Mathematics
Standards
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Grade: K |
Back to Big Cat Rescue's Teacher's Resource
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Big Idea1: Represent, compare, and order whole numbers and join and separate sets. |
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BENCHMARK CODE |
BENCHMARK |
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MA.K.A.1.1 |
Represent quantities with numbers
up to 20, verbally, in writing, and with manipulatives. |
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MA.K.A.1.2 |
Solve problems including those
involving sets by counting, by using cardinal and ordinal numbers, by
comparing, by ordering, and by creating sets up to 20. |
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MA.K.A.1.3 |
Solve word problems involving
simple joining and separating situations. |
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Big Idea2: Describe shapes and space. |
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BENCHMARK CODE |
BENCHMARK |
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MA.K.G.2.1 |
Describe, sort and re-sort objects
using a variety of attributes such as shape, size, and position. |
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MA.K.G.2.2 |
Identify, name, describe and sort
basic two-dimensional shapes such as squares, triangles, circles, rectangles,
hexagons, and trapezoids. |
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MA.K.G.2.3 |
Identify, name, describe, and sort
three-dimensional shapes such as spheres, cubes and cylinders. |
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MA.K.G.2.4 |
Interpret the physical world with
geometric shapes, and describe it with corresponding vocabulary. |
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MA.K.G.2.5 |
Use basic shapes, spatial
reasoning, and manipulatives to model objects in the environment and to
construct more complex shapes. |
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Big Idea3: Order objects by measurable attributes. |
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BENCHMARK CODE |
BENCHMARK |
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MA.K.G.3.1 |
Compare and order objects
indirectly or directly using measurable attributes such as length, height,
and weight. |
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Supporting Idea4: Algebra |
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BENCHMARK CODE |
BENCHMARK |
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MA.K.A.4.1 |
Identify and duplicate simple
number and non-numeric repeating and growing patterns. |
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Supporting Idea5: Geometry and Measurement |
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BENCHMARK CODE |
BENCHMARK |
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MA.K.G.5.1 |
Demonstrate an understanding of the
concept of time using identifiers such as morning, afternoon, day, week,
month, year, before/after, shorter/longer. |
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Grade: 1 |
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Big Idea1: Develop understandings of addition and subtraction strategies for basic addition facts and related subtraction facts. |
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BENCHMARK CODE |
BENCHMARK |
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MA.1.A.1.1 |
Model addition and subtraction
situations using the concepts of "part-whole," "adding
to," "taking away from," "comparing," and missing
addend." |
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MA.1.A.1.2 |
Identify, describe, and apply
addition and subtraction as inverse operations. |
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MA.1.A.1.3 |
Create and use increasingly
sophisticated strategies, and use properties such as Commutative, Associative
and Additive Identity, to add whole numbers. |
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MA.1.A.1.4 |
Use counting strategies, number
patterns, and models as a means for solving basic addition and subtraction
fact problems. |
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Big Idea2: Develop an understanding of whole number relationships, including grouping by tens and ones. |
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BENCHMARK CODE |
BENCHMARK |
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MA.1.A.2.1 |
Compare and order whole numbers at
least to 100. |
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MA.1.A.2.2 |
Represent two digit numbers in
terms of tens and ones. |
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MA.1.A.2.3 |
Order counting numbers, compare
their relative magnitudes, and represent numbers on a number line. |
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Big Idea3: Compose and decompose two-dimensional and three-dimensional geometric shapes. |
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BENCHMARK CODE |
BENCHMARK |
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MA.1.G.3.1 |
Use appropriate vocabulary to
compare shapes according to attributes and properties such as number and
lengths of sides and number of vertices. |
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MA.1.G.3.2 |
Compose and decompose plane and
solid figures, including making predictions about them, to build an
understanding of part-whole relationships and properties of shapes. |
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Supporting Idea4: Algebra |
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BENCHMARK CODE |
BENCHMARK |
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MA.1.A.4.1 |
Extend repeating and growing
patterns, fill in missing terms, and justify reasoning. |
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Supporting Idea5: Geometry and Measurement |
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BENCHMARK CODE |
BENCHMARK |
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MA.1.G.5.1 |
Measure by using iterations of a
unit, and count the unit measures by grouping units. |
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MA.1.G.5.2 |
Compare and order objects according
to descriptors of length, weight, and capacity. |
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Supporting Idea6: Number and Operations |
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BENCHMARK CODE |
BENCHMARK |
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MA.1.A.6.1 |
Use mathematical reasoning and
beginning understanding of tens and ones, including the use of invented
strategies, to solve two-digit addition and subtraction problems. |
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MA.1.A.6.2 |
Solve routine and non-routine problems by acting them out, using
manipulatives, and drawing diagrams. |
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Grade: 2 |
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Big Idea1: Develop an understanding of base-ten numerations system and place-value concepts. |
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BENCHMARK CODE |
BENCHMARK |
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MA.2.A.1.1 |
Identify relationships between the
digits and their place values through the thousands, including counting by
tens and hundreds. |
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MA.2.A.1.2 |
Identify and name numbers through
thousands in terms of place value, and apply this knowledge to expanded
notation. |
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MA.2.A.1.3 |
Compare and order multi-digit
numbers through the thousands. |
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Big Idea2: Develop quick recall of addition facts and related subtraction facts and fluency with multi-digit addition and subtraction. |
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BENCHMARK CODE |
BENCHMARK |
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MA.2.A.2.1 |
Recall basic addition and related
subtraction facts. |
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MA.2.A.2.2 |
Add and subtract multi-digit whole
numbers through three digits with fluency by using a variety of strategies,
including invented and standard algorithms and explanations of those
procedures. |
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MA.2.A.2.3 |
Estimate solutions to multi-digit
addition and subtraction problems through three digits. |
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MA.2.A.2.4 |
Solve addition and subtraction
problems that involve measurement and geometry. |
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Big Idea3: Develop an understanding of linear measurement and facility in measuring lengths. |
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BENCHMARK CODE |
BENCHMARK |
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MA.2.G.3.1 |
Estimate and use standard units,
including inches and centimeters, to partition and measure lengths of
objects. |
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MA.2.G.3.2 |
Describe the inverse relationship
between the size of a unit and number of units needed to measure a given
object. |
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MA.2.G.3.3 |
Apply the Transitive Property when
comparing lengths of objects. |
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MA.2.G.3.4 |
Estimate, select an appropriate
tool, measure, and/or compute lengths to solve problems. |
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Supporting Idea4: Algebra |
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BENCHMARK CODE |
BENCHMARK |
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MA.2.A.4.1 |
Extend number patterns to build a
foundation for understanding multiples and factors – for example, skip
counting by 2's, 5's, 10's. |
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MA.2.A.4.2 |
Classify numbers as odd or even and
explain why. |
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MA.2.A.4.3 |
Generalize numeric and non-numeric
patterns using words and tables. |
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MA.2.A.4.4 |
Describe and apply equality to
solve problems, such as in balancing situations. |
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MA.2.A.4.5 |
Recognize and state rules for
functions that use addition and subtraction. |
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Supporting Idea5: Geometry and Measurement |
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BENCHMARK CODE |
BENCHMARK |
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MA.2.G.5.1 |
Use geometric models to demonstrate
the relationships between wholes and their parts as a foundation to
fractions. |
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MA.2.G.5.2 |
Identify time to the nearest hour
and half hour. |
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MA.2.G.5.3 |
Identify, combine, and compare
values of money in cents up to $1 and in dollars up to $100, working with a
single unit of currency. |
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MA.2.G.5.4 |
Measure weight/mass and
capacity/volume of objects. Include the use of the appropriate unit of
measure and their abbreviations including cups, pints, quarts, gallons,
ounces (oz), pounds (lbs), grams (g), kilograms (kg), milliliters (mL) and
liters (L). |
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Supporting Idea6: Number and Operations |
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BENCHMARK CODE |
BENCHMARK |
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MA.2.A.6.1 |
Solve problems that involve
repeated addition. |
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Grade: 3 |
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Big Idea1: Develop understandings of multiplication and division and strategies for basic multiplication facts and related division facts. |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.A.1.1 |
Model multiplication and division
including problems presented in context: repeated addition, multiplicative
comparison, array, how many combinations, measurement, and partitioning. |
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MA.3.A.1.2 |
Solve multiplication and division
fact problems by using strategies that result from applying number
properties. |
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MA.3.A.1.3 |
Identify, describe, and apply
division and multiplication as inverse operations. |
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Big Idea2: Develop an understanding of fractions and fraction equivalence. |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.A.2.1 |
Represent fractions, including
fractions greater than one, using area, set, and linear models. |
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MA.3.A.2.2 |
Describe how the size of the
fractional part is related to the number of equal sized pieces in the whole. |
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MA.3.A.2.3 |
Compare and order fractions,
including fractions greater than one, using models and strategies. |
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MA.3.A.2.4 |
Use models to represent equivalent
fractions, including fractions greater than 1, and identify representations
of equivalence. |
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Big Idea3: Describe and analyze properties of two-dimensional shapes. |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.G.3.1 |
Describe, analyze, compare, and
classify two-dimensional shapes using sides and angles - including acute,
obtuse, and right angles - and connect these ideas to the definition of
shapes. |
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MA.3.G.3.2 |
Compose, decompose, and transform
polygons to make other polygons, including concave and convex polygons with
three, four, five, six, eight, or ten sides. |
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MA.3.G.3.3 |
Build, draw, and analyze
two-dimensional shapes from several orientations in order to examine and
apply congruence and symmetry. |
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Supporting Idea4: Algebra |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.A.4.1 |
Create, analyze, and represent
patterns and relationships using words, variables, tables, and graphs. |
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Supporting Idea5: Geometry and Measurement |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.G.5.1 |
Select appropriate units,
strategies, and tools to solve problems involving perimeter. |
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MA.3.G.5.2 |
Measure objects using fractional
parts of linear units such as 1/2, 1/4, and 1/10. |
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MA.3.G.5.3 |
Tell time to the nearest minute and
to the nearest quarter hour, and determine the amount of time elapsed. |
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Supporting Idea6: Number and Operations |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.A.6.1 |
Represent, compute, estimate, and
solve problems using numbers through hundred thousands. |
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MA.3.A.6.2 |
Solve non-routine problems by
making a table, chart ,or list and searching for patterns. |
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Supporting Idea7: Data Analysis |
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BENCHMARK CODE |
BENCHMARK |
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MA.3.S.7.1 |
Construct and analyze frequency
tables, bar graphs, pictographs, and line plots from data, including data
collected through observations, surveys, and experiments. |
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Grade: 4 |
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Big Idea1: Develop quick recall of multiplication facts and related division facts and fluency with whole number multiplication. |
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BENCHMARK CODE |
BENCHMARK |
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MA.4.A.1.1 |
Use and describe various models for
multiplication in problem-solving situations, and demonstrate recall of basic
multiplication and related division facts with ease. |
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MA.4.A.1.2 |
Multiply multi-digit whole numbers
through four digits fluently, demonstrating understanding of the standard
algorithm, and checking for reasonableness of results, including solving
real-world problems. |
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Big Idea2: Develop an understanding of decimals, including the connection between fractions and decimals. |
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BENCHMARK CODE |
BENCHMARK |
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MA.4.A.2.1 |
Use decimals through the
thousandths place to name numbers between whole numbers. |
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MA.4.A.2.2 |
Describe decimals as an extension
of the base-ten number system. |
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MA.4.A.2.3 |
Relate equivalent fractions and
decimals with and without models, including locations on a number line. |
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MA.4.A.2.4 |
Compare and order decimals, and
estimate fraction and decimal amounts in real-world problems. |
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Big Idea3: Develop an understanding of area and determine the area of two-dimensional shapes. |
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BENCHMARK CODE |
BENCHMARK |
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MA.4.G.3.1 |
Describe and determine area as the
number of same-sized units that cover a region in the plane, recognizing that
a unit square is the standard unit for measuring area. |
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MA.4.G.3.2 |
Justify the formula for the area of
the rectangle "area = base x height". |
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MA.4.G.3.3 |
Select and use appropriate units,
both customary and metric, strategies, and measuring tools to estimate and
solve real-world area problems. |
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Supporting Idea4: Algebra |
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BENCHMARK CODE |
BENCHMARK |
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MA.4.A.4.1 |
Generate algebraic rules and use
all four operations to describe patterns, including nonnumeric growing or
repeating patterns. |
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MA.4.A.4.2 |
Describe mathematics relationships
using expressions, equations, and visual representations. |
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MA.4.A.4.3 |
Recognize and write algebraic
expressions for functions with two operations. |
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Supporting Idea5: Geometry and Measurement |
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BENCHMARK CODE |
BENCHMARK |
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MA.4.G.5.1 |
Classify angles of two-dimensional
shapes using benchmark angles (45°, 90°, 180°, and 360°) |
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MA.4.G.5.2 |
Identify and describe the results
of translations, reflections, and rotations of 45, 90, 180, 270, and 360
degrees, including figures with line and rotational symmetry. |
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MA.4.G.5.3 |
Identify and build a
three-dimensional object from a two-dimensional representation of that object
and vice versa. |
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Supporting Idea6: Number and Operations |
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BENCHMARK CODE |
BENCHMARK |
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MA.4.A.6.1 |
Use and represent numbers through
millions in various contexts, including estimation of relative sizes of amounts
or distances. |
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MA.4.A.6.2 |
Use models to represent division
as:
|
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MA.4.A.6.3 |
Generate equivalent fractions and
simplify fractions. |
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MA.4.A.6.4 |
Determine factors and multiples for
specified whole numbers. |
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MA.4.A.6.5 |
Relate halves, fourths, tenths, and
hundredths to decimals and percents. |
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MA.4.A.6.6 |
Estimate and describe
reasonableness of estimates; determine the appropriateness of an estimate
versus an exact answer. |
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Grade: 5 |
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Big Idea1: Develop an understanding of and fluency with division of whole numbers. |
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BENCHMARK CODE |
BENCHMARK |
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MA.5.A.1.1 |
Describe the process of finding quotients
involving multi-digit dividends using models, place value, properties, and
the relationship of division to multiplication. |
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MA.5.A.1.2 |
Estimate quotients or calculate
them mentally depending on the context and numbers involved. |
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MA.5.A.1.3 |
Interpret solutions to division
situations including those with remainders depending on the context of the
problem. |
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MA.5.A.1.4 |
Divide multi-digit whole numbers
fluently, including solving real-world problems, demonstrating understanding
of the standard algorithm and checking the reasonableness of results. |
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Big Idea2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals. |
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BENCHMARK CODE |
BENCHMARK |
|
MA.5.A.2.1 |
Represent addition and subtraction
of decimals and fractions with like and unlike denominators
using models, place value, or properties. |
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MA.5.A.2.2 |
Add and subtract fractions and
decimals fluently, and verify the reasonableness of results, including in
problem situations. |
|
MA.5.A.2.3 |
Make reasonable estimates of
fraction and decimal sums and differences, and use techniques for rounding. |
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MA.5.A.2.4 |
Determine the prime factorization
of numbers. |
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Big Idea3: Describe three-dimensional shapes and analyze their properties, including volume and surface area. |
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BENCHMARK CODE |
BENCHMARK |
|
MA.5.G.3.1 |
Analyze and compare the properties
of two-dimensional figures and three-dimensional solids (polyhedra),
including the number of edges, faces, vertices, and types of faces. |
|
MA.5.G.3.2 |
Describe, define, and determine surface
area and volume of prisms by using appropriate units and selecting strategies
and tools. |
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Supporting Idea4: Algebra |
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BENCHMARK CODE |
BENCHMARK |
|
MA.5.A.4.1 |
Use the properties of equality to
solve numerical and real world situations. |
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MA.5.A.4.2 |
Construct and describe a graph
showing continuous data, such as a graph of a quantity that changes over
time. |
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Supporting Idea5: Geometry and Measurement |
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BENCHMARK CODE |
BENCHMARK |
|
MA.5.G.5.1 |
Identify and plot ordered pairs on
the first quadrant of the coordinate plane. |
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MA.5.G.5.2 |
Compare, contrast, and convert
units of measure within the same dimension (length, mass, or time) to solve
problems. |
|
MA.5.G.5.3 |
Solve problems requiring attention
to approximation, selection of appropriate measuring tools, and precision of
measurement. |
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MA.5.G.5.4 |
Derive and apply formulas for areas
of parallelograms, triangles, and trapezoids from the area of a rectangle. |
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Supporting Idea6: Number and Operations |
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BENCHMARK CODE |
BENCHMARK |
|
MA.5.A.6.1 |
Identify and relate prime and
composite numbers, factors, and multiples within the context of fractions. |
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MA.5.A.6.2 |
Use the order of operations to
simplify expressions which include exponents and parentheses. |
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MA.5.A.6.3 |
Describe real-world situations
using positive and negative numbers. |
|
MA.5.A.6.4 |
Compare, order, and graph integers,
including integers shown on a number line. |
|
MA.5.A.6.5 |
Solve non-routine problems using
various strategies including “solving a simpler problem” and “guess, check,
and revise”. |
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Supporting Idea7: Data Analysis |
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BENCHMARK CODE |
BENCHMARK |
|
MA.5.S.7.1 |
Construct and analyze line graphs
and double bar graphs. |
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MA.5.S.7.2 |
Differentiate between continuous
and discrete data, and determine ways to represent those using graphs and
diagrams. |
|
Grade: 6 |
|
Big Idea1: Develop an understanding of and fluency with multiplication and division of fractions and decimals. |
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BENCHMARK CODE |
BENCHMARK |
|
MA.6.A.1.1 |
Explain and justify procedures for
multiplying and dividing fractions and decimals. |
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MA.6.A.1.2 |
Multiply and divide fractions and
decimals efficiently. |
|
MA.6.A.1.3 |
Solve real-world problems involving
multiplication and division of fractions and decimals. |
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Big Idea2: Connect ratio and rates to multiplication and division. |
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BENCHMARK CODE |
BENCHMARK |
|
MA.6.A.2.1 |
Use reasoning about multiplication
and division to solve ratio and rate problems. |
|
MA.6.A.2.2 |
Interpret and compare ratios and
rates. |
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Big Idea3: Write, interpret, and use mathematical expressions and equations. |
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BENCHMARK CODE |
BENCHMARK |
|
MA.6.A.3.1 |
Write and evaluate mathematical
expressions that correspond to given situations. |
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MA.6.A.3.2 |
Write, solve, and graph one- and
two- step linear equations and inequalities. |
|
MA.6.A.3.3 |
Work backward with two-step
function rules to undo expressions. |
|
MA.6.A.3.4 |
Solve problems given a formula. |
|
MA.6.A.3.5 |
Apply the Commutative, Associative,
and Distributive Properties to show that two expressions are equivalent. |
|
MA.6.A.3.6 |
Construct and analyze tables,
graphs, and equations to describe linear functions and other simple relations
using both common language and algebraic notation. |
|
Supporting Idea4: Geometry and Measurement |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.6.G.4.1 |
Understand the concept of Pi, know
common estimates of Pi (3.14; 22/7) and use these values to estimate and
calculate the circumference and the area of circles. |
|
MA.6.G.4.2 |
Find the perimeters and areas of
composite two-dimensional figures, including non-rectangular figures (such as
semicircles) using various strategies. |
|
MA.6.G.4.3 |
Determine a missing dimension of a
plane figure or prism given its area or volume and some of the dimensions, or
determine the area or volume given the dimensions. |
|
Supporting Idea5: Number and Operations |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.6.A.5.1 |
Use equivalent forms of fractions,
decimals, and percents to solve problems. |
|
MA.6.A.5.2 |
Compare and order fractions,
decimals, and percents, including finding their approximate location on a
number line. |
|
MA.6.A.5.3 |
Estimate the results of
computations with fractions, decimals, and percents, and judge the
reasonableness of the results. |
|
Supporting Idea6: Data Analysis |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.6.S.6.1 |
Determine the measures of central
tendency (mean, median, mode) and variability (range) for a given set of
data. |
|
MA.6.S.6.2 |
Select and analyze the measures of
central tendency or variability to represent, describe, analyze, and/or
summarize a data set for the purposes of answering questions appropriately. |
|
Grade: 7 |
|
Big Idea1: Develop an understanding of and apply proportionality, including similarity. |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.A.1.1 |
Distinguish between situations that
are proportional or not proportional, and use proportions to solve problems. |
|
MA.7.A.1.2 |
Solve percent problems, including
problems involving discounts, simple interest, taxes, tips, and percents of
increase or decrease. |
|
MA.7.A.1.3 |
Solve problems involving similar
figures. |
|
MA.7.A.1.4 |
Graph proportional relationships
and identify the unit rate as the slope of the related linear function. |
|
MA.7.A.1.5 |
Distinguish direct variation from
other relationships, including inverse variation. |
|
MA.7.A.1.6 |
Apply proportionality to
measurement in multiple contexts, including scale drawings and constant
speed. |
|
Big Idea2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes. |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.G.2.1 |
Justify and apply formulas for
surface area and volume of pyramids, prisms, cylinders, and cones. |
|
MA.7.G.2.2 |
Use formulas to find surface areas
and volume of three-dimensional composite shapes. |
|
Big Idea3: Develop an understanding of operations on all rational numbers and solving linear equations. |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.A.3.1 |
Use and justify the rules for
adding, subtracting, multiplying, dividing, and finding the absolute value of
integers. |
|
MA.7.A.3.2 |
Add, subtract, multiply, and divide
integers, fractions, and terminating decimals, and perform exponential
operations with rational bases and whole number exponents including solving
problems in everyday contexts. |
|
MA.7.A.3.3 |
Formulate and use different
strategies to solve one-step and two-step linear equations, including
equations with rational coefficients. |
|
MA.7.A.3.4 |
Use the properties of equality to
represent an equation in a different way and to show that two equations
are equivalent in a given context. |
|
Supporting Idea4: Geometry and Measurement |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.G.4.1 |
Determine how changes in dimensions
affect the perimeter, area, and volume of common geometric figures, and apply
these relationships to solve problems. |
|
MA.7.G.4.2 |
Predict the results of
transformations, and draw transformed figures with and without the coordinate
plane. |
|
MA.7.G.4.3 |
Identify and plot ordered pairs in
all four quadrants of the coordinate plane. |
|
MA.7.G.4.4 |
Compare, contrast, and convert
units of measure between different measurement systems (US customary or
metric (SI)), dimensions, and derived units to solve problems. |
|
Supporting Idea5: Number and Operations |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.A.5.1 |
Express rational numbers as
terminating or repeating decimals. |
|
MA.7.A.5.2 |
Solve non-routine problems by
working backwards. |
|
Supporting Idea6: Data Analysis |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.S.6.1 |
Evaluate the reasonableness of a
sample to determine the appropriateness of generalizations made about the
population. |
|
MA.7.S.6.2 |
Construct and analyze histograms,
stem-and-leaf plots, and circle graphs. |
|
Supporting Idea7: Probability |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.7.P.7.1 |
Determine the outcome of an
experiment and predict which events are likely or unlikely, and if the
experiment is fair or unfair. |
|
MA.7.P.7.2 |
Determine, compare, and make
predictions based on experimental or theoretical probability of independent
or dependent events, |
|
Grade: 8 |
|
Big Idea1: Analyze and represent linear functions, and solve linear equations and systems of linear equations. |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.8.A.1.1 |
Create and interpret tables,
graphs, and models to represent, analyze, and solve problems related to
linear equations, including analysis of domain, range, and the difference
between discrete and continuous data. |
|
MA.8.A.1.2 |
Interpret the slope and the x- and
y-intercepts when graphing a linear equation for a real-world problem. |
|
MA.8.A.1.3 |
Use tables, graphs, and models to
represent, analyze, and solve real-world problems related to systems of
linear equations. |
|
MA.8.A.1.4 |
Identify the solution to a system
of linear equations using graphs. |
|
MA.8.A.1.5 |
Translate among verbal, tabular,
graphical, and algebraic representations of linear functions. |
|
MA.8.A.1.6 |
Compare the graphs of linear and
non-linear functions for real-world situations. |
|
Big Idea2: Analyze two- and three-dimensional figures by using distance and angle. |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.8.G.2.1 |
Use similar triangles to solve
problems that include height and distances. |
|
MA.8.G.2.2 |
Classify and determine the measure
of angles, including angles created when parallel lines are cut by
transversals. |
|
MA.8.G.2.3 |
Demonstrate that the sum of the
angles in a triangle is 180-degrees and apply this fact to find unknown
measure of angles and the sum of angles in polygons. |
|
MA.8.G.2.4 |
Validate and apply Pythagorean
Theorem to find distances in real world situations or between points in the
coordinate plane. |
|
Big Idea3: Analyze and summarize data sets. |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.8.S.3.1 |
Select, organize and construct
appropriate data displays, including box and whisker plots, scatter plots,
and lines of best fit to convey information and make conjectures about
possible relationships. |
|
MA.8.S.3.2 |
Determine and describe how changes
in data values impact measures of central tendency. |
|
Supporting Idea4: Algebra |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.8.A.4.1 |
Solve literal equations for a
specified variable. |
|
MA.8.A.4.2 |
Solve and graph one- and two-step
inequalities in one variable. |
|
Supporting Idea5: Geometry and Measurement |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.8.G.5.1 |
Compare, contrast, and convert
units of measure between different measurement systems (US customary or
metric (SI)) and dimensions including temperature, area, volume, and derived
units to solve problems. |
|
Supporting Idea6: Number and Operations |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.8.A.6.1 |
Use exponents and scientific
notation to write large and small numbers and vice versa and to solve
problems. |
|
MA.8.A.6.2 |
Make reasonable approximations of
square roots and mathematical expressions that include square roots, and use
them to estimate solutions to problems and to compare mathematical
expressions involving real numbers and radical expressions. |
|
MA.8.A.6.3 |
Simplify real number expressions
using the laws of exponents. |
|
MA.8.A.6.4 |
Perform operations on real numbers
(including integer exponents, radicals, percents, scientific notation,
absolute value, rational numbers, and irrational numbers) using multi-step
and real world problems. |
|
Grade: 912 |
|
ALGEBRA |
|
Standard1: Real and
Complex Number Systems |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.1.1 |
Know equivalent forms of real
numbers (including integer exponents and radicals, percents, scientific notation,
absolute value, rational numbers, irrational numbers). |
|
MA.912.A.1.2 |
Compare real number expressions. |
|
MA.912.A.1.3 |
Simplify real number expressions
using the laws of exponents. |
|
MA.912.A.1.4 |
Perform operations on real numbers
(including integer exponents, radicals, percents, scientific notation,
absolute value, rational numbers, irrational numbers) using multi-step and
real-world problems. |
|
MA.912.A.1.5 |
Use dimensional (unit) analysis to
perform conversions between units of measure, including rates. |
|
MA.912.A.1.6 |
Identify the real and imaginary
parts of complex numbers and perform basic operations. |
|
MA.912.A.1.7 |
Represent complex numbers
geometrically. |
|
MA.912.A.1.8 |
Use the zero product property of
real numbers in a variety of contexts to identify solutions to equations. |
|
Standard2: Relations and
Functions |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.2.1 |
Create a graph to represent a
real-world situation. |
|
MA.912.A.2.2 |
Interpret a graph representing a
real-world situation. |
|
MA.912.A.2.3 |
Describe the concept of a function,
use function notation, determine whether a given relation is a function, and
link equations to functions. |
|
MA.912.A.2.4 |
Determine the domain and range of a
relation. |
|
MA.912.A.2.5 |
Graph absolute value equations and
inequalities in two variables. |
|
MA.912.A.2.6 |
Identify and graph common functions
(including but not limited to linear, rational, quadratic, cubic, radical,
absolute value). |
|
MA.912.A.2.7 |
Perform operations (addition,
subtraction, division, and multiplication) of functions algebraically,
numerically, and graphically. |
|
MA.912.A.2.8 |
Determine the composition of
functions. |
|
MA.912.A.2.9 |
Recognize, interpret, and graph
functions defined piece-wise with and without technology. |
|
MA.912.A.2.10 |
Describe and graph transformations
of functions |
|
MA.912.A.2.11 |
Solve problems involving functions
and their inverses. |
|
MA.912.A.2.12 |
Solve problems using direct,
inverse, and joint variations. |
|
MA.912.A.2.13 |
Solve real-world problems involving
relations and functions. |
|
Standard3: Linear
Equations and Inequalities |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.3.1 |
Solve linear equations in one
variable that include simplifying algebraic expressions. |
|
MA.912.A.3.2 |
Identify and apply the
distributive, associative, and commutative properties of real numbers and the
properties of equality. |
|
MA.912.A.3.3 |
Solve literal equations for a
specified variable. |
|
MA.912.A.3.4 |
Solve and graph simple and compound
inequalities in one variable and be able to justify each step in a solution. |
|
MA.912.A.3.5 |
Symbolically represent and solve
multi-step and real-world applications that involve linear equations and
inequalities. |
|
MA.912.A.3.6 |
Solve and graph the solutions of
absolute value equations and inequalities with one variable. |
|
MA.912.A.3.7 |
Rewrite equations of a line into
slope-intercept form and standard form. |
|
MA.912.A.3.8 |
Graph a line given any of the
following information: a table of values, the x- and y-intercepts, two
points, the slope and a point, the equation of the line in slope-intercept
form, standard form, or point-slope form . |
|
MA.912.A.3.9 |
Determine the slope, x-intercept,
and y-intercept of a line given its graph, its equation, or two points on the
line. |
|
MA.912.A.3.10 |
Write an equation of a line given
any of the following information: two points on the line, its slope and one
point on the line, or its graph. Also, find an equation of a new line
parallel to a given line, or perpendicular to a given line, through a given
point on the new line. |
|
MA.912.A.3.11 |
Write an equation of a line that
models a data set, and use the equation or the graph to make predictions.
Describe the slope of the line in terms of the data, recognizing that the
slope is the rate of change. |
|
MA.912.A.3.12 |
Graph a linear equation or
inequality in two variables with and without graphing technology. Write an
equation or inequality represented by a given graph. |
|
MA.912.A.3.13 |
Use a graph to approximate the
solution of a system of linear equations or inequalities in two variables
with and without technology. |
|
MA.912.A.3.14 |
Solve systems of linear equations
and inequalities in two and three variables using graphical, substitution,
and elimination methods. |
|
MA.912.A.3.15 |
Solve real-world problems involving
systems of linear equations and inequalities in two and three variables. |
|
Standard4: Polynomials |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.4.1 |
Simplify monomials and monomial
expressions using the laws of integral exponents. |
|
MA.912.A.4.2 |
Add, subtract, and multiply
polynomials. |
|
MA.912.A.4.3 |
Factor polynomial expressions. |
|
MA.912.A.4.4 |
Divide polynomials by monomials and
polynomials with various techniques, including synthetic division. |
|
MA.912.A.4.5 |
Graph polynomial functions with and
without technology and describe end behavior. |
|
MA.912.A.4.6 |
Use theorems of polynomial behavior
(including but not limited to the Fundamental Theorem of Algebra, Remainder
Theorem, the Rational Root Theorem, Descartes' Rule of Signs, and the
Conjugate Root Theorem) to find the zeros of a polynomial function. |
|
MA.912.A.4.7 |
Write a polynomial equation for a
given set of real and/or complex roots. |
|
MA.912.A.4.8 |
Describe the relationships among
the solutions of an equation, the zeros of a function, the x-intercepts of a
graph, and the factors of a polynomial expression with and without
technology. |
|
MA.912.A.4.9 |
Use graphing technology to find
approximate solutions for polynomial equations. |
|
MA.912.A.4.10 |
Use polynomial equations to solve
real-world problems. |
|
MA.912.A.4.11 |
Solve a polynomial inequality by
examining the graph with and without the use of technology. |
|
MA.912.A.4.12 |
Apply the Binomial Theorem. |
|
Standard5: Rational
Expressions and Equations |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.5.1 |
Simplify algebraic ratios. |
|
MA.912.A.5.2 |
Add, subtract, multiply, and divide
rational expressions. |
|
MA.912.A.5.3 |
Simplify complex fractions. |
|
MA.912.A.5.4 |
Solve algebraic proportions. |
|
MA.912.A.5.5 |
Solve rational equations. |
|
MA.912.A.5.6 |
Identify removable and non-removable
discontinuities, and vertical, horizontal, and oblique asymptotes of a graph
of a rational function, find the zeros, and graph the function. |
|
MA.912.A.5.7 |
Solve real-world problems involving
rational equations (mixture, distance, work, interest, and ratio). |
|
Standard6: Radical
Expressions and Equations |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.6.1 |
Simplify radical expressions |
|
MA.912.A.6.2 |
Add, subtract, multiply, and divide
radical expressions (square roots and higher). |
|
MA.912.A.6.3 |
Simplify expressions using
properties of rational exponents. |
|
MA.912.A.6.4 |
Convert between rational exponent
and radical forms of expressions. |
|
MA.912.A.6.5 |
Solve equations that contain
radical expressions. |
|
Standard7: Quadratic
Equations |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.7.1 |
Graph quadratic equations with and
without graphing technology. |
|
MA.912.A.7.2 |
Solve quadratic equations over the
real numbers by factoring and by using the quadratic formula. |
|
MA.912.A.7.3 |
Solve quadratic equations over the
real numbers by completing the square. |
|
MA.912.A.7.4 |
Use the discriminant to determine
the nature of the roots of a quadratic equation. |
|
MA.912.A.7.5 |
Solve quadratic equations over the
complex number system. |
|
MA.912.A.7.6 |
Identify the axis of symmetry, vertex,
domain, range and intercept(s) for a given parabola. |
|
MA.912.A.7.7 |
Solve non-linear systems of
equations with and without using technology. |
|
MA.912.A.7.8 |
Use quadratic equations to solve
real-world problems. |
|
MA.912.A.7.9 |
Solve optimization problems. |
|
MA.912.A.7.10 |
Use graphing technology to find
approximate solutions of quadratic equations. |
|
Standard8: Logarithmic
and Exponential Functions |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.8.1 |
Define exponential and logarithmic
functions and determine their relationship |
|
MA.912.A.8.2 |
Define and use the properties of
logarithms to simplify logarithmic expressions and to find their approximate
values. |
|
MA.912.A.8.3 |
Graph exponential and logarithmic
functions. |
|
MA.912.A.8.4 |
Prove laws of logarithms. |
|
MA.912.A.8.5 |
Solve logarithmic and exponential
equations. |
|
MA.912.A.8.6 |
Use the change of base formula. |
|
MA.912.A.8.7 |
Solve applications of exponential
growth and decay. |
|
Standard9: Conic
Sections |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.9.1 |
Write the equations of conic
sections in standard form and general form, in order to identify the conic
section and to find its geometric properties (foci, asymptotes, eccentricity,
etc.). |
|
MA.912.A.9.2 |
Graph conic sections with and
without using graphing technology. |
|
MA.912.A.9.3 |
Solve real-world problems involving
conic sections |
|
Standard10:
Mathematical Reasoning and Problem Solving |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.A.10.1 |
Use a variety of problem-solving
strategies, such as drawing a diagram, making a chart, guessing-
and-checking, solving a simpler problem, writing an equation, working
backwards, and creating a table. |
|
MA.912.A.10.2 |
Decide whether a solution is
reasonable in the context of the original situation. |
|
MA.912.A.10.3 |
Decide whether a given statement is
always, sometimes, or never true (statements involving linear or quadratic
expressions, equations, or inequalities, rational or radical expressions, or
logarithmic or exponential functions). |
|
MA.912.A.10.4 |
Use counterexamples to show that
statements are false. |
|
CALCULUS |
|
Standard1: Limits and
Continuity |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.C.1.1 |
Understand the concept of limit and
estimate limits from graphs and tables of values. |
|
MA.912.C.1.2 |
Find limits by substitution. |
|
MA.912.C.1.3 |
Find limits of sums, differences,
products, and quotients. |
|
MA.912.C.1.4 |
Find limits of rational functions
that are undefined at a point. |
|
MA.912.C.1.5 |
Find one-sided limits. |
|
MA.912.C.1.6 |
Find limits at infinity. |
|
MA.912.C.1.7 |
Decide when a limit is infinite and
use limits involving infinity to describe asymptotic behavior. |
|
MA.912.C.1.8 |
Find special limits such as |
|
MA.912.C.1.9 |
Understand continuity in terms of
limits. |
|
MA.912.C.1.10 |
Decide if a function is continuous
at a point. |
|
MA.912.C.1.11 |
Find the types of discontinuities
of a function. |
|
MA.912.C.1.12 |
Understand and use the Intermediate
Value Theorem on a function over a closed interval. |
|
MA.912.C.1.13 |
Understand and apply the Extreme
Value Theorem: If f(x) is continuous over a closed interval, then f has a
maximum and a minimum on the interval. |
|
Standard2: Differential
Calculus |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.C.2.1 |
Understand the concept of
derivative geometrically, numerically, and analytically, and interpret the
derivative as an instantaneous rate of change or as the slope of the tangent
line. |
|
MA.912.C.2.2 |
State, understand, and apply the
definition of derivative. |
|
MA.912.C.2.3 |
Find the derivatives of functions,
including algebraic, trigonometric, logarithmic, and exponential functions. |
|
MA.912.C.2.4 |
Find the derivatives of sums,
products, and quotients. |
|
MA.912.C.2.5 |
Find the derivatives of composite
functions using the Chain Rule. |
|
MA.912.C.2.6 |
Find the derivatives of
implicitly-defined functions. |
|
MA.912.C.2.7 |
Find derivatives of inverse functions. |
|
MA.912.C.2.8 |
Find second derivatives and
derivatives of higher order. |
|
MA.912.C.2.9 |
Find derivatives using logarithmic
differentiation. |
|
MA.912.C.2.10 |
Understand and use the relationship
between differentiability and continuity. |
|
MA.912.C.2.11 |
Understand and apply the Mean Value
Theorem. |
|
Standard3:
Applications of Derivatives |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.C.3.1 |
Find the slope of a curve at a
point, including points at which there are vertical tangent lines and no
tangent lines. |
|
MA.912.C.3.2 |
Find an equation for the tangent
line to a curve at a point and a local linear approximation. |
|
MA.912.C.3.3 |
Decide where functions are
decreasing and increasing. Understand the relationship between the increasing
and decreasing behavior of f and the sign of f'. |
|
MA.912.C.3.4 |
Find local and absolute maximum and
minimum points. |
|
MA.912.C.3.5 |
Find points of inflection of
functions. Understand the relationship between the concavity of f and the
sign of f". Understand points of inflection as places where concavity
changes. |
|
MA.912.C.3.6 |
Use first and second derivatives to
help sketch graphs. Compare the corresponding characteristics of the graphs
of f, f', and f". |
|
MA.912.C.3.7 |
Use implicit differentiation to
find the derivative of an inverse function. |
|
MA.912.C.3.8 |
Solve optimization problems. |
|
MA.912.C.3.9 |
Find average and instantaneous
rates of change. Understand the instantaneous rate of change as the limit of
the average rate of change. Interpret a derivative as a rate of change in
applications, including velocity, speed, and acceleration. |
|
MA.912.C.3.10 |
Find the velocity and acceleration
of a particle moving in a straight line. |
|
MA.912.C.3.11 |
Model rates of change, including
related rates problems. |
|
MA.912.C.3.12 |
Solve problems using the
Newton-Raphson method. |
|
Standard4: Integral
Calculus |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.C.4.1 |
Use rectangle approximations to
find approximate values of integrals. |
|
MA.912.C.4.2 |
Calculate the values of Riemann
Sums over equal subdivisions using left, right, and midpoint evaluation
points. |
|
MA.912.C.4.3 |
Interpret a definite integral as a
limit of Riemann sums. |
|
MA.912.C.4.4 |
Interpret a definite integral of
the rate of change of a quantity over an interval as the change of the
quantity over the interval. That is, |
f'
|
MA.912.C.4.5 |
Use the Fundamental Theorem of
Calculus to evaluate definite and indefinite integrals and to represent
particular antiderivatives. Perform analytical and graphical analysis of
functions so defined. |
|
MA.912.C.4.6 |
Use these properties of definite
integrals:
|
[f(x)
+ g(x)]dx = 
f(x)dx
= 0 
f(x)dx
f(x)dx
= 
f(x)dx
|
MA.912.C.4.7 |
Use integration by substitution (or
change of variable) to find values of integrals. |
|
MA.912.C.4.8 |
Use Riemann Sums, the Trapezoidal
Rule, and technology to approximate definite integrals of functions
represented algebraically, geometrically, and by tables of values. |
|
Standard5:
Applications of Integration |
|
BENCHMARK CODE |
BENCHMARK |
|
MA.912.C.5.1 |
Find specific antiderivatives using
initial conditions, including finding velocity functions from acceleration
functions, finding position functions from velocity functions, and solving
applications related to motion along a line. |
|
MA.912.C.5.2 |
Solve separable differential
equations, and use them in modeling. |
|
MA.912.C.5.3 |
Solve differential equations of the
form |
as applied to growth and decay problems.
|
MA.912.C.5.4 |