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. Factor whole numbers into primes
2. Determine common factors and common multiples
for pairs of whole numbers
3. Find the greatest common factor (GCF) and
least common multiple (LCM) for whole numbers in the context of
problem-solving
4. Recognize and compute equivalent
representations of fractions and decimals (i.e., halves, thirds,
fourths, fifths, eighths, tenths, hundredths)
5. Decide which representation (i.e. fraction or
decimal) of a positive number is appropriate in a real-life situation
N-2-M demonstrating number sense and
estimation skills to describe, order, and compare rational numbers
(e.g., magnitude, integers, fractions, decimals, and percents)
6. Compare positive fractions, decimals, and
positive and negative integers using symbols (i.e., < , = , >)
and number lines
N-3-M reading, writing, representing, and
using rational numbers in a variety of forms (e.g., integers, mixed
numbers, and improper fractions)
4. Recognize and compute equivalent
representations of fractions and decimals (i.e., halves, thirds,
fourths, fifths, eighths, tenths, hundredths)
7. Read and write numerals and words for decimals
through ten-thousandths
8. Demonstrate
the meaning of positive and negative numbers and their opposites in
real-life situations
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
N-5-M applying an understanding of rational
numbers and arithmetic operations to real-life situations
5. Decide which representation (i.e., fraction or
decimal) of a positive number is appropriate in a real-life situation
8. Demonstrate the meaning of positive and
negative numbers and their opposites in real life situations
9. Add and subtract fractions and decimals in
real-life situations
N-6-M constructing, using, and explaining
procedures to compute and estimate with rational numbers employing
mental math strategies
10. Use and explain estimation strategies to
predict computational results with positive fractions and decimals
11. Mentally multiply and divide by powers of 10
(e.g., 25/10=2.5; 12.56 x 100=1,256)
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)
12. Divide
4-digit numbers by 2-digit numbers with the quotient written as a mixed
number or a decimal
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)
13. Use models and pictures to explain concepts or
solve problems involving ratio, proportion, and percent with whole
numbers
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.)
14. Model and identify perfect squares up to 144
15. Match
algebraic equations and expressions with verbal statements and vice
versa
A-2-M modeling and developing methods for
solving equations and inequalities (e.g., using charts, graphs,
manipulatives, and/or standard algebraic procedures)
16. Evaluate simple algebraic expressions using
substitution
17. Find solutions to 2-step equations with
positive integer solutions (e.g., 3x-5=13, 2x+3x=20)
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)
15. Match algebraic equations and expressions with
verbal statements and vice versa
29. Collect, organize, label, display, and
interpret data in frequency tables, stem-and-leaf plots, and scatter
plots and discuss patterns in the data verbally and in writing
A-4-M analyzing tables and graphs to identify
relationships exhibited by the data and making generalizations based
upon these relationships
38. Describe
patterns in sequences of arithmetic and geometric growth and now-next
relationships (i.e., growth patterns where the next term is dependent
on the present term( with numbers and figures
A-5-M demonstrating the connection of algebra
to the other strands and to real-life situations
15. Match algebraic equations and expressions with
verbal statements and vice versa
20. Calculate,
interpret, and compare rates such as $/lb., mpg, and mph
M-1-M applying the concepts of length, area,
surface area, volume, capacity, weight, mass, money, time, temperature,
and rate to real-world experiences
18. Measure length and read linear measurements to
the nearest sixteenth-inch and mm
19. Calculate perimeter and area of triangles,
parallelograms, and trapezoids
20. Calculate, interpret, and compare rates such
as $/lb., mpg, and mph
M-2-M demonstrating an intuitive sense of
measurement (e.g., estimating and determining reasonableness of
measures)
15. Match algebraic equations and expressions with
verbal statements and vice versa
21. Demonstrate an intuitive sense of relative
sizes of common units for length and area of familiar objects in
real-life problems (e.g., estimate the area of a desktop in square
feet, the average adult is between 1.5 and 2 meters tall)
22. Estimate perimeter and area of any
2-dimensional figure (regular and irregular using standard units
31. Demonstrate an understanding of precision,
accuracy, and error in measurement
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)
23. Identify and select appropriate units to
measure area
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)
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)
M-6-M - demonstrating the connection of
measurement to the other strands and to real-life situations
G-1-M using estimation skills to describe,
order, and compare geometric measures
21. Demonstrate an intuitive sense of relative
sizes of common units for length and area of familiar objects in
real-life problems (e.g., estimate the area of a desktop in square
feet, the average adult is between 1.5 and 2 meters tall)
26. Apply concepts, properties, and relationships
of points, lines, line segments, rays, diagonals, circles, and right,
acute, and obtuse angles and triangles in real life situations,
including estimating sizes of angles
G-2-M identifying, describing, comparing,
constructing, and classifying geometric figures and concepts
24. Use mathematical terms to describe the basic
properties of 3-dimensional objects (edges, vertices, faces, base, etc.)
25. Relate polyhedra to their 2-dimensional shapes
by drawing or sketching their faces
26. Apply concepts, properties, and relationships
of points, lines, line segments, rays, diagonals, circles, and right,
acute, and obtuse angles and triangles in real life situations,
including estimating sizes of angles
G-3-M making predictions regarding
transformations of geometric figures (e.g., make predictions regarding
translations, reflections, and rotations of common figures)
27. Make and test predictions regarding
tessellations with geometric shapes
G-4-M constructing two- and three-dimensional
models
25. Relate
polyhedra to their 2-dimensional shapes by drawing or sketching their
faces
G-5-M making and testing conjectures about
geometric shapes and their properties
26. Apply concepts, properties, and relationships
of points, lines, line segments, rays, diagonals, circles, and right,
acute, and obtuse angles and triangles in real life situations,
including estimating sizes of angles
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)
28. Use a rectangular grid and ordered pairs to
plot simple shapes and find horizontal and vertical lengths and area
G-7-M demonstrating the connection of
geometry to the other strands and to real-life situations (e.g.,
applications of the Pythagorean Theorem)\\20. Determine
the perimeter and area of composite plane figures by subdivision and
area addition
D-1-M systematically collecting, organizing,
describing, and displaying data in charts, tables, plots, graphs,
and/or spreadsheets
29. Collect, organize, label, display, and
interpret data in frequency tables, stem-and-leaf plots, and scatter
plots and discuss patterns in the data verbally and in writing
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)
29. Collect, organize, label, display, and
interpret data in frequency tables, stem-and-leaf plots, and scatter
plots and discuss patterns in the data verbally and in writing
30. Describe and analyze trends and patterns
observed in graphic displays
31. Demonstrate an understanding of precision,
accuracy, and error in measurement
32. Calculate and discuss mean, median, mode, and
range of a set of discrete data to solve real-life problems
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”)
33. Create and use Venn diagrams with two
overlapping categories to solve counting logic problems
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)
34. Use lists, tree diagrams, and tables to
determine the possible combinations from two disjoint sets when
choosing one item from each set
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)
35. Illustrate and apply the concept of
complementary events
36. Apply the meaning of equally likely
and equally probable to real-life situations
D-6-M demonstrating the connections of data
analysis, probability, and discrete math to other strands and to
real-life situations
36. Apply the meaning of equally likely
and equally probable 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)
37. Describe, complete, and apply a pattern of
differences found in an input-output table
P-2-M describing
and representing relationships using tables, rules, simple equations,
and graphs
15. Match algebraic equations and expressions with
verbal state vice versa (A-1-M) (A-3-M) (A-5-M) (P-2-M)
25. Match algebraic equations and expressions with
verbal statements and vice versa
37. Describe, complete, and apply a pattern of
differences found in an input-output table
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)
37. Describe, complete, and apply a pattern of
differences found in an input-output table
38. Describe patterns in sequences of arithmetic
and geometric growth and now-next relationships (i.e., growth patterns
where the next term is dependent on the present term( with numbers and
figures
P-4-M demonstrating the pervasive use of
patterns, relations, and functions in other strands and in real-life
situations