangle trigonometry.
Sub-skill C.b: Spatial relationships and transformations
Grade 8
4) Use proportional reasoning to solve congruence and similarity problems (e.g., scale
drawings and similar geometric figures).
Grade 8
5) Use transformations and symmetry to solve problems.
Grades 8-10
6) Visualize 3-dimensional figures in problem-solving situations.
Sub-skill C.c: Coordinate systems
Grade 8
7) Use the two-dimensional rectangular coordinate system to describe and characterize
properties of geometric figures. Identify and apply symmetry about an axis.
Grade 9
8) Use the two-dimensional rectangular coordinate system and algebraic procedures to describe
and characterize geometric properties and relationships (e.g., slope, intercepts, parallelism, and
perpendicularity, Pythagorean Theorem, distance formula).
Note: Teachers in Grade 8 and Grade 9 grade share the Beginning of Grade 10 Descriptors.
Some Descriptors are more relevant to one grade than the other.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
D. Measurement
Grade 8
MPS Learning Target #3
(Grade 8)
Select and use appropriate tools and procedures to solve problems requiring direct measurements and indirect
measurements (e.g., perimeter, area, surface area, volume, angles, and segments).
Descriptors
Direct measurement: 2
Indirect measurement: 3, 4, 5
Grade of
Wisconsin Sub-skill Descriptors (Beginning of Grade 10)
Emphasis
Sub-skill D.a: Measurable attributes
Grade 9
1) Identify, describe and use derived attributes to represent and solve problems (e.g., speed,
acceleration, density, money conversion).
Sub-skill D.b: Direct measurement
Grades 8-9
2) Select and use tools with appropriate degree of precision to determine measurements
directly.
Sub-skill D.c: Indirect measurement
Grades 8-9
3) Determine the perimeter/area of two-dimensional figures.
Grade 8
4) Determine the surface area/volume of three-dimensional figures.
Grades 8-10
5) Solve for angles and segments in similar polygons and arcs in circles.
Note: Grades 8-9 emphasize similar polygons. Grade 10 emphasize arcs in circles.
Grade 10
6) Use right-triangle trig functions and the Pythagorean Theorem to solve right-triangle
problems.
Grade 9
7) Use formulas in applications (e.g., Distance Formula, simple and compound interest).
Note: Teachers in Grade 8 and Grade 9 grade share the Beginning of Grade 10 Descriptors.
Some Descriptors are more relevant to one grade than the other.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
E. Statistics and Probability
Grade 8
MPS Learning Target #4
(Grade 8)
Design and conduct investigations, display data using
appropriate representations, analyze and summarize
data using measures of central tendency and variation,
and evaluate methods and conclusions.
MPS Learning Target #5
(Grade 8)
Design and analyze experiments with simple and
complex events, predict likelihood of outcomes, and
justify strategies based on theoretical and experimental
probabilities.
Descriptors
Data analysis and statistics: 1, 2, 3
Descriptors
Probability: 4
Grade of
Wisconsin Sub-skill Descriptors (Beginning of Grade 10)
Emphasis
Sub-skill E.a: Data analysis and statistics
Grades 8-9
1) Organize, display, compare, and interpret data in a variety of ways in mathematical and realworld contexts (e.g., histograms, line graphs, stem-and-leaf plots, scatter plots, box-and
whiskers, bar charts, Venn diagrams, tables, circle graphs).
Note: Grade 9 emphasize organize, display, compare and interpret data in a variety of ways in
mathematical and real-world contexts e.g. histograms, stem-and-leaf plots, scatter plots,
boxplots, and tables.
Grades 8-9
2) Interpret, analyze, and make predictions from organized and displayed data (e.g., measures
of central tendency, such as mean, median, mode, and, measures of variation such as standard
deviation, mean, median, mode, range, dispersion, outliers, line of best fit, percentiles).
Note: Grade 8 emphasize organize, display, compare and interpret data in a variety of ways in
mathematical and real-world contexts e.g. histograms, stem-and-leaf plots, scatter plots,
boxplots, and tables.
Note: Grade 9 emphasize interpret, analyze and make predictions from organized and
displayed data e.g. measures of variation such as standard deviation, mean, median, mode,
range, dispersion, outliers, line of best fit, percentiles.
Grades 8-9
3) Analyze, evaluate, and critique methods and conclusions of statistical experiments (e.g.,
randomness, sampling, techniques, surveys).
Sub-skill E.b: Probability
Grades 8-9
4) Determine the likelihood of occurrence of simple and complex events (e.g., combinations
and permutations, fundamental counting principle, experimental versus theoretical probability
and independent, dependent and conditional probability).
Note: Grade 8 emphasize on likelihood of occurrence of simple and complex events using
experimental and theoretical probability.
Note: Teachers in Grade 8 and Grade 9 grade share the Beginning of Grade 10 Descriptors.
Some Descriptors are more relevant to one grade than the other.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.
Version 2.0
F. Algebraic Relationships
Grade 8
MPS Learning Target #6
(Grade 8)
Analyze, describe, and generalize
mathematical and real-world patterns
of change and functional
relationships with emphasis on the
role of variable quantities.
Descriptors
Patterns, relations, & functions: 1, 2
Expressions, equations, &
inequalities: 5
MPS Learning Target #7
(Grade 8)
Model, justify, and solve linear
equations and relationships using
translations among tables,
graphs/grids, and symbolic forms.
MPS Learning Target #8
(Grade 8)
Explain use of properties (e.g.,
commutative, associative,
distributive) to evaluate expressions
and solve linear equations.
Descriptors
Patterns, relations, & functions: 1
Expressions, equations, &
inequalities: 3, 4, 5
Properties: 7
Descriptors
Expressions, equations, &
inequalities: 3, 4
Properties: 6, 7
Grade of
Wisconsin Sub-skill Descriptors (Beginning of Grade 10)
Emphasis
Sub-skill F.a: Patterns, relations, and functions
Grades 8-9
1) Describe, recognize, interpret and translate graphical representations of mathematical and
real-world phenomena on coordinate grids (e.g., slope, intercepts, rate of change, linear and
non-linear functions, and quadratic, exponential and constant functions).
Grades 8-9
2) Analyze, generalize, and represent patterns of change (e.g., direct and inverse variations,
including numerical sequences, patterns to a given term, algebraic expressions and equations).
Sub-skill F.b: Expressions, equations, and inequalities
Grades 8-9
3) Solve linear and quadratic equations, linear inequalities and systems of linear equations and
inequalities.
Note: Grade 8 emphasize solve linear equations.
Grades 8-9
4) Model and solve a variety of mathematical and real-world problems by using algebraic
expressions, equations and inequalities (e.g., linear, exponential, quadratic).
Grades 8-9
5) Translate between different representations and describe the relationship among variable
quantities in a problem (e.g., tables, graphs, functional notations, formulas).
Sub-skill F.c: Properties
Grades 8-9
6) Demonstrate understanding of properties by evaluating and simplifying expressions.
Note: Grade 8 emphasize demonstrate understanding of the Distributive, Commutative, and
Associative properties by evaluating and simplifying expressions.
Grades 8-9
7) Demonstrate understanding of properties by solving linear and quadratic equations, linear
inequalities, and systems of linear equations and inequalities with one or two variables.
Note: Grade 8 emphasize demonstrate understanding of properties by solving linear equations.
Note: Teachers in Grade 8 and Grade 9 grade share the Beginning of Grade 10 Descriptors.
Some Descriptors are more relevant to one grade than the other.
MPS Mathematics Learning Targets 2.0 (rev 8/1/06)
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under
Grant No. 0314898.