Nebraska+Math+Standards

=** Kindergarten **=
 * Adopted by the State Board of Education, October 8, 2009 **


 * MA 0.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 0.1.1 Number System: Students will demonstrate, represent, and show relationships among whole numbers within the base-ten number system. **


 * MA 0.1.1.a Count, read and write numbers 0 – 20
 * MA 0.1.1.b Count objects using one-to-one correspondence 0 – 20
 * MA 0.1.1.c Sequence objects using ordinal numbers (first through fifth)
 * MA 0.1.1.d Match numerals to the quantities they represent 0 – 20, using a variety of models and representations
 * MA 0.1.1.e Demonstrate and identify multiple equivalent representations for numbers 1 – 10 (e.g., 10 is 1 and 9; 10 is 6 and 4)
 * MA 0.1.1.f Demonstrate relative position of whole numbers 0 – 10 (e.g., 5 is between 2 and 10; 7 is greater than 3)


 * MA 0.1.2 Operations: Students will demonstrate the meaning of addition and subtraction with whole numbers. **


 * MA 0.1.2.a Use objects and words to explain the meaning of addition as a joining action (e.g., Two girls are sitting at a table. Two more girls join them. How many girls are sitting at the table?)
 * MA 0.1.2.b Use objects and words to explain the meaning of addition as parts of a whole (e.g., Three boys and two girls are going to the zoo. How many children are going to the zoo?)
 * MA 0.1.2.c Use objects and words to explain the meaning of subtraction as a separation action (e.g., Five girls are sitting at a table. Two girls leave. How many girls are left sitting at the table?)
 * MA 0.1.2.d Use objects and words to explain the meaning of subtraction as finding part of a whole (e.g., Jacob has 5 pencils. Three are blue and the rest are red. How many red pencils does Jacob have?)


 * MA 0.1.3 Computation: Mastery not expected at this level. **


 * MA 0.1.4 Estimation: Mastery not expected at this level. **


 * MA 0.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 0.2.1 Characteristics: Students will identify two-dimensional geometric shapes. **


 * MA 0.2.1.a Sort and name two-dimensional shapes (e.g., square, circle, rectangle, triangle)


 * MA 0.2.2 Coordinate Geometry: Mastery not expected at this level. **


 * MA 0.2.3 Transformations: Mastery not expected at this level. **


 * MA 0.2.4 Spatial Modeling: Students will communicate relative positions in space. **


 * MA 0.2.4.a Demonstrate positional words (e.g., above/below, near/far, over/ under, in/out, down/up, around/through)


 * MA 0.2.5 Measurement: Students will measure using nonstandard units and time. **


 * MA 0.2.5.a Identify the name and amount of a penny, nickel, dime, and quarter
 * MA 0.2.5.b Identify time to the hour
 * MA 0.2.5.c Measure using nonstandard units
 * MA 0.2.5.d Compare objects according to length


 * MA 0.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 0.3.1 Relationships: Students will sort, classify, and order objects by relationships. **


 * MA 0.3.1.a Sort by color, shape, or size
 * MA 0.3.1.b Create own rule for sorting other than color, shape, and size


 * MA 0.3.2 Modeling in Context: Students will use objects as models to represent mathematical situations. **


 * MA 0.3.2.a Model situations that involve the addition and subtraction of whole numbers 0 – 10 using objects


 * MA 0.3.3 Procedures: Students will use concrete and verbal representations to solve number stories. **


 * MA 0.3.3.a Use objects to solve addition and subtraction of whole numbers 0 – 10


 * MA 0.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 0.4.1 Display and Analysis: Students will sort, classify, represent, describe, and compare sets of objects. **


 * MA 0.4.1.a Sort and classify objects according to an attribute (e.g., size, color, shape)
 * MA 0.4.1.b Identify the attributes of sorted data
 * MA 0.4.1.c Compare the attributes of the data (e.g., most, least, same)


 * MA 0.4.2 Predictions and Inferences: Mastery not expected at this level. **


 * MA 0.4.3 Probability: Mastery not expected at this level. **

= Grade 1 =


 * MA 1.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 1.1.1 Number System: Students will demonstrate, represent, and show relationships among whole numbers within the base-ten number system. **


 * MA 1.1.1.a Count, read, and write numbers 0 – 100
 * MA 1.1.1.b Count by multiples of 2 up to 50
 * MA 1.1.1.c Count by multiples of 5 up to 100
 * MA 1.1.1.d Count by multiples of 10 up to 100
 * MA 1.1.1.e Sequence objects using ordinal numbers (first through tenth)
 * MA 1.1.1.f Count backwards from 10 – 0
 * MA 1.1.1.g Connect number words to the quantities they represent 0 – 20
 * MA 1.1.1.h Demonstrate and identify multiple equivalent representations for numbers 1 – 100 (e.g., 23 is 2 tens and 3 ones; 23 is 1 ten and 13 ones; 23 is 23 ones)
 * MA 1.1.1.i Compare and order whole numbers 0 – 100
 * MA 1.1.1.j Demonstrate relative position of whole numbers 0 – 100 (e.g., 52 is between 50 and 60; 83 is greater than 77)


 * MA 1.1.2 Operations: Students will demonstrate the meaning of addition and subtraction with whole numbers. **


 * MA 1.1.2.a Use objects, drawings, words, and symbols to explain addition as a joining action
 * MA 1.1.2.b Use objects, drawings, words, and symbols to explain addition as parts of a whole
 * MA 1.1.2.c Use objects, drawings, words, and symbols to explain subtraction as a separation action
 * MA 1.1.2.d Use drawings, words, and symbols to explain subtraction as finding part of a whole
 * MA 1.1.2.e Use objects, drawings, words, and symbols to explain subtraction as a comparison (e.g., Nancy has 8 hair ribbons. Jane has 5 hair ribbons. How many more hair ribbons does Nancy have than Jane?)


 * MA 1.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 1.1.3.a Fluently add whole number sums up to 10
 * MA 1.1.3.b Fluently subtract whole number differences from 10
 * MA 1.1.3.c Add and subtract two-digit numbers without regrouping
 * MA 1.1.3.d Use a variety of methods and tools to compute sums and differences (e.g., models, mental computation, paper-pencil)


 * MA 1.1.4 Estimation: Mastery not expected at this level. **


 * MA 1.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 1.2.1 Characteristics: Students will identify characteristics of two-dimensional geometric shapes. **


 * MA 1.2.1.a Compare two-dimensional shapes (e.g., square, circle, rectangle, triangle)
 * MA 1.2.1.b Describe attributes of two-dimensional shapes (e.g., square, circle, rectangle, triangle)


 * MA 1.2.2 Coordinate Geometry: Students will identify locations on a number line. **


 * MA 1.2.2.a Identify the position of a whole number on a horizontal number line


 * MA 1.2.3 Transformations: Students will identify a line of symmetry. **


 * MA 1.2.3.a Identify one line of symmetry in two-dimensional shapes (e.g., circle, square, rectangle, triangle)


 * MA 1.2.4 Spatial Modeling: Students will communicate relative positions in space and create two-dimensional shapes. **


 * MA 1.2.4.a Demonstrate positional words (e.g., left/right)
 * MA 1.2.4.b Sketch two-dimensional shapes (e.g., square, circle, rectangle, triangle)


 * MA 1.2.5 Measurement: Students will measure using standard units, time, and money. **


 * MA 1.2.5.a Count like coins to $1.00
 * MA 1.2.5.b Identify time to the half hour
 * MA 1.2.5.c Identify past, present, and future as orientation in time
 * MA 1.2.5.d Select an appropriate tool for the attribute being measured (e.g., clock, calendar, thermometer, scale, ruler)
 * MA 1.2.5.e Measure length using inches
 * MA 1.2.5.f Compare and order objects according to length


 * MA 1.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 1.3.1 Relationships: Students will identify and describe relationships. **


 * MA 1.3.1.a Sort or order objects by their attributes (e.g., color, shape, size, number) then identify the classifying attribute
 * MA 1.3.1.b Create multiple rules for sorting beyond color, shape, and size
 * MA 1.3.1.c Identify, describe, and extend patterns (e.g., patterns with a repeating core)
 * MA 1.3.1.d Use <, =, > to compare quantities


 * MA 1.3.2 Modeling in Context: Students will use objects and pictures as models to represent mathematical situations. **


 * MA 1.3.2.a Model situations that involve the addition and subtraction of whole numbers 0 – 20, using objects and pictures
 * MA 1.3.2.b Describe and model quantitative change (e.g., a student growing taller)


 * MA 1.3.3 Procedures: Students will use concrete, verbal, and visual representations to solve number sentences. **


 * MA 1.3.3.a Write number sentences to represent fact families
 * MA 1.3.3.b Use concrete, pictorial, and verbal representations of the commutative property of addition


 * MA 1.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 1.4.1 Display and Analysis: Students will sort, classify, organize, describe, and compare data. **


 * MA 1.4.1.a Sort and classify objects by more than one attribute
 * MA 1.4.1.b Organize data by using concrete objects
 * MA 1.4.1.c Represent data by using tally marks
 * MA 1.4.1.d Compare and interpret information from displayed data (e.g., more, less, fewer)


 * MA 1.4.2 Predictions and Inferences: Mastery not expected at this level. **


 * MA 1.4.3 Probability: Mastery not expected at this level. **

= Grade 2 =


 * MA 2.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 2.1.1 Number System: Students will demonstrate, represent, and show relationships among whole numbers within the base-ten number system. **


 * MA 2.1.1.a Read and write numbers 0 – 1,000 (e.g., count numbers from 400 – 500; write numbers from 400 – 500)
 * MA 2.1.1.b Count by multiples of 2 up to 100
 * MA 2.1.1.c Count backwards from 20 – 0
 * MA 2.1.1.d Connect number words to the quantities they represent 0 – 100
 * MA 2.1.1.e Demonstrate multiple equivalent representations for numbers 1 – 1,000 (e.g., 423 is 4 hundreds, 2 tens and 3 ones; 423 is 3 hundreds 12 tens and 3 ones)
 * MA 2.1.1.f Compare and order whole numbers 0 – 1,000
 * MA 2.1.1.g Demonstrate relative position of whole numbers 0 – 1,000 (e.g., 624 is between 600 and 700; 593 is greater than 539)
 * MA 2.1.1.h Use visual models to represent fractions of one-half as a part of a whole


 * MA 2.1.2 Operations: Students will demonstrate the meaning of addition and subtraction with whole numbers. **


 * MA 2.1.2.a Use objects, drawings, words, and symbols to explain the relationship between addition and subtraction (e.g., if 2 + 3 = 5 then 5 – 3 = 2)
 * MA 2.1.2.b Use objects, drawings, words, and symbols to explain the use of subtraction to find a missing addend (e.g., if 3 + __= 7, then 7- 3 =__ .)


 * MA 2.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 2.1.3.a Fluently add whole number facts with sums to 20
 * MA 2.1.3.b Fluently subtract whole number facts with differences from 20
 * MA 2.1.3.c Add and subtract three-digit whole numbers with regrouping
 * MA 2.1.3.d Use a variety of methods and tools to compute sums and differences (e.g., models, mental computation, paper–pencil)


 * MA 2.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 2.1.4.a Estimate the results of two-digit whole number sums and differences and check the reasonableness of such results
 * MA 2.1.4 b Estimate the number of objects in a group


 * MA 2.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 2.2.1 Characteristics: Students will describe characteristics of two-dimensional shapes and identify three-dimensional objects. **


 * MA 2.2.1.a Describe attributes of two-dimensional shapes (e.g., trapezoid, parallelogram)
 * MA 2.2.1.b Determine if two shapes are congruent
 * MA 2.2.1.c Compare two-dimensional shapes (e.g., trapezoid, parallelogram)
 * MA 2.2.1.d Identify solid shapes (e.g., triangular prism, rectangular prisms, cones, cylinders, pyramids, spheres)


 * MA 2.2.2 Coordinate Geometry: Students will describe direction on a positive number line. **


 * MA 2.2.2.a Identify numbers using location on a vertical number line
 * MA 2.2.2.b Compare whole numbers using location on a horizontal number line
 * MA 2.2.2.c Identify the direction moved for adding and subtracting using a horizontal number line


 * MA 2.2.3 Transformations: Students will identify lines of symmetry. **


 * MA 2.2.3.a Identify lines of symmetry in two-dimensional shapes
 * MA 2.2.3.b Draw a line of symmetry in two-dimensional shapes


 * MA 2.2.4 Spatial Modeling: Students will create two-dimensional shapes. **


 * MA 2.2.4.a Sketch two-dimensional shapes (e.g., trapezoid, parallelogram)


 * MA 2.2.5 Measurement: Students will measure using standard units, time and money. **


 * MA 2.2.5.a Count mixed coins to $1.00
 * MA 2.2.5.b Identify time to 5 minute intervals
 * MA 2.2.5.c Identify and use appropriate tools for the attribute being measured (e.g., clock, calendar, thermometer, scale, ruler)
 * MA 2.2.5.d Measure length using feet and yards
 * MA 2.2.5.e Compare and order objects using inches, feet and yards


 * MA 2.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 2.3.1 Relationships: Students will identify, describe, and extend relationships. **


 * MA 2.3.1.a Create and describe patterns using concrete and pictorial representations


 * MA 2.3.2 Modeling in Context: Students will use objects, pictures, and symbols as models to represent mathematical situations. **


 * MA 2.3.2.a Model situations that involve the addition and subtraction of whole numbers 0 – 100, using objects and number lines
 * MA 2.3.2.b Describe and model quantitative change involving addition (e.g., a student grew 2 inches)


 * MA 2.3.3 Procedures: Students will use concrete, verbal, visual, and symbolic representations to solve number sentences. **


 * MA 2.3.3.a Use symbolic representations of the commutative property of addition (e.g., 2 + 3 =  + 2)


 * MA 2.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 2.4.1 Display and Analysis: Students will organize, display, compare, and interpret data. **


 * MA 2.4.1.a Represent data using pictographs
 * MA 2.4.1.b Interpret data using pictographs (e.g., 7 more; 2 less; 12 all together)


 * MA 2.4.2 Predictions and Inferences: Mastery not expected at this level. **

**MA 2.4.3 Probability: Mastery not expected at this level**.

= Grade 3 =


 * MA 3.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 3.1.1 Number System: Students will represent and show relationships among positive rational numbers within the base-ten number system. **


 * MA 3.1.1.a Read and write numbers to one-hundred thousand (e.g., 4,623 is the same as four thousand six hundred twenty three)
 * MA 3.1.1.b Count by multiples of 5 to 200
 * MA 3.1.1c Count by multiples of 10 to 400
 * MA 3.1.1.d Count by multiples of 100 to 1,000
 * MA 3.1.1.e Demonstrate multiple equivalent representations for numbers up to 10,000 (e.g., 10 tens is 1 hundred; 10 ten thousands is 1 hundred thousand; 2,350 is 235 tens; 2,350 is 2,000 + 300 + 50; 2,350 is 23 hundreds and 5 tens)
 * MA 3.1.1.f Demonstrate multiple equivalent representations for decimal numbers through the tenths place (e.g., 3 and 6 tenths is 3.6; 7.4 is 7 + .4)
 * MA 3.1.1.g Compare and order whole numbers through the thousands
 * MA 3.1.1.h Find parts of whole and parts of a set for ½, ⅓, or ¼
 * MA 3.1.1.i Round a given number to tens, hundreds, or thousands


 * MA 3.1.2 Operations: Students demonstrate the meaning of multiplication with whole numbers. **


 * MA 3.1.2.a Represent multiplication as repeated addition using objects, drawings, words, and symbols (e.g., 3 x 4 = 4 + 4 + 4)
 * MA 3.1.2.b Use objects, drawings, words and symbols to explain the relationship between multiplication and division (e.g., if 3 x 4 = 12 then 12 ÷ 3 = 4.)
 * MA 3.1.2.c Use drawings, words, and symbols to explain the meaning of the factors and product in a multiplication sentence (e.g., in 3 x 4 = 12, 3 and 4 are factors and 12 is the total or product. The first factor (3) tells how many sets while the second factor tells how many are in each set. Another way to say this is that 3 groups of 4 equals 12 total.)
 * MA 3.1.2.d Use drawings, words, and symbols to explain the meaning of multiplication using an array (e.g., an array with 3 rows and 4 columns represents the multiplication sentence 3 x 4 = 12)


 * MA 3.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 3.1.3.a Compute whole number multiplication facts 0 – 10 fluently
 * MA 3.1.3.b Add and subtract through four-digit whole numbers with regrouping
 * MA 3.1.3.c Select and apply the appropriate methods of computation when problem solving with four-digit whole numbers through the thousands (e.g., models, mental computation, paper-pencil)


 * MA 3.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 3.1.4.a Estimate the two-digit product of whole number multiplication and check the reasonableness


 * MA 3.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 3.2.1 Characteristics: Students will identify characteristics and describe properties of two-dimensional shapes and three-dimensional objects. **


 * MA 3.2.1.a Identify the number of sides, angles, and vertices of two-dimensional shapes
 * MA 3.2.1.b Identify congruent two-dimensional figures given multiple two-dimensional shapes
 * MA 3.2.1.c Identify lines, line segments, rays, and angles
 * MA 3.2.1.d Describe attributes of solid shapes (e.g., triangular prism, rectangular prisms, cones, cylinders, pyramids, spheres)


 * MA 3.2.2 Coordinate Geometry: Students will identify distances on a number line. **


 * MA 3.2.2.a Draw a number line and plot points
 * MA 3.2.2.b Determine the distance between two whole number points on a number line


 * MA 3.2.3 Transformations: Students will draw all lines of symmetry. **


 * MA 3.2.3.a Draw all possible lines of symmetry in two-dimensional shapes


 * MA 3.2.4 Spatial Modeling: Students will create two-dimensional shapes and three-dimensional objects. **


 * MA 3.2.4.a Sketch and label lines, rays, line segments, and angles
 * MA 3.2.4.b Build three-dimensional objects (e.g., using clay for rectangular prisms, cone, cylinder)


 * MA 3.2.5 Measurement: Students will apply appropriate procedures and tools to determine measurements using customary and metric units. **


 * MA 3.2.5.a Select and use appropriate tools to measure perimeter of simple two-dimensional shapes (e.g., triangle, square, rectangle)
 * MA 3.2.5.b Count mixed coins and bills greater than $1.00
 * MA 3.2.5.c Identify time of day (e.g., am, pm, noon, midnight)
 * MA 3.2.5.d State multiple ways for the same time using 15 minute intervals (e.g., 2:15, or quarter past 2, 2:45 or a quarter until 3)
 * MA 3.2.5.e Identify the appropriate customary unit for measuring length, weight, and capacity/volume
 * MA 3.2.5.f Measure length to the nearest ½ inch and centimeter (e.g., requires rounding)
 * MA 3.2.5.g Compare and order objects according to length using centimeters and meters


 * MA 3.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 3.3.1 Relationships: Students will represent relationships. **


 * MA 3.3.1.a Identify, describe, and extend numeric and non-numeric patterns
 * MA 3.3.1.b Identify patterns using words, tables, and graphs


 * MA 3.3.2 Modeling in Context: Students will create and use models to represent mathematical situations. **


 * MA 3.3.2.a Model situations that involve the addition and subtraction of whole numbers using objects, number lines, and symbols
 * MA 3.3.2.b Describe and model quantitative change involving subtraction (e.g., temperature dropped two degrees)


 * MA 3.3.3 Procedures: Students will identify and apply properties of whole numbers to solve equations involving addition and subtraction. **


 * MA 3.3.3.a Use symbolic representation of the identity property of addition (e.g., 3 = 0 + 3)
 * MA 3.3.3.b Solve simple one-step whole number equations involving addition and subtraction (e.g.,  + 2 = 3)
 * MA 3.3.3.c Explain the procedure(s) used in solving simple one-step whole number equations involving addition and subtraction


 * MA 3.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 3.4.1 Display and Analysis: Students will organize, display, compare, and interpret data. **


 * MA 3.4.1.a Represent data using horizontal and vertical bar graphs
 * MA 3.4.1.b Use comparative language to describe the data (e.g., increasing, decreasing)
 * MA 3.4.1.c Interpret data using horizontal and vertical bar graphs


 * MA 3.4.2 Predictions and Inferences: Mastery not expected at this level. **


 * MA 3.4.3 Probability: Students will find and describe experimental probability. **


 * MA 3.4.3.a Perform simple experiments (e.g., flip a coin, toss a number cube, spin a spinner) and describe outcomes as possible, impossible, or certain

= Grade 4 =


 * MA 4.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 4.1.1 Number System: Students will represent and show relationships among positive rational numbers within the base-ten number system. **


 * MA 4.1.1.a Read and write numbers through the millions (e.g., 2,347,589 is the same as 2 million three hundred forty seven thousand five hundred eighty nine)
 * MA 4.1.1.b Demonstrate multiple equivalent representations for decimal numbers through the hundredths place (e.g., 2 and 5 hundredths is 2.05; 6.23 is 6 + .2 +.03)
 * MA 4.1.1.c Compare and order whole numbers and decimals through the hundredths place (e.g., money)
 * MA 4.1.1.d Classify a number as even or odd
 * MA 4.1.1.e Represent a fraction as parts of a whole and/or parts of a set
 * MA 4.1.1.f Use visual models to find equivalent fractions (e.g.,2/4= 1/2,2/8= 1/4,1=2/2=5/5,3/3
 * MA 4.1.1.g Determine the size of a fraction relative to one half using equivalent forms (e.g., Is 3/8 more or less than one half?)
 * MA 4.1.1.h Locate fractions on a number line
 * MA 4.1.1.i Round a whole number to millions


 * MA 4.1.2 Operations: Students will demonstrate the meaning of division with whole numbers. **


 * MA 4.1.2.a Use drawings, words, and symbols to explain the meaning of division [(e.g., as repeated subtraction: Sarah has 24 candies. She put them into bags of 6 candies each. How many bags did Sarah use?) (e.g., as equal sharing: Paul has 24 candies. He wants to share them equally among his 6 friends. How many candies will each friend receive?)]


 * MA 4.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 4.1.3.a Compute whole number division facts 0 – 10 fluently
 * MA 4.1.3.b Add and subtract decimals to the hundredths place (e.g., money)
 * MA 4.1.3.c Multiply two-digit whole numbers
 * MA 4.1.3.d Divide a three-digit number with one digit divisor with and without a remainder
 * MA 4.1.3.e Mentally compute multiplication and division involving powers of 10
 * MA 4.1.3.f Select and apply the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil)


 * MA 4.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 4.1.4.a Estimate the three-digit product and the two-digit quotient of whole number multiplication and division and check the reasonableness


 * MA 4.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 4.2.1 Characteristics: Students will classify two-dimensional shapes and three-dimensional objects. **


 * MA 4.2.1.a Identify two- and three-dimensional shapes according to their sides and angle properties
 * MA 4.2.1.b Classify an angle as acute, obtuse, and right
 * MA 4.2.1.c Identify parallel, perpendicular, and intersecting lines
 * MA 4.2.1.d Identify the property of congruency when dealing with plane geometric shapes


 * MA 4.2.2 Coordinate Geometry: Students will describe locations using coordinate geometry. **


 * MA 4.2.2.a Identify the ordered pair of a plotted point in first quadrant by its location (e.g., (2, 3) is a point two right and three up from the origin)


 * MA 4.2.3 Transformations: Students will identify simple transformations. **


 * MA 4.2.3.a Given two congruent geometric shapes, identify the transformation (e.g., translation, rotation, reflection) applied to an original shape to create a transformed shape


 * MA 4.2.4 Spatial Modeling: Student will use geometric models to solve problems. **


 * MA 4.2.4.a Given a geometric model, use it to solve a problem (e.g., what shapes make a cylinder; streets run parallel and perpendicular)


 * MA 4.2.5 Measurement: Students will apply appropriate procedures and tools to estimate and determine measurement using customary and metric units. **


 * MA 4.2.5.a Select and use appropriate tools to measure perimeter of polygons
 * MA 4.2.5.b Identify time to the minute on an analog clock
 * MA 4.2.5.c Solve problems involving elapsed time
 * MA 4.2.5.d Identify the appropriate metric unit for measuring length, weight, and capacity/volume (e.g., cm, m, Km; g, Kg; mL, L)
 * MA 4.2.5.e Estimate and measure length using customary (nearest ½ inch) and metric (nearest centimeter) units
 * MA 4.2.5.f Measure weight and temperature using customary units
 * MA 4.2.5.g Compute simple unit conversions for length within a system of measurement


 * MA 4.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 4.3.1 Relationships: Students will represent and analyze relationships. **


 * MA 4.3.1.a Describe, extend, and apply rules about numeric patterns
 * MA 4.3.1.b Represent and analyze a variety of patterns using words, tables, and graphs
 * MA 4.3.1.c Use ,  symbols to compare quantities
 * MA 4.3.1.d Select appropriate operational and relational symbols to make a number sentence true


 * MA 4.3.2 Modeling in Context: Students will create and use models to represent mathematical situations. **


 * MA 4.3.2.a Model situations that involve the multiplication of whole numbers using number lines and symbols
 * MA 4.3.2.b Describe and model quantitative change involving multiplication (e.g., money doubling)


 * MA 4.3.3 Procedures: Students will identify and apply properties of whole numbers to solve equations involving multiplication and division. **


 * MA 4.3.3.a Represent the idea of a variable as an unknown quantity using a letter or a symbol (e.g., n + 3, b – 2)
 * MA 4.3.3.b Use symbolic representation of the identity property of multiplication (e.g., 5 * 1 = 5)
 * MA 4.3.3.c Use symbolic representations of the commutative property of multiplication (e.g., 2 * 3 =  * 2)
 * MA 4.3.3.d Solve simple one-step whole number equations (e.g., x + 2 = 3, 3 * y = 6)
 * MA 4.3.3.e Explain the procedure(s) used in solving simple one-step whole number equations


 * MA 4.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 4.4.1 Display and Analysis: Students will organize, display, compare, and interpret data. **


 * MA 4.4.1.a Represent data using dot/line plots
 * MA 4.4.1.b Compare different representations of the same data
 * MA 4.4.1.c Interpret data and draw conclusions using dot/line plots
 * MA 4.4.1.d Find the mode and range for a set of whole numbers
 * MA 4.4.1.e Find the whole number mean for a set of whole numbers


 * MA 4.4.2 Predictions and Inferences: Students will construct predictions based on data. **


 * MA 4.4.2.a Make predictions based on data to answer questions from tables and bar graphs


 * MA 4.4.3 Probability: Students will find, describe, and compare experimental probabilities. **


 * MA 4.4.3.a Perform simple experiments and compare the degree of likelihood (e.g., more likely, equally likely, or less likely)

= Grade 5 =


 * MA 5.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 5.1.1 Number System: Students will represent and show relationships among positive rational numbers. **


 * MA 5.1.1.a Demonstrate multiple equivalent representations for whole numbers and decimals through the thousandths place (e.g., 3.125 is 3 + .1 + .02 + .005)
 * MA 5.1.1.b Compare and order whole numbers, fractions, and decimals through the thousandths place
 * MA 5.1.1.c Identify and name fractions in their simplest form and find common denominators for fractions
 * MA 5.1.1.d Recognize and generate equivalent forms of commonly used fractions, decimals, and percents (e.g., one third, one fourth, one half, two thirds, three fourths)
 * MA 5.1.1.e Classify a number as prime or composite
 * MA 5.1.1.f Identify factors and multiples of any whole number
 * MA 5.1.1.g Round whole numbers and decimals to any given place


 * MA 5.1.2 Operations: Students will demonstrate the meaning of arithmetic operations with whole numbers. **


 * MA 5.1.2.a Use words and symbols to explain the meaning of the identity properties for addition and multiplication
 * MA 5.1.2.b Use words and symbols to explain the meaning of the commutative and associative properties of addition and multiplication
 * MA 5.1.2.c Use words and symbols to explain the distributive property of multiplication over addition (e.g., 5 (y + 2) = 5y + 5 x 2)


 * MA 5.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 5.1.3.a Add and subtract positive rational numbers (e.g., proper and improper fractions, mixed numbers, fractions with common and uncommon denominators, decimals through the thousandths place)
 * MA 5.1.3.b Select, apply and explain the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil, technology)
 * MA 5.1.3.c Multiply decimals
 * MA 5.1.3.d Divide a decimal by a whole number


 * MA 5.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 5.1.4.a Estimate the sums and differences of positive rational numbers to check the reasonableness of such results


 * MA 5.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 5.2.1 Characteristics: Students will describe relationships among two-dimensional shapes and three-dimensional objects. **


 * MA 5.2.1.a Identify the number of edges, faces, and vertices of triangular and rectangular prisms
 * MA 5.2.1.b Justify congruence of two-dimensional shapes
 * MA 5.2.1.c Justify the classification of two-dimensional shapes (e.g., triangles by angles and sides)
 * MA 5.2.1.d Identify degrees on a circle (e.g., 45, 90, 180, 270, 360)


 * MA 5.2.2 Coordinate Geometry: Students will identify locations using coordinate geometry. **


 * MA 5.2.2.a Plot the location of an ordered pair in the first quadrant


 * MA 5.2.3 Transformations: Students will identify and use simple transformations. **


 * MA 5.2.3.a Perform one-step transformations on two dimensional shapes (e.g., translation, rotation, reflection, of 90, 180, and 270)


 * MA 5.2.4 Spatial Modeling: Students will create and use geometric models to solve problems. **


 * MA 5.2.4.a Build or sketch a geometric model to solve a problem
 * MA 5.2.4.b Sketch congruent shapes
 * MA 5.2.4.c Build rectangular prisms using cubes


 * MA 5.2.5 Measurement: Students will apply appropriate procedures, tools, and formulas to determine measurements using customary and metric units. **


 * MA 5.2.5.a Select and use appropriate tools to measure perimeter and angles
 * MA 5.2.5.b Identify correct unit (customary or metric) to the measurement situation (e.g., distance from home to school; measure length of a room)
 * MA 5.2.5.c Estimate and measure length with customary units to the nearest ¼ inch
 * MA 5.2.5.d Measure capacity/volume with customary units
 * MA 5.2.5.e Measure weight (mass) and temperature using metric units
 * MA 5.2.5.f Determine the area of rectangles and squares


 * MA 5.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 5.3.1 Relationships: Students will represent, analyze, and generalize relationships. **


 * MA 5.3.1.a Describe, extend, apply rules, and make generalizations about numeric, and geometric patterns
 * MA 5.3.1.b Create and analyze numeric patterns using words, tables, and graphs
 * MA 5.3.1.c Communicate relationships using expressions and equations


 * MA 5.3.2 Modeling in Context: Students will create, use, and compare models representing mathematical situations. **


 * MA 5.3.2.a Model situations that involve the addition, subtraction, and multiplication of positive rational numbers using words, graphs, and tables
 * MA 5.3.2.b Represent a variety of quantitative relationships using tables and graphs
 * MA 5.3.2.c Compare different models to represent mathematical situations


 * MA 5.3.3 Procedures: Students will apply properties of simple positive rational numbers to solve one-step equations. **


 * MA 5.3.3.a Explain the addition property of equality (e.g., if a = b, then a + c = b + c)
 * MA 5.3.3.b Use symbolic representations of the associative property (e.g., (2 + 3) + 4 = 2 + (3 + n), (2 * 3) * 4 = 2 * (3 * n))
 * MA 5.3.3.c Evaluate numerical expressions by using parentheses with respect to order of operations(e.g., 6 + (3 * 5))
 * MA 5.3.3.d Evaluate simple algebraic expressions involving addition and subtraction
 * MA 5.3.3.e Solve one-step addition and subtraction equations involving common positive rational numbers
 * MA 5.3.3.f Identify and explain the properties of equality used in solving one-step equations involving common positive rational numbers


 * MA 5.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 5.4.1 Display and Analysis: Students will organize, display, compare, and interpret data. **


 * MA 5.4.1.a Represent data using line plots
 * MA 5.4.1.b Represent the same set of data in different formats (e.g., table, pictographs, bar graphs, line plots)
 * MA 5.4.1.c Draw conclusions based on a set of data
 * MA 5.4.1.d Find the mean, median, mode, and range for a set of whole numbers
 * MA 5.4.1.e Generate questions and answers from data sets and their graphical representations


 * MA 5.4.2 Predictions and Inferences: Students will construct predictions based on data. **


 * MA 5.4.2.a Make predictions based on data to answer questions from tables, bar graphs, and line plots


 * MA 5.4.3 Probability: Students will determine theoretical probabilities. **


 * MA 5.4.3.a Perform and record results of probability experiments
 * MA 5.4.3.b Generate a list of possible outcomes for a simple event
 * MA 5.4.3.c Explain that the likelihood of an event that can be represented by a number from 0 (impossible) to 1 (certain)

= Grade 6 =


 * MA 6.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 6.1.1 Number System: Students will represent and show relationships among positive rational numbers and integers. **


 * MA 6.1.1.a Show equivalence among common fractions, decimals and percents
 * MA 6.1.1.b Compare and order positive and negative integers
 * MA 6.1.1.c Identify integers less than 0 on a number line
 * MA 6.1.1.d Represent large numbers using exponential notation (e.g., 1,000 = 103)
 * MA 6.1.1.e Identify the prime factorization of numbers (e.g., 12 = 2 x 2 x 3 or 22 x 3)
 * MA 6.1.1.f Classify numbers as natural, whole, or integer


 * MA 6.1.2 Operations: Students will demonstrate the meaning of arithmetic operations with positive fractions and decimals. **


 * MA 6.1.2.a Use drawings, words, and symbols to explain the meaning of addition and subtraction of fractions
 * MA 6.1.2.b Use drawings, words, and symbols to explain the meaning of addition and subtraction of decimals


 * MA 6.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 6.1.3.a Multiply and divide positive rational numbers
 * MA 6.1.3.b Select and apply the appropriate method of computation when problem solving (e.g., models, mental computation, paper-pencil, technology, divisibility rules)


 * MA 6.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 6.1.4.a Use appropriate estimation methods to check the reasonableness of solutions for problems involving positive rational numbers


 * MA 6.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 6.2.1 Characteristics: Students will compare and contrast properties among two-dimensional shapes and among three-dimensional objects. **


 * MA 6.2.1.a Justify the classification of three dimensional objects


 * MA 6.2.2 Coordinate Geometry: Students will label points using coordinate geometry. **


 * MA 6.2.2.a Identify the ordered pair of a plotted point in the coordinate plane


 * MA 6.2.3 Transformations: Students will use and describe results of transformations on geometric shapes. **


 * MA 6.2.3.a Perform and describe positions and orientation of shapes under single transformations (translation, rotation, reflection) not on a coordinate plane


 * MA 6.2.4 Spatial Modeling: Students will use visualization of geometric models to solve problems. **


 * MA 6.2.4.a Identify two-dimensional drawings of three-dimensional objects


 * MA 6.2.5 Measurement: Students will apply appropriate procedures, tools, and formulas to determine measurements. **


 * MA 6.2.5.a Estimate and measure length with customary and metric units to the nearest 1/16 inch and mm
 * MA 6.2.5.b Measure volume/capacity using the metric system
 * MA 6.2.5.c Convert length, weight (mass), and liquid capacity from one unit to another within the same system
 * MA 6.2.5.d Determine the perimeter of polygons
 * MA 6.2.5.e Determine the area of parallelograms and triangles
 * MA 6.2.5.f Determine the volume of rectangular prisms


 * MA 6.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 6.3.1 Relationships: Students will represent, analyze, and use relationships to make generalizations. **


 * MA 6.3.1.a Describe and create simple algebraic expressions (e.g., one operation, one variable) from words and tables
 * MA 6.3.1.b Use a variable to describe a situation with an equation (e.g., one-step, one variable)
 * MA 6.3.1.c Identify relationships as increasing, decreasing, or constant


 * MA 6.3.2 Modeling in Context: Students will create, use, and interpret models of quantitative relationships. **


 * MA 6.3.2.a Model contextualized problems using various representations (e.g., graphs, tables)
 * MA 6.3.2.b Represent a variety of quantitative relationships using symbols and words


 * MA 6.3.3 Procedures: Students will apply properties to solve equations. **


 * MA 6.3.3.a Explain the multiplication property of equality (e.g., if a = b, then ac = bc)
 * MA 6.3.3.b Evaluate numerical expressions containing multiple operations with respect to order of operations (e.g., 2 + 4 x 5)
 * MA 6.3.3.c Evaluate simple algebraic expressions involving multiplication and division
 * MA 6.3.3.d Solve one-step equations involving positive rational numbers
 * MA 6.3.3.e Identify and explain the properties of equality used in solving one-step equations (e.g., addition, subtraction, division)


 * MA 6.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 6.4.1 Display and Analysis: Students will organize, display, compare, and interpret data. **


 * MA 6.4.1.a Represent data using stem and leaf plots, histograms, and frequency charts
 * MA 6.4.1.b Compare and interpret data sets and their graphical representations
 * MA 6.4.1.c Find the mean, median, mode, and range for a set of data
 * MA 6.4.1.d Compare the mean, median, mode, and range from two sets of data


 * MA 6.4.2 Predictions and Inferences: Students will construct predictions based on data. **


 * MA 6.4.2.a Make predictions based on data and create questions to further investigate the quality of the predictions


 * MA 6.4.3 Probability: Students will apply basic concepts of probability. **


 * MA 6.4.3.a Describe the theoretical probability of an event using a fraction, percentage, decimal, or ratio
 * MA 6.4.3.b Compute theoretical probabilities for independent events
 * MA 6.4.3.c Find experimental probability for independent events

= Grade 7 =


 * MA 7.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 7.1.1 Number System: Students will represent and show relationships among rational numbers. **


 * MA 7.1.1.a Show equivalence among fractions, decimals, and percents
 * MA 7.1.1.b Compare and order rational numbers (e.g., fractions, decimals, percents)
 * MA 7.1.1.c Represent large numbers using scientific notation
 * MA 7.1.1.d Classify numbers as natural, whole, integer, or rational
 * MA 7.1.1 e Find least common multiple and greatest common divisor given two numbers


 * MA 7.1.2 Operations: Students will demonstrate the meaning of arithmetic operations with positive fractions, decimals, and integers. **


 * MA 7.1.2.a Use drawings, words, and symbols to explain the meaning of multiplication and division of fractions (e.g., 2/3 x 6 as two-thirds of six, or 6 x 2/3 as 6 groups of two-thirds, or 6 ÷ 2/3 as how many two-thirds there are in six.)
 * MA 7.1.2.b Use drawings, words, and symbols to explain the meaning of multiplication and division of decimals
 * MA 7.1.2.c Use drawings, words, and symbols to explain the addition and subtraction of integers


 * MA 7.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 7.1.3.a Compute accurately with integers
 * MA 7.1.3.b Select, apply, and explain the method of computation when problem solving using integers and positive rational numbers (e.g., models, mental computation, paper-pencil, technology, divisibility rules)
 * MA 7.1.3.c Solve problems involving percent of numbers (e.g., percent of, % increase, % decrease)


 * MA 7.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 7.1.4.a Use estimation methods to check the reasonableness of solutions for problems involving integers and positive rational numbers


 * MA 7.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 7.2.1 Characteristics: Students will describe, compare, and contrast characteristics, properties, and relationships of geometric shapes and objects. **


 * MA 7.2.1.a Identify and describe similarity of two-dimensional shapes using side and angle measurements
 * MA 7.2.1.b Name line, line segment, ray, and angle


 * MA 7.2.2 Coordinate Geometry: Students will specify locations and describe relationships using coordinate geometry. **


 * MA 7.2.2.a Plot the location of an ordered pair in the coordinate plane
 * MA 7.2.2.b Identify the quadrant of a given point in the coordinate plane
 * MA 7.2.2.c Find the distance between points along horizontal and vertical lines of a coordinate plane (e.g., what is the distance between (0, 3) and (0, 9))


 * MA 7.2.3 Transformations: Students will use transformations and symmetry to analyze geometric shapes. **


 * MA 7.2.3.a Identify lines of symmetry for a reflection
 * MA 7.2.3.b Perform and describe positions and orientation of shapes under a single transformation (e.g., translation, rotation, reflection) on a coordinate plane


 * MA 7.2.4 Spatial Modeling: Students will use visualization to create geometric models in solving problems. **


 * MA 7.2.4.a Identify the shapes that make up the three-dimensional object
 * MA 7.2.4.b Create two-dimensional representations of three-dimensional objects to visualize and solve problems (e.g., perspective drawing of surface area)
 * MA 7.2.4.c Draw angles to given degree


 * MA 7.2.5 Measurement: Students will select and apply appropriate procedures, tools, and formulas to determine measurements. **


 * MA 7.2.5.a Measure angles to the nearest degree
 * MA 7.2.5.b Determine the area of trapezoids and circles, and the circumference of circles
 * MA 7.2.5.c Recognize the inverse relationship between the size of a unit and the number of units used when measuring


 * MA 7.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 7.3.1 Relationships: Students will represent and analyze relationships using algebraic symbols. **


 * MA 7.3.1.a Describe and create algebraic expressions from words, tables, and graphs
 * MA 7.3.1.b Use a variable to describe a situation with an inequality (e.g., one-step, one variable)
 * MA 7.3.1.c Recognize and generate equivalent forms of simple algebraic expressions


 * MA 7.3.2 Modeling in Context: Students will create, use, and interpret models of quantitative relationships. **


 * MA 7.3.2.a Model contextualized problems using various representations (e.g., one-step/variable expressions, one-step/variable equations)
 * MA 7.3.2.b Represent a variety of quantitative relationships using algebraic expressions and one-step equations


 * MA 7.3.3 Procedures: Students will apply properties to solve equations and inequalities. **


 * MA 7.3.3.a Explain additive inverse of addition (e.g., 7 + -7 = 0)
 * MA 7.3.3.b Use symbolic representation of the distributive property (e.g., 2(x + 3) = 2x + 6)
 * MA 7.3.3.c Given the value of the variable(s), evaluate algebraic expressions with respect to order of operations
 * MA 7.3.3.d Solve two-step equations involving integers and positive rational numbers
 * MA 7.3.3.e Solve one-step inequalities involving positive rational numbers
 * MA 7.3.3.f Identify and explain the properties used in solving two-step equations (e.g., addition, subtraction, multiplication and division)


 * MA 7.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 7.4.1 Display and Analysis: Students will formulate questions that can be addressed with data and then organize, display, and analyze the relevant data to answer their questions. **


 * MA 7.4.1.a Analyze data sets and interpret their graphical representations
 * MA 7.4.1.b Find and interpret mean, median, mode, and range for sets of data
 * MA 7.4.1.c Explain the difference between a population and a sample
 * MA 7.4.1.d List biases that may be created by various data collection processes
 * MA 7.4.1.e Formulate a question about a characteristic within one population that can be answered by simulation or a survey


 * MA 7.4.2 Predictions and Inferences: Students will evaluate predictions and make inferences based on data. **


 * MA 7.4.2.a Determine if data collected from a sample can be used to make predictions about a population


 * MA 7.4.3 Probability: Students will apply and interpret basic concepts of probability. **


 * MA 7.4.3.a Find the probability of independent compound events (e.g., tree diagram, organized list)
 * MA 7.4.3.b Compare and contrast theoretical and experimental probabilities

**Grade 8**


 * MA 8.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 8.1.1 Number System: Students will represent and show relationships among real numbers. **


 * MA 8.1.1.a Compare and order real numbers
 * MA 8.1.1.b Demonstrate relative position of real numbers on the number line (e.g., square root of 2 is left of 1.5)
 * MA 8.1.1.c Represent small numbers using scientific notation
 * MA 8.1.1.d Classify numbers as natural, whole, integer, rational, irrational, or real


 * MA 8.1.2 Operations: Students will demonstrate the meaning of arithmetic operations with integers. **


 * MA 8.1.2.a Use drawings, words, and symbols to explain the meaning of addition, subtraction, multiplication, and division of integers.
 * MA 8.1.2.b Use words and symbols to explain the zero property of multiplication (e.g., if ab = 0 then a or b or both must be zero)
 * MA 8.1.2.c Use words and symbols to explain why division by zero is undefined


 * MA 8.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 8.1.3.a Compute accurately with rational numbers
 * MA 8.1.3.b Evaluate expressions involving absolute value of integers
 * MA 8.1.3.c Calculate squares of integers, the square roots of perfect squares, and the square roots of whole numbers using technology
 * MA 8.1.3.d Select, apply, and explain the method of computation when problem solving using rational numbers (e.g., models, mental computation, paper-pencil, technology, divisibility rules)
 * MA 8.1.3.e Solve problems involving ratios and proportions (e.g., x/(5 ) = 10/17 )


 * MA 8.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 8.1.4.a Use estimation methods to check the reasonableness of solutions for problems involving rational numbers


 * MA 8.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 8.2.1 Characteristics: Students will describe, compare, and contrast characteristics, properties, and relationships of geometric shapes and objects. **


 * MA 8.2.1.a Identify and describe similarity of three-dimensional objects
 * MA 8.2.1.b Compare and contrast relationships between similar and congruent objects
 * MA 8.2.1.c Identify geometric properties of parallel lines cut by a transversal and related angles (e.g., perpendicular and parallel lines with transversals) and angles (e.g., corresponding, alternate interior, alternate exterior)
 * MA 8.2.1.d Identify pairs of angles (e.g., adjacent, complementary, supplementary, vertical)
 * MA 8.2.1.e Examine the relationships of the interior angles of a triangle (e.g., the sum of the angles is 180 degrees)


 * MA 8.2.2 Coordinate Geometry: Students will specify locations and describe relationships using coordinate geometry. **


 * MA 8.2.2.a Use coordinate geometry to represent and examine the properties of rectangles and squares using horizontal and vertical segments


 * MA 8.2.3 Transformations: Students will perform transformations and use them to analyze the orientation and size of geometric shapes. **


 * MA 8.2.3.a Identify the similarity of dilated shapes
 * MA 8.2.3.b Perform and describe positions and sizes of shapes under dilations (e.g., scale factor, ratios)


 * MA 8.2.4 Spatial Modeling: Students will use visualization, spatial reasoning, and geometric modeling to solve problems. **


 * MA 8.2.4.a Draw geometric objects with specified properties (e.g., parallel sides, number of sides, angle measures, number of faces)


 * MA 8.2.5 Measurement: Students will select and apply appropriate procedures, tools, and formulas to determine measurements. **


 * MA 8.2.5.a Use strategies to find the perimeter and area of complex shapes
 * MA 8.2.5.b Determine surface area and volume of three-dimensional objects (e.g., rectangular prisms, cylinders)
 * MA 8.2.5.c Apply the Pythagorean theorem to find missing lengths in right triangles and to solve problems
 * MA 8.2.5.d Use scale factors to find missing lengths in similar shapes
 * MA 8.2.5.e Convert between metric and standard units of measurement, given conversion factors (e.g., meters to yards)


 * MA 8.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 8.3.1 Relationships: Students will represent and analyze relationships using algebraic symbols. **


 * MA 8.3.1.a Represent and analyze a variety of patterns with tables, graphs, words, and algebraic equations
 * MA 8.3.1.b Describe relationships using algebraic expressions, equations, and inequalities (e.g., two-step, one variable)
 * MA 8.3.1.c Identify constant slope from tables and graphs


 * MA 8.3.2 Modeling in Context: Students will create, use, and interpret models of quantitative relationships. **


 * MA 8.3.2.a Model contextualized problems using various representations (e.g., two-step/one variable equations)
 * MA 8.3.2.b Represent a variety of quantitative relationships using algebraic expressions and two-step/one variable equations


 * MA 8.3.3 Procedures: Students will apply properties to solve equations and inequalities. **


 * MA 8.3.3.a Explain the multiplicative inverse (e.g., 4 * ¼= 1)
 * MA 8.3.3.b Evaluate numerical expressions containing whole number exponents (e.g., if x = 4, then (x + 3)2 + 5x = ?)
 * MA 8.3.3.c Solve multi-step equations involving rational numbers
 * MA 8.3.3.d Solve two-step inequalities involving rational numbers
 * MA 8.3.3.e Identify and explain the properties used in solving two-step inequalities and multi-step equations


 * MA 8.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 8.4.1 Display and Analysis: Students will formulate questions that can be addressed with data, and then organize, display, and analyze the relevant data to answer their questions. **


 * MA 8.4.1.a Represent data using circle graphs and box plots with and without the use of technology
 * MA 8.4.1.b Compare characteristics between sets of data or within a given set of data
 * MA 8.4.1.c Find, interpret, and compare measures of central tendency (mean, median, mode) and the quartiles for sets of data
 * MA 8.4.1.d Select the most appropriate unit of central tendency for sets of data
 * MA 8.4.1.e Identify misrepresentation and misinterpretation of data represented in circle graphs and box plots


 * MA 8.4.2 Predictions and Inferences: Students will evaluate predictions and make inferences based on data. **


 * MA 8.4.2.a Evaluate predictions to formulate new questions and plan new studies
 * MA 8.4.2.b Compare and contrast two sets of data to make inferences


 * MA 8.4.3 Probability: Students will apply and interpret basic concepts of probability. **


 * MA 8.4.3.a Identify complementary events and calculate their probabilities
 * MA 8.4.3.b Compute probabilities for independent compound events

= Grade 12 =


 * MA 12.1 Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 12.1.1 Number System: Students will represent and show relationships among complex numbers. **


 * MA 12.1.1.a Demonstrate multiple equivalent forms of irrational numbers (e.g., √8=8^(1/2)=2√2)
 * MA 12.1.1.b Compare, contrast and apply the properties of numbers and the real number system, including rational, irrational, imaginary, and complex numbers


 * MA 12.1.2 Operations: Students will demonstrate the meaning and effects of arithmetic operations with real numbers. **


 * MA 12.1.2.a Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities (e.g., if you take the square root of a number, will the result always be smaller than the original number? (e.g., √(1/4)=1/2 ))
 * MA 12.1.2.b Use drawings, words, and symbols to explain that the distance between two numbers on the number line is the absolute value of their difference


 * MA 12.1.3 Computation: Students will compute fluently and accurately using appropriate strategies and tools. **


 * MA 12.1.3.a Compute accurately with real numbers
 * MA 12.1.3.b Simplify exponential expressions (e.g., powers of -1, 0, ½, 3^2* 3^2= 3^4)
 * MA 12.1.3.c Multiply and divide numbers using scientific notation
 * MA 12.1.3.d Select, apply, and explain the method of computation when problem solving using real numbers (e.g., models, mental computation, paper-pencil, or technology)


 * MA 12.1.4 Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools. **


 * MA 12.1.4.a Use estimation methods to check the reasonableness of real number computations and decide if the problem calls for an approximation or an exact number (e.g., 10  (pi) is approximately 31.4, square and cube roots)
 * MA 12.1.4.b Distinguish relevant from irrelevant information, identify missing information and either find what is needed or make appropriate estimates


 * MA 12.2 Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 12.2.1 Characteristics: Students will analyze characteristics, properties, and relationships among geometric shapes and objects. **


 * MA12.2.1.a Identify and explain the necessity of and give examples of definitions and theorems
 * MA 12.2.1.b Analyze properties and relationships among classes of two and three dimensional geometric objects using inductive reasoning and counterexamples
 * MA 12.2.1 c State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles)
 * MA 12.2.1.d Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)
 * MA 12.2.1.e Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)
 * MA 12.2.1.f Recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true
 * MA12.2.1.g Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems


 * MA 12.2.2 Coordinate Geometry: Student will use coordinate geometry to analyze and describe relationships in the coordinate plane. **


 * MA 12.2.2.a Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)
 * MA 12.2.2.b Apply the midpoint formula
 * MA 12.2.2.c Apply the distance formula
 * MA 12.2.2.d Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square)


 * MA 12.2.3 Transformations: Students will apply and analyze transformations. **


 * MA 12.2.3.a Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes
 * MA 12.2.3.b Perform and describe multiple transformations


 * MA 12.2.4 Spatial Modeling: Students will use visualization, spatial reasoning, and geometric modeling to solve problems. **


 * MA 12.2.4.a Sketch and draw appropriate representations of geometric objects using ruler, protractor, or technology
 * MA 12.2.4.b Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room; scale model)


 * MA 12.2.5 Measurement: Students will apply the units, systems, and formulas to solve problems. **


 * MA 12.2.5.a Use strategies to find surface area and volume of complex objects
 * MA 12.2.5.b Apply appropriate units and scales to solve problems involving measurement
 * MA 12.2.5.c Convert between various units of area and volume, such as square feet to square yards
 * MA 12.2.5.d Convert equivalent rates (e.g., feet/second to miles/hour)
 * MA 12.2.5.e Find arc length and area of sectors of a circle
 * MA 12.2.5.f Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)
 * MA12.2.5.g Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively


 * MA 12.3 Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 12.3.1 Relationships: Students will generalize, represent, and analyze relationships using algebraic symbols. **

NON LINEAR FUNCTIONS INCLUDE: QUADRATIC, ABSOLUTE VALUE, SQUARE ROOT, EXPONENTIAL


 * MA 12.3.1.a Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)
 * MA 12.3.1.b Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear)
 * MA 12.3.1.c Identify the slope and intercepts of a linear relationship from an equation or graph
 * MA 12.3.1.d Identify characteristics of linear and non-linear functions
 * MA 12.3.1.e Graph linear and non-linear functions
 * MA 12.3.1.f Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations
 * MA 12.3.1.g Graph and interpret linear inequalities
 * MA 12.3.1.h Represent, interpret, and analyze functions and their inverses
 * MA 12.3.1.i Determine if a relation is a function


 * MA 12.3.2 Modeling in Context: Students will model and analyze quantitative relationships. **

CONTEXTUALIZED PROBLEM – A MATHEMATICAL SITUATION PLACED IN A PARTICULAR CONTEXT (E.G., USING WORDS, DIAGRAMS, TABLES, DRAWINGS, ETC.)


 * MA 12.3.2.a Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)
 * MA 12.3.2.b Represent a variety of quantitative relationships using linear equations and one variable inequalities
 * MA 12.3.2.c Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear)
 * MA 12.3.2.d Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value)


 * MA 12.3.3 Procedures: Students will represent and solve equations and inequalities. **


 * MA 12.3.3.a Explain/apply the reflexive, symmetric, and transitive properties of equality
 * MA 12.3.3.b Simplify algebraic expressions involving exponents (e.g., (3x4)2)
 * MA 12.3.3.c Add and subtract polynomials
 * MA 12.3.3.d Multiply and divide polynomials (e.g., divide x3 – 8 by x – 2, divide x4 – 5x3 – 2x by x2)
 * MA 12.3.3.e Factor polynomials
 * MA 12.3.3.f Identify and generate equivalent forms of linear equations
 * MA 12.3.3.g Solve linear equations and inequalities including absolute value
 * MA 12.3.3.h Identify and explain the properties used in solving equations and inequalities
 * MA 12.3.3.i Solve quadratic equations (e.g., factoring, graphing, quadratic formula)
 * MA 12.3.3.j Add, subtract, and simplify rational expressions
 * MA 12.3.3.k Multiply, divide, and simplify rational expressions
 * MA 12.3.3.l Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables
 * MA 12.3.3.m Derive and use the formulas for the general term and summation of finite arithmetic and geometric series
 * MA 12.3.3.n Combine functions by composition, as well as by addition, subtraction, multiplication, and division
 * MA 12.3.3.o Solve an equation involving several variables for one variable in terms of the others
 * MA 12.3.3.p Analyze and solve systems of two linear equations in two variables algebraically and graphically


 * MA 12.4 Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines. **


 * MA 12.4.1 Display and Analysis: Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data. **


 * MA 12.4.1.a Interpret data represented by the normal distribution and formulate conclusions
 * MA 12.4.1.b Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set
 * MA 12.4.1.c Explain how sample size and transformations of data affect measures of central tendency
 * MA 12.4.1.d Describe the shape and determine spread (variance, standard deviation) and outliers of a data set
 * MA 12.4.1.e Explain how statistics are used or misused in the world
 * MA 12.4.1.f Create scatter plots, analyze patterns, and describe relationships in paired data
 * MA 12.4.1.g Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made
 * MA 12.4.1.h Explain the differences between randomized experiment and observational studies


 * MA 12.4.2 Predictions and Inferences: Students will develop and evaluate inferences to make predictions. **


 * MA 12.4.2.a Compare data sets and evaluate conclusions using graphs and summary statistics
 * MA 12.4.2.b Support inferences with valid arguments
 * MA 12.4.2.c Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient
 * MA 12.4.2.d Recognize when arguments based on data confuse correlation with causation


 * MA 12.4.3 Probability: Students will apply and analyze concepts of probability. **


 * MA 12.4.3.a Construct a sample space and a probability distribution
 * MA 12.4.3.b Identify dependent and independent events and calculate their probabilities
 * MA 12.4.3.c Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)
 * MA 12.4.3.d Analyze events to determine if they are mutually exclusive
 * MA 12.4.3.e Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome