04-05
05-06
06-07
07-08
08-09
BENCHMARK
GLEs
N-1-M demonstrating that a rational number
can be expressed in many forms, and selecting an appropriate form for a
given situation (e.g., fractions, decimals, and percents)
1. Compare rational numbers using symbols (i.e., <, #, =, $ , > )
and position on a number line
2. Use whole
number exponents (0-3) in problem-solving contexts
N-2-M demonstrating number sense and
estimation skills to describe, order, and compare rational numbers
(e.g., magnitude, integers, fractions, decimals, and percents)
1. Compare rational numbers using symbols (i.e., <, #, =, $ , > ) and position on a number line
3. Estimate the
answer to an operation involving rational numbers based on the original
numbers
N-3-M reading, writing, representing, and
using rational numbers in a variety of forms (e.g., integers, mixed
numbers, and improper fractions)
4. Read and
write numbers in scientific notation with positive exponents
N-4-M demonstration a conceptual
understanding of the meaning of the basic arithmetic operations (add,
subtract, multiply and divide) and their relationships to each other
5. Simplify
expressions involving operations on integers, grouping symbols, and
whole number exponents using order of operations
N-5-M applying an understanding of rational
numbers and arithmetic operations to real-life situations
2. Use whole number exponents (0-3) in
problem-solving contexts)
6. Identify missing information or suggest a
strategy for solving a real-life, rational-number problem
8. Solve real-life problems involving
percentages, including percentages less than 1 or greater than 100
9. Find unit/cost rates and apply them in
real-life problems
N-6-M constructing, using, and explaining
procedures to compute and estimate with rational numbers employing
mental math strategies
3. Estimate the
answer to an operation involving rational numbers based on the original
numbers
N-7-M selecting and using appropriate
computational methods and tools for given situations involving rational
numbers (e.g., estimation, or exact computation using mental
arithmetic, calculator, computer, or paper and pencil)
N-8-M demonstrating a conceptual
understanding and applications of proportional reasoning (e.g.,
determining equivalent ratios, finding a missing term of a given
proportion)
7. Use proportional reasoning to model and solve
real-life problems
8. Solve real-life problems involving
percentages, including percentages less than 1 or greater than 100
9. Find unit/cost rates and apply them in
real-life problems
18. Apply rate of change in real-life problems,
including density, velocity, and international monetary conversions
30. Construct, interpret, and use scale drawings
in real-life situations
A-1-M demonstrating a conceptual
understanding of variables, expressions, equations, and inequalities
(e.g., symbolically represent real-world problems as linear terms,
equations, or inequalities, etc.)
10. Write real-life meanings of expressions and
equations involving rational numbers and variables
11. Translate real-life situations that can be
modeled by linear or exponential relationships to algebraic
expressions, equations, and inequalities
A-2-M modeling and developing methods for
solving equations and inequalities (e.g., using charts, graphs,
manipulatives, and/or standard algebraic procedures)
12. Solve and graph solutions of multi-step linear
equations and inequalities
14. Construct a
table of x- and y- values satisfying a linear equation
and construct a graph of the line on the coordinate plane
A-3-M representing situations and number
patterns with tables, graphs, and verbal and written statements, while
exploring the relationships among these representations (e.g., multiple
representations for the same situation)
13. Switch between functions represented as
tables, equations, graphs, and verbal representations, with and without
technology
14. Construct a table of x- and y-
values satisfying a linear equation and construct a graph of the line
on the coordinate plane
A-4-M analyzing tables and graphs to identify
relationships exhibited by the data and making generalizations based
upon these relationships
11. Translate
real-life situations that can be modeled by linear or exponential
relationships to algebraic expressions, equation inequalities
(A-1-M)
(A-4-M) (A-5-M)
13. Switch between functions represented as
tables, equations, graphs, and verbal representations with and without
technology
15. Describe and compare situations with constant
or varying rates of change
16. Explain and formulate generalizations about
how a change in one variable results in a change in another variable
38. Sketch and
interpret a trend line (i.e., line of best fit) on a scatterplot
A-5-M demonstrating the connection of algebra
to the other strands and to real-life situations
9. Find unit/cost rates and apply them in
real-life problems
10. Write real-life meanings of expressions and
equations involving rational numbers and variables
11. Translate real-life situations that can be
modeled by linear or exponential relationships to algebraic
expressions, equations, and inequalities
29. Solve problems involving lengths of side of
similar triangles
38. Sketch and interpret a trend line (i.e., line
of best fit) on a scatterplot
39. Represent the nth term in a pattern as a
formula and test the representation
47. Represent the n^th term in a pattern as a
formula and test the representation (P-1-M) (P-2-M) (P-3-M) (A-5-M)
M-1-M applying the concepts of length, area,
surface area, volume, capacity, weight, mass, money, time, temperature,
and rate to real-world experiences
17. Determine the volume and surface area of
prisms and cylinders
18. Apply rate
of change in real-life problems, including density, velocity, and
international monetary conversions
M-2-M demonstrating an intuitive sense of
measurement (e.g., estimating and determining reasonableness of
measures)
19. Demonstrate an intuitive sense of the relative
sizes of common units of volume in relation to real-life applications
and use this sense when estimating
M-3-M selecting appropriate units and tools
for tasks by considering the purpose for the measurement and the
prevision required for the task (e.g., length of a room in feet rather
than inches)
20/ Identify
and select appropriate units for measuring volume
M-4-M using intuition and estimation skills
to describe, order, and compare formal and informal measures (e.g.,
ordering cup, pint, quart, gallon; comparing a meter to a yard)
21. Compare and estimate measurements of volume
and capacity within and between the
M-5-M converting from one unit of measurement
to another within the same system (Comparisons between systems,
customary and metric, should be based on intuitive reference points,
not formal computation)
22. Convert units of volume/capacity within
systems for
M-6-M - demonstrating the connection of
measurement to the other strands and to real-life situations
18. Apply rate of change in real-life problems,
including density, velocity, and international monetary conversions
30. Construct,
interpret, and use scale drawings in real-life situations
G-1-M using estimation skills to describe,
order, and compare geometric measures
19. Demonstrate an intuitive sense of the relative
sizes of common units of volume in relation to real-life applications
and use this sense when estimating
21. Compare and
estimate measurements of volume and capacity within and between the
G-2-M identifying, describing, comparing,
constructing, and classifying geometric figures and concepts
23. Define and apply the terms measure, distance,
midpoint, bisect, bisector, and perpendicular bisector
24. Demonstrate conceptual and practical
understanding of symmetry, similarity, and congruence and identify
similar and congruent figures
G-3-M making predictions regarding
transformations of geometric figures (e.g., make predictions regarding
translations, reflections, and rotations of common figures)
25. Predict, draw, and discuss the resulting
changes in lengths, orientation, angle measures, and coordinates when
figures are translated, reflected across horizontal or vertical lines,
and rotated on a grid
26. Predict, draw, and discuss the resulting
changes in lengths, orientation, and angle measures that occur in
figures under a similarity transformation (dilation
G-4-M constructing two- and three-dimensional
models
27. Construct
polyhedra using 2-dimensional patterns (nets)
G-5-M making and testing conjectures about
geometric shapes and their properties
28. Apply concepts, properties, and relationships
of adjacent, corresponding, vertical, alternate interior,
complementary, and supplementary angles
29. Solve problems involving lengths of sides of
similar triangles
30. Construct, interpret, and use scale drawings
in real-life situations
31. Use area to justify the Pythagorean theorem
and apply the Pythagorean theorem and its converse in real-life problems
32. Model and explain the relationship between the
dimensions of a rectangular prism and its volume (i.e., how scale
change in linear dimension(s) affects volume)
G-6-M demonstrating an understanding of the
coordinate system (e.g., locate points, identify coordinates, and graph
points in a coordinate plane to represent real-world situations)
25. Predict, draw, and discuss the resulting
changes in lengths, orientation, angle measures, and coordinates when
figures are translated, reflected across horizontal or vertical lines,
and rotated on a grid
26. Predict, draw, and discuss the resulting
changes in lengths, orientation, and angle measures that occur in
figures under a similarity transformation (dilation)
33. Graph solutions to real-life problems on the
coordinate plane
G-7-M demonstrating the connection of
geometry to the other strands and to real-life situations (e.g.,
applications of the Pythagorean Theorem)
17. Determine the volume and surface area of
prisms and cylinders
31. Use area to
justify the Pythagorean theorem and apply the Pythagorean theorem and
its converse in real-life problems
D-1-M systematically collecting, organizing,
describing, and displaying data in charts, tables, plots, graphs,
and/or spreadsheets
34. Determine what kind of data display is
appropriate for a given situation
35. Match a data set or graph to a described
situation, and vice-versa
36. Organize and display data using circle graphs
37. Collect and organize data using
box-and-whisker plots and use the plots to interpret quartiles and range
D-2-M analyzing, interpreting, evaluating,
drawing inferences, and making estimations, predictions, decisions, and
convincing arguments based on organized data (e.g., analyze data using
concepts of mean, median, mode, range, random samples, sample size,
bias, and data extremes)
37. Collect and organize data using
box-and-whisker plots and use the plots to interpret quartiles and range
38. Sketch and interpret a trend line (i.e., line
of best fit) on a scatterplot
39. Analyze and make predictions from discovered
data patterns
40. Explain factors in a data set that would
affect measures of central tendency (e.g., impact of extreme values)
and discuss which measure is most appropriate for a given situation
41. Select random samples that are representative
of the population, including sampling with and without replacement, and
explain the effect of sampling on bias
D-3-M describing informal thinking procedures
(e.g., solving elementary logic problems using Venn diagrams, tables,
charts, and/or elementary logic operatives to solve logic problems in
real-life situations; reach valid conclusions in elementary logic
problems involving “and, or not if/then”)
D-4-M analyzing various counting and
enumeration procedures with and without replacement (e.g., find the
total number of possible outcomes or possible choices in a given
situation)
41. Select random samples that are representative
of the population, including sampling with and without replacement, and
explain the effect of sampling on bias
42. Use lists, tree diagrams, and tables to apply
the concept of permutations to represent an ordering with and without
replacement
43. Use lists and tables to apply the concept of
combinations to represent the number of possible ways a set of objects
can be selected from a group
D-5-M comparing experimental probability
results with theoretical probability (e.g., representing probabilities
of concrete situations as common fractions, investigating single-event
and multiple-event probability, using sample spaces, geometric figures,
tables, and/or graphs)
44. Use experimental data presented in tables and
graphs to make outcome predictions of independent events
45. Calculate, illustrate, and apply single- and
multiple-event probabilities, including mutually exclusive, independent
events and non-mutually exclusive dependent events
D-6-M demonstrating the connections of data
analysis, probability, and discrete math to other strands and to
real-life situations
P-1-M describing, extending, analyzing, and
creating a wide variety of numerical, geometrical, and statistical
patterns (e.g., skip counting of rational numbers and simple
exponential number patterns)
46. Distinguish between and explain when real-life
numerical patterns are linear/arithmetic (i.e., grows by addition) or
exponential/geometric (i.e., grows by multiplication)
47. Represent the nth term in a pattern as a
formula and test the representation
P-2-M describing
and representing relationships using tables, rules, simple equations,
and graphs
13. Switch between functions represented as
tables, equations, graphs, and verbal representations, with and without
technology
47. Represent
the nth term in a pattern as a formula and test the representation
P-3-M analyzing relationships to explain how
a change in one quantity results in a change in another (e.g.,change in
the dimensions of a rectangular solid affects the volume)
47. Represent the nth term in a pattern as a
formula and test the representation
48. Illustrate patterns of change in dimension(s)
and corresponding changes in volumes of rectangular solids
P-4-M demonstrating the pervasive use of
patterns, relations, and functions in other strands and in real-life
situations
46. Distinguish between and explain when real-life
numerical patterns are linear/arithmetic (i.e., grows by addition) or
exponential/geometric (i.e., grows by multiplication)