May 25th
May 25th
Grades Five and Six Math Benchmarks
Strand 1: Number Sense and Operations
Concepts
Students will understand:
• the value of each in dividual digit in a number;
• the relationship between the base and exponent;
• that powers of 10 can be re presented using a base of ten and an exponent;
• that numbers can be classified;
• the relationships between addition/subtraction and multiplication/division;
• fractions as ratios of whole numbers, as parts of unit wholes, and as parts of
a
collection;
• that a percent is a part of a whole based on a denominator of 100.
| Standard |
Grade 5 Skills |
Grade 6 Skills |
| 6.N.2 |
Read, write, compare, order and identify
place value in whole numbers to the
hundred millions place (M) |
Read, write, compare, order and
identify
place value in whole numbers to the
hundred billions place (M) |
| APS |
Round whole numbers to the hundred
millions place (M) |
Round whole numbers to the hundred
billions place (M) |
| 6.N.7 |
Read, write, compare, order and identify
place value in decimal numbers to
hundredths understand (M) |
Read, write compare, order and
identify
place value in decimal numbers to
thousandths understand (M) |
| APS |
Round decimals to the hundredths place, to
the tenths place, or the nearest whole
number (M) |
Round decimals to the thousandths
place, to
the nearest hundredth, or tenth (M) |
| 6.N.6 |
Identify positive and negative integers,
fractions, decimals, and mixed numbers on a
number line (W) |
Identify positive and negative
integers,
fractions, decimals, and mixed numbers on a
number line (M) |
| 6.N.16 |
Make reasonable estimates of quantities (W) |
Make reasonable estimates of
quantities (W) |
| 6.N.16 |
Make reasonable estimates of results of
computation with whole numbers, fractions,
mixed numbers, decimals and percents (W) |
Make reasonable estimates of results
of
computation with whole numbers, fractions,
mixed numbers, decimals and percents (W) |
| 6.N.3 |
Convert between expanded and standard
notation for numbers as large as hundred
millions and as small as hundredths
(Example: 9724 = 9000+700+20+4) (M) |
Convert between expanded and standard
notation for numbers as large as hundred
millions and as small as thousandths
(Example: 9724 = 9000+700+20+4) (M) |
| 6.N.1 |
Model and identify square numbers (I/W) |
Recognize and find the squares/square
roots
of numbers through 12 /144 (M) |
| 6.N.1 |
Convert between standard and exponential
notation (I/W) |
Convert between standard and
exponential
notation for exponents larger than 2 (I/W) |
| 6.N.1 |
Represent large numbers to hundred million
using powers of 10 (I/W) |
Represent large numbers to hundred
billions
using powers of 10 (W) |
| APS |
Multiply and divide by multiples of 10 (I/W) |
Multiply and divide by multiples of
10 (W) |
| 6.N.8 |
Identify prime and composite numbers
(I/W) |
Identify prime and composite numbers
(M) |
| 6.N.8 |
Find the prime factorization of a number
(I/W) |
Find the prime factorization of a
number (M) |
| 6.N.8 |
Find the least common multiple and greatest
common factor (W) |
Find the least common multiple and
greatest
common factor (M) |
| 6.N.8 |
Apply divisibility rules (I/W) |
Apply divisibility rules (W) |
| 6.N.13 |
2- and 3-digit multiplication (M) |
|
| 6.N.13 |
Divide up to a 3-digit whole number with a
2-digit divisor (M) |
|
| APS |
Report division remainders as fractions (M) |
Report division remainders as
fractions and
decimals (M) |
6.N.15
APS |
|
Add and subtract positive and
negative
integers (I/W) |
| APS |
Recognize commutative, associative and
identity (0 and 1) properties (I/W) |
Recognize and apply commutative,
associative and identity (0 and 1)properties
(W) |
| 6.N.11 |
Recognize and apply order of operations (I) |
Recognize and apply order of
operations
(I/W) |
| 6.N.5 |
Find equivalent fractions (M) |
|
| 6.N.14 |
Simplify fractions to lowest terms (I/W) |
Simplify fractions to lowest terms
(M) |
| 6.N.5 |
Find decimal and percent equivalents for
familiar fractions (W) |
Find decimal and percent equivalents
for
fractions (M) |
| 6.N.14 |
Add and subtract fractions with
common
denominators (M) |
|
| 6.N.14 |
Add and subtract fractions with un like
denominators (I/W) |
Add and subtract fractions with
unlike
denominators (M) |
| 6.N.14 |
Multiply fractions (I/W) |
Multiply fractions (M) |
| APS |
Find the reciprocal of a number (I/W) |
Find the reciprocal of a number (M) |
| 6.N.14 |
Divide fractions (I) |
Divide fractions (W/concept)
(M/algorithm) |
| 6.N.5 |
Convert between improper fractions and
mixed numbers (I/W) |
Convert between improper fractions
and
mixed numbers (M) |
| 6.N.14 |
Add mixed numbers with common
denominators (M) |
Add mixed numbers with unlike
denominators (M) |
| 6.N.14 |
Subtract mixed numbers with common
denominators/borrowing (I) |
Subtract mixed numbers with unlike
denominators/borrowing (W) |
| 6.N.4 |
|
Identify ratios (I/W) |
| APS |
|
Solve proportions (I/W) |
| 6.N.5 |
Find equivalent decimals (e.g., 0.750=0.75)
(M) |
|
| 6.N.5 |
Find fraction and percent equivalents for
decimals (W) |
Find fraction and percent equivalents
for
decimals (M) |
| 6.N.13 |
Add, subtract and multiply decimals (I/W) |
Add, subtract and multiply decimals
(M) |
| 6.N.13 |
Divide decimals by a whole number (I) |
Divide decimals by a decimal (I/W) |
| 6.N.5 |
Find decimal and fraction equivalents for
percentages (W) |
Find decimal and fraction equivalents
for
percentages (M) |
| APS |
Find the percent of a number (I) |
Find the percent of a number (W) |
Strand 2: Patterns, Relations and Algebra
Concepts
Students will understand:
• that a variable or icon can be used to represent and solve for unknown
quantities
in simple equations for addition, subtraction, multiplication and division;
• that mathematical situations and structures can be represented using algebraic
symbols.
| Standard |
Grade 5 Skills |
Grade 6 Skills |
| 6.P.4 |
Solve simple, whole-number function
problems (e.g.: input-out problems, what’s
my rule?) (M) |
Solve multi-step function problems
involving fractions and decimals (e.g.:input-out
problems, what’s my rule?) (I/W) |
| 6.P.2 |
Translate words to expressions and/or
sentences involving variables (W) |
Translate words to expressions and/or
sentences involving variables (M) |
| 6.P.2 |
Given the value of a variable, evaluate a
simple expression (e.g.: for N=5, evaluate
11*N) (W) |
Given the value of a variable,
evaluate a
simple expression (M) |
| 6.P.3 |
Identify the value of the variable in a simple
equation (e.g.: for 11*N=55, find the value of
N) (W) |
Identify the value of the variable in
a simple
equation (M) |
| 6.P.5 |
Solve linear equations using concrete
models, tables, graphs, and paper and pencil
methods (W) |
Solve linear equations using concrete
models, tables, graphs, and paper and pencil
methods (W) |
| 6.P.7 |
|
Model situations with proportional
relationships/rate tables and solve problems
(I/W) |
| 6.P.1 |
Analyze and determine the rules for
extending symbolic, arithmetic , and
geometric patterns and progressions
(e.g.: ABBCCC….) (W) |
Analyze and determine the rules for
extending symbolic, arithmetic, and
geometric patterns and progressions
(e.g.: ABBCCC….) (W) |
| 6.P.5 |
See Strand 5 |
See Strand 5 |
Strand 3: Geometry
Concepts
Students will understand:
• that the characteristics and properties of two- and three-dimensional shapes
can be
used to classify the shapes and analyze them;
• that locations and spatial relationships can be represented using coordinate
geometry.
| Standard |
Grade 5 Skills |
Grade 6 Skills |
| APS |
Measure angles using a protractor
(I/W) |
Measure angles using a protractor (M) |
| APS |
Review identification of acute, right
and
obtuse angles |
Identify straight and reflex angles (I) |
| APS |
|
Analyze the relationship of angles formed by
intersecting lines (e.g., complementary and
supplementary) (I) |
| APS |
|
Investigate tessellations/tilings (I) |
| 6.G.1 |
Identify polygons (e.g. squares,
rectangles,
paralle lograms , rhombuses, trapezoids and
isosceles, equilateral and right triangles)
based on their properties (e.g., types of
interior angles, perpendicular and parallel
sides and congruence) (W) |
Identify polygons (e.g., squares, rectangles,
parallelograms, rhombuses, trapezoids and
isosceles, equilateral and right triangles)
based on their properties (e.g., types of
interior angles, perpendicular and parallel
sides and congruence) (M) |
| 6.G.2 |
Identify three-dimensional shapes
(e.g.
cubes , prisms, spheres, cones, and pyramids)
based on their properties, such as edges and
faces (W) |
Identify three-dimensional shapes (e.g.
cubes, prisms, spheres, cones, and pyramids)
based on their properties, such as edges and
faces (M) |
| 6.G.9 |
Match three-dimensional objects and
their
two-dimensional representations (e.g., nets,
projections and perspective drawings.)(W) |
Match three-dimensional objects and their
two-dimensional representations (e.g., nets,
projections and perspective drawings.)(W) |
| 6.G.3 |
Identify relationships between lines
(e.g.,
intersecting, parallel and perpendicular) (M) |
Identify relationships between planes (e.g.,
intersecting, parallel and perpendicular)
(I/M) |
| 6.G.4 |
Graph and read points on quadrant 1
(positives only) of the Cartesian coordinate
grid (M) |
Graph and read points on all four quadrants
of the Cartesian coordinate grid (I/M) |
| 6.G.5 |
See Strand 1 |
See Strand 1 |
| 6.G.6 |
Predict, describe and perform
transformations on two dimensional shapes
(e.g., translations, rotations, and reflections)
(W) |
Predict, describe and perform
transformations on two-dimensional shapes
(e.g., translations, rotations, and reflections)
(M) |
| 6.G.7 |
Identify types of symmetry, including
line
and rotational (W) |
Identify types of symmetry, including line
and rotational (W) |
| 6.G.8 |
Determine if two shapes are congruent
by
measurement or transformation (W) |
Determine if two shapes are congruent by
measurement or transformation (M) |
Strand 4: Measurement
Concepts
Students will understand:
• attributes such as length, area, weight, volume and size of angle;
• the need for measuring with standard units;
• that measurements are approximations;
• how differences in units affect precision;
• the difference between metric and conventional systems of measurement ;
• relationships among units;
• select and use units of appropriate size and type to measure angles,
perimeter,
area, surface area and volume.
| Standard |
Grade 5 Skills |
Grade 6 Skills |
| APS |
Select and apply appropriate
conventional
and/or metric units and tools to measure
length, area, volume, weight, time,
temperature and the size of angles (W) |
Select and apply appropriate conventional
and/or metric units and tools to measure
length, area, volume, weight, time,
temperature and the size of angles (W) |
| APS |
Use a ruler to measure length to
nearest 1/8
of an inch and 1/2 of a centimeter (M) |
Use a ruler to measure length to nearest 1/16
of an inch and nearest millimeter (W) |
| 6.M.3 |
Solve problems involving proportional
relationships and units of measure (e.g.,
same-system unit conversions, scale models,
maps and speed) (W) |
Solve problems involving proportional
relationships and units of measure (e.g.,
same-system unit conversions, scale models,
maps and speed) (W) |
| 6.M.2 |
Use a protractor to measure and
construct
angles (W) |
Use a protractor to measure and construct
angles, triangles and quadrilaterals (W) |
| 6.M.1 |
Find the perimeter of all polygons
(M) |
|
6.M.1
6.M.4 |
Explore various models for finding
the area
of a square, rectangle, triangle and
parallelogram (W) |
Know and apply the formulas for the area of
rectangles, squares, triangles and
parallelograms (W/M) |
| 6.M.7 |
Find the sum of angles in triangles
and
quadrilaterals (W) |
Find the sum of angles in triangles and
quadrilaterals (M) |
| 6.M.7 |
Find the sum of angles in polygons
with
more than four sides (I) |
Find the sum of angles in polygons with
more than four sides (W) |
| 6.M.6 |
Find the volumes and surface areas of
rectangular prisms (I) |
Find the volumes and surface areas of
rectangular prisms (W) |
| 6.M.6 |
|
Investigate volumes and surface areas of
cylinders, cones, spheres, pyramids and
triangular prisms (I) |
| 6.M.5 |
Identify and measure the radius and
diameter of a circle (W/M) |
|
| 6.M.5 |
Explore the relationship between the
diameter and circumference of a circle; the
value of pi (I) |
Given the formula, find the circumference of
a circle (W) |
| 6.M.5 |
|
Explore various models and the formula for
finding the area of a circle (I/W) |
| 6.M.5 |
Use a compass to draw a circle (I) |
Use a compass to draw a circle (W) |
| APS |
Explore the use of a balance scale
(W) |
Explore the use of a balance scale (W) |
Strand 5: Data Analysis, Statistics and Probability
Concepts
Students will understand:
• how the nature of data collection affects the data set;
• how increasing the number of trials affects experimental results;
• the differences in representing categorical and numerical data ;
• the correspondence between data sets and their graphic representations;
• what constitutes a fair game of chance.
| Standard |
Grade 5 Skills |
Grade 6 Skills |
| 6.D.1 |
Identify the mode, median, mean,
range and
outlier in a given set of data (W) |
Given a set of data, identify the mode,
median, mean, range and outlier (M) |
| 6.D.2 |
Construct and interpret tally charts ,
bar
graphs, line graphs and pictographs (M) |
|
| APS |
Read and interpret scales on a graph
(M) |
Read and interpret intervals on graph (M) |
| APS |
|
Select appropriate scale/intervals and
construct graphs for a set of data (I/W) |
| 6.D.2 |
Construct and interpret line plots
and stemand-
leaf plots (W) |
Construct and interpret line plots and stemand-leaf
plots (W) |
| 6.D.2 |
Interpret circle graphs (W) |
Interpret circle graphs (M) |
| 6.D.2 |
|
Construct circle graphs (I) |
| 6.D.2 |
|
Construct and interpret frequency graphs (I) |
| 6.D.4 |
Predict the probability of simple
experiments
(tossing coins, rolling dice, spinning a
spinner) and test the predications (W) |
Predict the probability of simple experiments
(tossing coins, rolling dice, spinning a
spinner) and test the predications (M) |
| 6.D.4 |
Use appropriate ratios between 0 and
1
(fractions or percents) to represent the
probability of an outcome (W) |
Use appropriate ratios between 0 and 1
(fractions or percents) to represent the
probability of an outcome (M) |
| 6.D.3 |
Use tree diagrams and other models
(e.g.,
lists and tables) to represent and analyze
possible actual outcomes of trials (I) |
Use tree diagrams and other models (e.g.,
lists and tables) to represent and analyze
possible actual outcomes of trials (W) |
|
|
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