South Caroline Standards Alignment K-8

This alignment shows the Media4Math resources that support the standards shown below. Click on a grade to see the South Carolina standards for that grade. Then click on a specific standard to see all the Media4Math resources that support it.

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K

Gr 1

Gr 2

Gr 3

Gr 4

Gr 5

Gr 6

Gr 7

Gr 8

Kindergarten

Standard	Description
K.NS.1	Count forward by ones and tens to 100.
K.NS.2	Count forward by ones beginning from any number less than 100.
K.NS.3	Read numbers from 0 – 20 and represent a number of objects 0 – 20 with a written numeral.
K.NS.4	Understand the relationship between number and quantity. Connect counting to cardinality by demonstrating an understanding that: a. the last number said tells the number of objects in the set (cardinality); b. the number of objects is the same regardless of their arrangement or the order in which they are counted (conservation of number); c. each successive number name refers to a quantity that is one more and each previous number name refers to a quantity that is one less.
K.NS.5	Count a given number of objects from 1 – 20 and connect this sequence in a one-to- one manner.
K.NS.6	Recognize a quantity of up to ten objects in an organized arrangement (subitizing).
K.NS.7	Determine whether the number of up to ten objects in one group is more than, less than, or equal to the number of up to ten objects in another group using matching and counting strategies.
K.NS.8	Compare two written numerals up to 10 using more than, less than or equal to.
K.NS.9	Identify first through fifth and last positions in a line of objects.
K.NSBT.1	Compose and decompose numbers from 11 - 19 separating ten ones from the remaining ones using objects and drawings.
K.ATO.1	Model situations that involve addition and subtraction within 10 using objects, fingers, mental images, drawings, acting out situations, verbal explanations, expressions, and equations.
K.ATO.2	Solve real-world/story problems using objects and drawings to find sums up to 10 and differences within 10.
K.ATO.3	Compose and decompose numbers up to 10 using objects, drawings, and equations.
K.ATO.4	Create a sum of 10 using objects and drawings when given one of two addends 1 - 9.
K.ATO.5	Add and subtract fluently within 5.
K.ATO.6	Describe simple repeating patterns using AB, AAB, ABB, and ABC type patterns.
K.G.1	Describe positions of objects by appropriately using terms, including below, above, beside, between, inside, outside, in front of, or behind.
K.G.2	Identify and describe a given shape and shapes of objects in everyday situations to include two-dimensional shapes (i.e., triangle, square, rectangle, hexagon, and circle) and three-dimensional shapes (i.e., cone, cube, cylinder, and sphere).
K.G.3	Classify shapes as two-dimensional/flat or three-dimensional/solid and explain the reasoning used.
K.G.4	Analyze and compare two- and three-dimensional shapes of different sizes and orientations using informal language.
K.G.5	Draw two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, and circle) and create models of three-dimensional shapes (i.e., cone, cube, cylinder, and sphere).
K.MDA.1	Identify measurable attributes (length, weight) of an object.
K.MDA.2	Compare objects using words such as shorter/longer, shorter/taller, and lighter/heavier.
K.MDA.3	Sort and classify data into 2 or 3 categories with data not to exceed 20 items in each category.
K.MDA.4	Represent data using object and picture graphs and draw conclusions from the graphs.

Grade 1

Standard	Description
1.NSBT.1	Extend the number sequence to: a. count forward by ones to 120 starting at any number; b. count by fives and tens to 100, starting at any number; c. read, write and represent numbers to 100 using concrete models, standard form, and equations in expanded form; d. read and write in word form numbers zero through nineteen, and multiples of ten through ninety.
1.NSBT.2	Understand place value through 99 by demonstrating that: a. ten ones can be thought of as a bundle (group) called a “ten”; b. the tens digit in a two-digit number represents the number of tens and the ones digit represents the number of ones; c. two-digit numbers can be decomposed in a variety of ways (e.g., 52 can be decomposed as 5 tens and 2 ones or 4 tens and 12 ones, etc.) and record the decomposition as an equation.
1.NSBT.3	Compare two two-digit numbers based on the meanings of the tens and ones digits, using the words greater than, equal to, or less than.
1.NSBT.4	Add through 99 using concrete models, drawings, and strategies based on place value to: a. add a two-digit number and a one-digit number, understanding that sometimes it is necessary to compose a ten (regroup); b. add a two-digit number and a multiple of 10.
1.NSBT.5	Determine the number that is 10 more or 10 less than a given number through 99 and explain the reasoning verbally and with multiple representations, including concrete models.
1.NSBT.6	Subtract a multiple of 10 from a larger multiple of 10, both in the range 10 to 90, using concrete models, drawings, and strategies based on place value.
1.ATO.1	Solve real-world/story problems using addition (as a joining action and as a part- part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 20 with unknowns in all positions.
1.ATO.2	Solve real-world/story problems that include three whole number addends whose sum is less than or equal to 20.
1.ATO.3	Apply Commutative and Associative Properties of Addition to find the sum (through 20) of two or three addends.
1.ATO.4	Understand subtraction as an unknown addend problem.
1.ATO.5	Recognize how counting relates to addition and subtraction.
1.ATO.6	Demonstrate: a. addition and subtraction through 20; b. fluency with addition and related subtraction facts through 10.
1.ATO.7	Understand the meaning of the equal sign as a relationship between two quantities
1.ATO.8	Determine the missing number in addition and subtraction equations within 20.
1.ATO.9	Create, extend and explain using pictures and words for: a. repeating patterns (e.g., AB, AAB, ABB, and ABC type patterns); b. growing patterns (between 2 and 4 terms/figures).
1.G.1	Distinguish between a two-dimensional shape’s defining (e.g., number of sides) and non-defining attributes (e.g., color).
1.G.2	Combine two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, rhombus, and trapezoid) or three-dimensional shapes (i.e., cube, rectangular prism, cone, and cylinder) in more than one way to form a composite shape.
1.G.3	Partition two-dimensional shapes (i.e., square, rectangle, circle) into two or four equal parts.
1.G.4	Identify and name two-dimensional shapes (i.e., square, rectangle, triangle, hexagon, rhombus, trapezoid, and circle).
1.MDA.1	Order three objects by length using indirect comparison.
1.MDA.2	Use nonstandard physical models to show the length of an object as the number of same size units of length with no gaps or overlaps.
1.MDA.3	Use analog and digital clocks to tell and record time to the hour and half hour.
1.MDA.4	Collect, organize, and represent data with up to 3 categories using object graphs, picture graphs, t-charts and tallies.
1.MDA.5	Draw conclusions from given object graphs, picture graphs, t-charts, tallies, and bar graphs.
1.MDA.6	Identify a penny, nickel, dime and quarter and write the coin values using a _ symbol.

Grade 2

Standard	Description
2.NSBT.1	Understand place value through 999 by demonstrating that: a. 100 can be thought of as a bundle (group) of 10 tens called a “hundred”; b. the hundreds digit in a three-digit number represents the number of hundreds, the tens digit represents the number of tens, and the ones digit represents the number of ones; c. three-digit numbers can be decomposed in multiple ways (e.g., 524 can be decomposed as 5 hundreds, 2 tens and 4 ones or 4 hundreds, 12 tens, and 4 ones, etc.).
2.NSBT.2	Count by tens and hundreds to 1,000 starting with any number.
2.NSBT.3	Read, write and represent numbers through 999 using concrete models, standard form, and equations in expanded form.
2.NSBT.4	Compare two numbers with up to three digits using words and symbols (i.e., >, =, or <).
2.NSBT.5	Add and subtract fluently through 99 using knowledge of place value and properties of operations.
2.NSBT.6	Add up to four two-digit numbers using strategies based on knowledge of place value and properties of operations.
2.NSBT.7	Add and subtract through 999 using concrete models, drawings, and symbols which convey strategies connected to place value understanding.
2.NSBT.8	Determine the number that is 10 or 100 more or less than a given number through 1,000 and explain the reasoning verbally and in writing.
2.ATO.1	Solve one- and two-step real-world/story problems using addition (as a joining action and as a part-part-whole action) and subtraction (as a separation action, finding parts of the whole, and as a comparison) through 99 with unknowns in all positions.
2.ATO.2	Demonstrate fluency with addition and related subtraction facts through 20.
2.ATO.3	Determine whether a number through 20 is odd or even using pairings of objects, counting by twos, or finding two equal addends to represent the number (e.g., 3 + 3 = 6).
2.ATO.4	Use repeated addition to find the total number of objects arranged in a rectangular array with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
2.G.1	Identify triangles, quadrilaterals, hexagons, and cubes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.
2.G.2	Partition a rectangle into rows and columns of same-size squares to form an array and count to find the total number of parts.
2.G.3	Partition squares, rectangles and circles into two or four equal parts, and describe the parts using the words halves, fourths, a half of, and a fourth of. Understand that when partitioning a square, rectangle or circle into two or four equal parts, the parts become smaller as the number of parts increases.
2.MDA.1	Select and use appropriate tools (e.g., rulers, yardsticks, meter sticks, measuring tapes) to measure the length of an object.
2.MDA.2	Measure the same object or distance using a standard unit of one length and then a standard unit of a different length and explain verbally and in writing how and why the measurements differ.
2.MDA.3	Estimate and measure length/distance in customary units (i.e., inch, foot, yard) and metric units (i.e., centimeter, meter).
2.MDA.4	Measure to determine how much longer one object is than another, using standard length units.
2.MDA.5	Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences through 99 on a number line diagram.
2.MDA.6	Use analog and digital clocks to tell and record time to the nearest five-minute interval using a.m. and p.m.
2.MDA.7	Solve real-world/story problems involving dollar bills using the $ symbol or involving quarters, dimes, nickels, and pennies using the ¢ symbol.
2.MDA.8	Generate data by measuring objects in whole unit lengths and organize the data in a line plot using a horizontal scale marked in whole number units.
2.MDA.9	Collect, organize, and represent data with up to four categories using picture graphs and bar graphs with a single-unit scale.
2.MDA.10	Draw conclusions from t-charts, object graphs, picture graphs, and bar graphs.

Grade 3

Standard	Description
3.NSBT.1	Use place value understanding to round whole numbers to the nearest 10 or 100.
3.NSBT.2	Add and subtract whole numbers fluently to 1,000 using knowledge of place value and properties of operations.
3.NSBT.3	Multiply one-digit whole numbers by multiples of 10 in the range 10 – 90, using knowledge of place value and properties of operations.
3.NSBT.4	Read and write numbers through 999,999 in standard form and equations in expanded form.
3.NSBT.5	Compare and order numbers through 999,999 and represent the comparison using the symbols >, =, or <.
3.NSF.1	Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers. a. A fraction 1/b (called a unit fraction) is the quantity formed by one part when a whole is partitioned into 𝑏 equal parts; b. A fraction 𝑎/b is the quantity formed by 𝑎 parts of size 1; c. A fraction is a number that can be represented on a number line based on counts of a unit fraction; d. A fraction can be represented using set, area, and linear models.
3.NSF.2	Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that: a. two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line; b. fraction equivalence can be represented using set, area, and linear models; c. whole numbers can be written as fractions (e.g., 4 = 4 and 1 = 4); 1 4 d. fractions with the same numerator or same denominator can be compared by reasoning about their size based on the same whole.
3.NSF.3	Develop an understanding of mixed numbers (i.e., denominators 2, 3, 4, 6, 8, 10) as iterations of unit fractions on a number line.
3.ATO.1	Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and explain the relationship between the factors (i.e., 0 –10) and the product.
3.ATO.2	Use concrete objects, drawings and symbols to represent division without remainders and explain the relationship among the whole number quotient (i.e., 0 – 10), divisor (i.e., 0 – 10), and dividend.
3.ATO.3	Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation with a symbol for the unknown.
3.ATO.4	Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient.
3.ATO.5	Apply properties of operations (i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and divide and explain the reasoning.
3.ATO.6	Understand division as a missing factor problem.
3.ATO.7	Demonstrate fluency with basic multiplication and related division facts of products and dividends through 100.
3.ATO.8	Solve two-step real-world problems using addition, subtraction, multiplication and division of whole numbers and having whole number answers. Represent these problems using equations with a letter for the unknown quantity.
3.ATO.9	Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table).
3.G.1	Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
3.G.2	Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction. Recognize that equal parts of identical wholes need not have the same shape.
3.G.3	Use a right angle as a benchmark to identify and sketch acute and obtuse angles.
3.G.4	Identify a three-dimensional shape (i.e., right rectangular prism, right triangular prism, pyramid) based on a given two-dimensional net and explain the relationship between the shape and the net.
3.MDA.1	Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes.
3.MDA.2	Estimate and measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (i.e., mL, L) to the nearest whole unit.
3.MDA.3	Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar graph to represent the data.
3.MDA.4	Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the data in a line plot using a horizontal scale marked off in appropriate units.
3.MDA.5	Understand the concept of area measurement. a. Recognize area as an attribute of plane figures; b. Measure area by building arrays and counting standard unit squares; c. Determine the area of a rectilinear polygon and relate to multiplication and addition.
3.MDA.6	Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Grade 4

Standard	Description
4.NSBT.1	Understand that, in a multi-digit whole number, a digit represents ten times what the same digit represents in the place to its right.
4.NSBT.2	Recognize math periods and number patterns within each period to read and write in standard form large numbers through 999,999,999.
4.NSBT.3	Use rounding as one form of estimation and round whole numbers to any given place value.
4.NSBT.4	Fluently add and subtract multi-digit whole numbers using strategies to include a standard algorithm.
4.NSBT.5	Multiply up to a four-digit number by a one-digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using rectangular arrays, area models and/or equations.
4.NSBT.6	Divide up to a four-digit dividend by a one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
4.NSF.1	Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), 𝑎/b , is equivalent to a fraction, (𝑛 x 𝑎)/(n x b) , by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NSF.2	Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/4 and represent the comparison using the symbols >, =, or <.
4.NSF.3	Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions. a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; c. Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
4.NSF.4	Apply and extend an understanding of multiplication by multiplying a whole number and a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). a. Understand a fraction 𝑎/b as a multiple of 1/b; b. Understand a multiple of 𝑎/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number; c. Solve real-world problems involving multiplication of a fraction by a whole number (i.e., use visual fraction models and equations to represent the problem).
4.NSF.5	Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100.
4.NSF.6	Write a fraction with a denominator of 10 or 100 using decimal notation, and read and write a decimal number as a fraction.
4.NSF.7	Compare and order decimal numbers to hundredths, and justify using concrete and visual models.
4.ATO.1	Interpret a multiplication equation as a comparison (e.g. interpret 35 = 5x7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.) Represent verbal statements of multiplicative comparisons as multiplication equations.
4.ATO.2	Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups unknown).
4.ATO.3	Solve multi-step, real-world problems using the four operations. Represent the problem using an equation with a variable as the unknown quantity.
4.ATO.4	Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range 1 – 100 and determine whether the whole number is prime or composite.
4.ATO.5	Generate a number or shape pattern that follows a given rule and determine a term that appears later in the sequence.
4.G.1	Draw points, lines, line segments, rays, angles (i.e., right, acute, obtuse), and parallel and perpendicular lines. Identify these in two-dimensional figures.
4.G.2	Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines.
4.G.3	Recognize right triangles as a category, and identify right triangles.
4.G.4	Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
4.MDA.1	Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit.
4.MDA.2	Solve real-world problems involving distance/length, intervals of time within 12 hours, liquid volume, mass, and money using the four operations.
4.MDA.3	Apply the area and perimeter formulas for rectangles.
4.MDA.4	Create a line plot to display a data set (i.e., generated by measuring length to the nearest quarter-inch and eighth-inch) and interpret the line plot.
4.MDA.5	Understand the relationship of an angle measurement to a circle.
4.MDA.6	Measure and draw angles in whole number degrees using a protractor.
4.MDA.7	Solve addition and subtraction problems to find unknown angles in real-world and mathematical problems.
4.MDA.8	Determine the value of a collection of coins and bills greater than $1.00.

Grade 5

Standard	Description
5.NSBT.1	Understand that, in a multi-digit whole number, a digit in one place represents 10 times what the same digit represents in the place to its right, and represents 1 times what the 10 same digit represents in the place to its left.
5.NSBT.2	Use whole number exponents to explain: a. patterns in the number of zeroes of the product when multiplying a number by powers of 10; b. patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
5.NSBT.3	Read and write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or <.
5.NSBT.4	Round decimals to any given place value within thousandths.
5.NSBT.5	Fluently multiply multi-digit whole numbers using strategies to include a standard algorithm.
5.NSBT.6	Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division.
5.NSBT.7	Add, subtract, multiply, and divide decimal numbers to hundredths using concrete area models and drawings.
5.NSF.1	Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area model and number line.
5.NSF.2	Solve real-world problems involving addition and subtraction of fractions with unlike denominators.
5.NSF.3	Understand the relationship between fractions and division of whole numbers by interpreting a fraction as the numerator divided by the denominator (i.e., a/b = 𝑎 ÷ 𝑏).
5.NSF.4	Extend the concept of multiplication to multiply a fraction or whole number by a fraction. a. Recognize the relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths; b. Interpret multiplication of a fraction by a whole number and a whole number by a fraction and compute the product; c. Interpret multiplication in which both factors are fractions less than one and compute the product.
5.NSF.5	Justify the reasonableness of a product when multiplying with fractions. a. Estimate the size of the product based on the size of the two factors; b. Explain why multiplying a given number by a number greater than 1 (e.g., improper fractions, mixed numbers, whole numbers) results in a product larger than the given number; c. Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; d. Explain why multiplying the numerator and denominator by the same number has the same effect as multiplying the fraction by 1.
5.NSF.6	Solve real-world problems involving multiplication of a fraction by a fraction, improper fraction and a mixed number.
5.NSF.7	Extend the concept of division to divide unit fractions and whole numbers by using visual fraction models and equations. a. Interpret division of a unit fraction by a non-zero whole number and compute the quotient; b. Interpret division of a whole number by a unit fraction and compute the quotient.
5.NSF.8	Solve real-world problems involving division of unit fractions and whole numbers, using visual fraction models and equations.
5.ATO.1	Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces).
5.ATO.2	Translate verbal phrases into numerical expressions and interpret numerical expressions as verbal phrases.
5.ATO.3	Investigate the relationship between two numerical patterns. a. Generate two numerical patterns given two rules and organize in tables; b. Translate the two numerical patterns into two sets of ordered pairs; c. Graph the two sets of ordered pairs on the same coordinate plane; d. Identify the relationship between the two numerical patterns.
5.G.1	Define a coordinate system. a. The x- and y- axes are perpendicular number lines that intersect at 0 (the origin); b. Any point on the coordinate plane can be represented by its coordinates; c. The first number in an ordered pair is the x-coordinate and represents the horizontal distance from the origin; d. The second number in an ordered pair is the y-coordinate and represents the vertical distance from the origin.
5.G.2	Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical situations.
5.G.3	Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
5.G.4	Classify two-dimensional figures in a hierarchy based on their attributes.
5.MDA.1	Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric (i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit.
5.MDA.2	Create a line plot consisting of unit fractions and use operations on fractions to solve problems related to the line plot.
5.MDA.3	Understand the concept of volume measurement. a. Recognize volume as an attribute of right rectangular prisms; b. Relate volume measurement to the operations of multiplication and addition by packing right rectangular prisms and then counting the layers of standard unit cubes; c. Determine the volume of right rectangular prisms using the formula derived from packing right rectangular prisms and counting the layers of standard unit cubes
5.MDA.4	Differentiate among perimeter, area and volume and identify which application is appropriate for a given situation.

Grade 6

Standard	Description
6.NS.1	Compute and represent quotients of positive fractions using a variety of procedures (e.g., visual models, equations, and real-world situations).
6.NS.2	Fluently divide multi-digit whole numbers using a standard algorithmic approach.
6.NS.3	Fluently add, subtract, multiply and divide multi-digit decimal numbers using a standard algorithmic approach.
6.NS.4	Find common factors and multiples using two whole numbers. a. Compute the greatest common factor (GCF) of two numbers both less than or equal to 100. b. Compute the least common multiple (LCM) of two numbers both less than or equal to 12. c. Express sums of two whole numbers, each less than or equal to 100, using the distributive property to factor out a common factor of the original addends.
6.NS.5	Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation.
6.NS.6	Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane. a. Understand the concept of opposite numbers, including zero, and their relative locations on the number line. b. Understand that the signs of the coordinates in ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane. c. Recognize when ordered pairs are reflections of each other on the coordinate plane across one axis, both axes, or the origin. d. Plot rational numbers on number lines and ordered pairs on coordinate planes.
6.NS.7	Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers. a. Interpret statements using equal to (=) and not equal to (≠). b. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. c. Use concepts of equality and inequality to write and to explain real-world and mathematical situations. d. Understand that absolute value represents a number’s distance from zero on the number line and use the absolute value of a rational number to represent real- world situations. e. Recognize the difference between comparing absolute values and ordering rational numbers. For negative rational numbers, understand that as the absolute value increases, the value of the negative number decreases.
6.NS.8	Extend knowledge of the coordinate plane to solve real-world and mathematical problems involving rational numbers. a. Plot points in all four quadrants to represent the problem. b. Find the distance between two points when ordered pairs have the same x- coordinates or same y-coordinates. c. Relate finding the distance between two points in a coordinate plane to absolute value using a number line.
6.NS.9	Investigate and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100.
6.RP.1	Interpret the concept of a ratio as the relationship between two quantities, including part to part and part to whole.
6.RP.2	Investigate relationships between ratios and rates. a. Translate between multiple representations of ratios (i.e., a/b, 𝑎: 𝑏, 𝑎 to 𝑏, visual models). b. Recognize that a rate is a type of ratio involving two different units. Convert from rates to unit rates.
6.RP.3	Apply the concepts of ratios and rates to solve real-world and mathematical problems. a. Create a table consisting of equivalent ratios and plot the results on the coordinate plane. b. Use multiple representations, including tape diagrams, tables, double number lines, and equations, to find missing values of equivalent ratios. c. Use two tables to compare related ratios. d. Apply concepts of unit rate to solve problems, including unit pricing and constant speed. e. Understand that a percentage is a rate per 100 and use this to solve problems involving wholes, parts, and percentages. f. Solve one-step problems involving ratios and unit rates (e.g., dimensional analysis).
6.EEI.1	Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the Order of Operations.
6.EEI.2	Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers. a. Translate between algebraic expressions and verbal phrases that include variables. b. Investigate and identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and factor. c. Evaluate real-world and algebraic expressions for specific values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to whole-numbers.
6.EEI.3	Apply mathematical properties (e.g., commutative, associative, distributive) to generate equivalent expressions.
6.EEI.4	Apply mathematical properties (e.g., commutative, associative, distributive) to justify that two expressions are equivalent.
6.EEI.5	Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.
6.EEI.6	Write expressions using variables to represent quantities in real-world and mathematical situations. Understand the meaning of the variable in the context of the situation.
6.EEI.7	Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and mathematical situations.
6.EEI.8	Extend knowledge of inequalities used to compare numerical expressions to include algebraic expressions in real-world and mathematical situations. a. Write an inequality of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 and graph the solution set on a number line. b. Recognize that inequalities have infinitely many solutions.
6.EEI.9	Investigate multiple representations of relationships in real-world and mathematical situations. a. Write an equation that models a relationship between independent and dependent variables. b. Analyze the relationship between independent and dependent variables using graphs and tables. c. Translate among graphs, tables, and equations.
6.GM.1	Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6.GM.2	Use visual models (e.g., model by packing) to discover that the formulas for the volume of a right rectangular prism (𝑉 = 𝑙𝑤ℎ, 𝑉 = 𝐵ℎ) are the same for whole or fractional edge lengths. Apply these formulas to solve real-world and mathematical problems.
6.GM.3	Apply the concepts of polygons and the coordinate plane to real-world and mathematical situations. a. Given coordinates of the vertices, draw a polygon in the coordinate plane. b. Find the length of an edge if the vertices have the same x-coordinates or same y- coordinates.
6.GM.4	Unfold three-dimensional figures into two-dimensional rectangles and triangles (nets) to find the surface area and to solve real-world and mathematical problems.
6.DS.1	Differentiate between statistical and non-statistical questions.
6.DS.2	Use center (mean, median, mode), spread (range, interquartile range, mean absolute value), and shape (symmetrical, skewed left, skewed right) to describe the distribution of a set of data collected to answer a statistical question.
6.DS.3	Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.DS.4	Select and create an appropriate display for numerical data, including dot plots, histograms, and box plots.
6.DS.5	Describe numerical data sets in relation to their real-world context. a. State the sample size. b. Describe the qualitative aspects of the data (e.g., how it was measured, units of measurement). c. Give measures of center (median, mean). d. Find measures of variability (interquartile range, mean absolute deviation) using a number line. e. Describe the overall pattern (shape) of the distribution. f.� Justify the choices for measure of center and measure of variability based on the shape of the distribution. g. Describe the impact that inserting or deleting a data point has on the measures of center (median, mean) for a data set.

Grade 7

Standard	Description
7.NS.1	Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line. a. Understand that the additive inverse of a number is its opposite and their sum is equal to zero. b. Understand that the sum of two rational numbers (𝑝 + 𝑞) represents a distance from p on the number line equal to \|q\| where the direction is indicated by the sign of q. c. Translate between the subtraction of rational numbers and addition using the additive inverse, 𝑝 − 𝑞 = 𝑝 + (−𝑞). d. Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference. Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers.
7.NS.2	Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. a. Understand that the multiplicative inverse of a number is its reciprocal and their product is equal to one. b. Understand sign rules for multiplying rational numbers. c. Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number. d. Apply mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide rational numbers. e. Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or decimal numbers that terminate or repeat.
7.NS.3	Apply the concepts of all four operations with rational numbers to solve real-world and mathematical problems.
7.NS.4	Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations. a. Write and fluently solve linear equations of the form ____ + __ = __ and __(__ + __) = __ where __, __, and __ are rational numbers. b. Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides. c. Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning. d. Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.
7.NS.5	Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions.
7.RP.1	Compute unit rates, including those involving complex fractions, with like or different units.
7.RP.2	Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams, verbal descriptions, and real-world situations. a. Determine when two quantities are in a proportional relationship. b. Recognize or compute the constant of proportionality. c. Understand that the constant of proportionality is the unit rate. d. Use equations to model proportional relationships. e. Investigate the graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation.
7.RP.3	Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis, percent increase/decrease, tax).
7.EEI.1	Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic expressions with rational coefficients.
7.EEI.2	Recognize that algebraic expressions may have a variety of equivalent forms and determine an appropriate form for a given real-world situation.
7.EEI.3	Extend previous understanding of Order of Operations to solve multi-step real-world and mathematical problems involving rational numbers. Include fraction bars as a grouping symbol.
7.EEI.4	Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations. a. Write and fluently solve linear equations of the form 𝑎𝑥 + 𝑏 = 𝑐 and 𝑎(𝑥 + 𝑏) = 𝑐 where 𝑎, 𝑏, and 𝑐 are rational numbers. b. Write and solve multi-step linear equations that include the use of the distributive property and combining like terms. Exclude equations that contain variables on both sides. c. Write and solve two-step linear inequalities. Graph the solution set on a number line and interpret its meaning. Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.
7.EEI.5	Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property) to simplify numerical expressions that include whole-number exponents.
7.GM.1	Determine the scale factor and translate between scale models and actual measurements (e.g., lengths, area) of real-world objects and geometric figures using proportional reasoning.
7.GM.2	Construct triangles and special quadrilaterals using a variety of tools (e.g., freehand, ruler and protractor, technology). a. Construct triangles given all measurements of either angles or sides. b. Decide if the measurements determine a unique triangle, more than one triangle, or no triangle. c. Construct special quadrilaterals (i.e., kite, trapezoid, isosceles trapezoid, rhombus, parallelogram, rectangle) given specific parameters about angles or sides.
7.GM.3	Describe two-dimensional cross-sections of three-dimensional figures, specifically right rectangular prisms and right rectangular pyramids.
7.GM.4	Investigate the concept of circles. a. Demonstrate an understanding of the proportional relationships between diameter, radius, and circumference of a circle. b. Understand that the constant of proportionality between the circumference and diameter is equivalent to p. c. Explore the relationship between circumference and area using a visual model. d. Use the formulas for circumference and area of circles appropriately to solve real-world and mathematical problems.
7.GM.5	Write equations to solve problems involving the relationships between angles formed by two intersecting lines, including supplementary, complementary, vertical, and adjacent.
7.GM.6	Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations. a. Understand that the concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons. b. Understand that the concepts of volume and surface area are applied to three- dimensional figures such as cubes, right rectangular prisms, and right triangular prisms. c. Decompose cubes, right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area. d. Use the formulas for area, volume, and surface area appropriately.
7.DSP.1	Investigate concepts of random sampling. a. Understand that a sample is a subset of a population and both possess the same characteristics. b. Differentiate between random and non-random sampling. c. Understand that generalizations from a sample are valid only if the sample is representative of the population. d. Understand that random sampling is used to gather a representative sample and supports valid inferences about the population.
7.DSP.2	Draw inferences about a population by collecting multiple random samples of the same size to investigate variability in estimates of the characteristic of interest.
7.DSP.3	Visually compare the centers, spreads, and overlap of two displays of data (i.e., dot plots, histograms, box plots) that are graphed on the same scale and draw inferences about this data.
7.DSP.4	Compare the numerical measures of center (mean, median, mode) and variability (range, interquartile range, mean absolute deviation) from two random samples to draw inferences about the populations.
7.DSP.5	Investigate the concept of probability of chance events. a. Determine probabilities of simple events. b. Understand that probability measures likelihood of a chance event occurring. c. Understand that the probability of a chance event is a number between 0 and 1. d. Understand that a probability closer to 1 indicates a likely chance event. e. Understand that a probability close to 1 indicates that a chance event is neither likely nor unlikely. f. Understand that a probability closer to 0 indicates an unlikely chance event.
7.DSP.6	Investigate the relationship between theoretical and experimental probabilities for simple events. a. Determine approximate outcomes using theoretical probability. b. Perform experiments that model theoretical probability. c. Compare theoretical and experimental probabilities.
7.DSP.7	Apply the concepts of theoretical and experimental probabilities for simple events. a. Differentiate between uniform and non-uniform probability models (distributions). b. Develop both uniform and non-uniform probability models. c. Perform experiments to test the validity of probability models.
7.DSP.8	Extend the concepts of simple events to investigate compound events. a. Understand that the probability of a compound event is between 0 and 1. b. Identify the outcomes in a sample space using organized lists, tables, and tree diagrams. c. Determine probabilities of compound events using organized lists, tables, and tree diagrams. d. Design and use simulations to collect data and determine probabilities. e. Compare theoretical and experimental probabilities for compound events.

Grade 8

Standard	Description
8.NS.1	Explore the real number system and its appropriate usage in real-world situations. a. Recognize the differences between rational and irrational numbers. b. Understand that all real numbers have a decimal expansion. c. Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.
8.NS.2	Estimate and compare the value of irrational numbers by plotting them on a number line.
8.NS.3	Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.
8.F.1	Explore the concept of functions. a. Understand that a function assigns to each input exactly one output. b. Relate inputs (𝑥-values or domain) and outputs (𝑦-values or range) to independent and dependent variables. c. Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions. d. Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions. e. Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.
8.F.2	Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.
8.F.3	Investigate the differences between linear and nonlinear functions using multiple representations (i.e., tables, graphs, equations, and verbal descriptions). a. Define an equation in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) as being a linear function. b. Recognize that the graph of a linear function has a constant rate of change. c. Provide examples of nonlinear functions.
8.F.4	Apply the concepts of linear functions to real-world and mathematical situations. a. Understand that the slope is the constant rate of change and the 𝑦-intercept is the point where 𝑥 = 0. b. Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions. c. Construct a function in slope-intercept form that models a linear relationship between two quantities. d. Interpret the meaning of the slope and the 𝑦-intercept of a linear function in the context of the situation. e. Explore the relationship between linear functions and arithmetic sequences.
8.F.5	Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations. a. Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous). b. Sketch the graph of a function from a verbal description. c. Write a verbal description from the graph of a function with and without scales.
8.EEI.1	Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents.
8.EEI.2	Explore the relationship between quantities in decimal and scientific notation. a. Express very large and very small quantities in scientific notation in the form 𝑎 × 10^𝑏 = 𝑝 where 1 ≤ 𝑎 < 10 and 𝑏 is an integer. b. Translate between decimal notation and scientific notation. c. Estimate and compare the relative size of two quantities in scientific notation
8.EEI.3	Explore the relationship between quantities in decimal and scientific notation. a. Express very large and very small quantities in scientific notation in the form __ _ 10^__ = __ where 1 ≤ __ < 10 and __ is an integer. b. Translate between decimal notation and scientific notation. c. Estimate and compare the relative size of two quantities in scientific notation.
8.EEI.4	Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems. a. Multiply and divide numbers expressed in both decimal and scientific notation. b. Select appropriate units of measure when representing answers in scientific notation. c. Translate how different technological devices display numbers in scientific notation.
8.EEI.5	Apply concepts of proportional relationships to real-world and mathematical situations. a. Graph proportional relationships. b. Interpret unit rate as the slope of the graph. c. Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.
8.EEI.6	Apply concepts of slope and 𝑦-intercept to graphs, equations, and proportional relationships. a. Explain why the slope, 𝑚, is the same between any two distinct points on a non- vertical line using similar triangles. b. Derive the slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) for a non-vertical line. c. Relate equations for proportional relationships (𝑦 = 𝑘𝑥) with the slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) where 𝑏 = 0.
8.EEI.7	Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. a. Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides. b. Recognize the three types of solutions to linear equations: one solution (𝑥 = 𝑎), infinitely many solutions (𝑎 = 𝑎), or no solutions (𝑎 = 𝑏). c. Generate linear equations with the three types of solutions. d. Justify why linear equations have a specific type of solution.
8.EEI.8	Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions. a. Graph systems of linear equations and estimate their point of intersection. b. Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines. c. Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection. d. Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.
8.GM.1	Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology). a. Verify that lines are mapped to lines, including parallel lines. b. Verify that corresponding angles are congruent. c. Verify that corresponding line segments are congruent.
8.GM.2	Apply the properties of rigid transformations (rotations, reflections, translations). a. Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin. b. Reflect geometric figures with respect to the 𝑥-axis and/or 𝑦-axis. c. Translate geometric figures vertically and/or horizontally. d. Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image. e. Given two congruent figures, describe the series of rigid transformations that justifies this congruence.
8.GM.3	Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software). a. Use coordinate geometry to describe the effect of transformations on two- dimensional figures. b. Relate scale drawings to dilations of geometric figures.
8.GM.4	Apply the properties of transformations (rotations, reflections, translations, dilations). a. Dilate geometric figures using scale factors that are positive rational numbers. b. Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image. c. Given two similar figures, describe the series of transformations that justifies this similarity. d. Use proportional reasoning to find the missing side lengths of two similar figures.
8.GM.5	Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal. a. Discover that the sum of the three angles in a triangle is 180 degrees. b. Discover and use the relationship between interior and exterior angles of a triangle. c. Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal. d. Recognize that two similar figures have congruent corresponding angles.
8.GM.6	Use models to demonstrate a proof of the Pythagorean Theorem and its converse.
8.GM.7	Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.
8.GM.8	Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.
8.GM.9	Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.
8.DSP.1	Investigate bivariate data. a. Collect bivariate data. b. Graph the bivariate data on a scatter plot. c. Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).
8.DSP.2	Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points.
8.DSP.3	Apply concepts of an approximate line of best fit in real-world situations. a. Find an approximate equation for the line of best fit using two appropriate data points. b. Interpret the slope and intercept. c. Solve problems using the equation.
8.DSP.4	Investigate bivariate categorical data in two-way tables. a. Organize bivariate categorical data in a two-way table. b. Interpret data in two-way tables using relative frequencies. c. Explore patterns of possible association between the two categorical variables.
8.DSP.5	Organize data in matrices with rational numbers and apply to real-world and mathematical situations. a. Understand that a matrix is a way to organize data. b. Recognize that a 𝑚 × 𝑛 matrix has 𝑚 rows and 𝑛 columns. c. Add and subtract matrices of the same size. d. Multiply a matrix by a scalar.

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