This alignment shows the Media4Math resources that support the standards shown below. Click on a grade to see the Georgia 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

NUMERICAL REASONING-- counting, money, place value, numbers to 20, addition, subtraction and fluency
GA.K.NR.1	Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the last number counted represents the total quantity in a set).
GA.K.NR.1.1	Count up to 20 objects in a variety of structured arrangements and up to 10 objects in a scattered arrangement.
GA.K.NR.1.2	When counting objects, explain that the last number counted represents the total quantity in a set (cardinality), regardless of the arrangement and order.
GA.K.NR.1.3	Given a number from 1-20, identify the number that is one more or one less.
GA.K.NR.1.4	Identify pennies, nickels, and dimes and know their name and value.
GA.K.NR.2	Use count sequences within 100 to count forward and backward in sequence.
GA.K.NR.2.1	Count forward to 100 by tens and ones and backward from 20 by ones.
GA.K.NR.2.2	Count forward beginning from any number within 100 and count backward from any number within 20.
GA.K.NR.3	Use place value understanding to compose and decompose numbers from 11–19.
GA.K.NR.3.1	Describe numbers from 11 to 19 by composing (putting together) and decomposing (breaking apart) the numbers into ten ones and some more ones.
GA.K.NR.4	Identify, write, represent, and compare numbers up to 20.
GA.K.NR.4.1	Identify written numerals 0- 20 and represent a number of objects with a written numeral 0-20 (with 0 representing a count of no
GA.K.NR.4.2	Compare two sets of up to 10 objects and identify whether the number of objects in one group is more or less than the other group, using the words “greater than,” “less than,” or “the same as”.
GA.K.NR.5	Explain the concepts of addition, subtraction, and equality and use these concepts to solve real-life problems within 10.
GA.K.NR.5.1	Compose (put together) and decompose (break apart) numbers up to 10 using objects and drawings.
GA.K.NR.5.2	Represent addition and subtraction within 10 from a given authentic situation using a variety of representations and strategies.
GA.K.NR.5.3	Use a variety of strategies to solve addition and subtraction problems within 10.
GA.K.NR.5.4	Fluently add and subtract within 5 using a variety of strategies to solve practical, mathematical problems.
PATTERNING & ALGEBRAIC REASONING -- repeating patterns and time
GA.K.PAR.6.1	Create, extend, and describe repeating patterns with numbers and shapes, and explain the rationale for the pattern.
GA.K.PAR.6.2	Describe patterns involving the passage of time using words and phrases related to actual events.
MEASUREMENT & DATA REASONING --attributes of objects, classifying objects
GA.K.MDR.7	Observe, describe, and compare the physical and measurable attributes of objects and analyze graphical displays of data.
GA.K.MDR.7.1	Directly compare, describe, and order common objects, using measurable attributes (length, height, width, or weight) and describe the difference.
GA.K.MDR.7.2	Classify and sort up to ten objects into categories by an attribute; count the number of objects in each category and sort the categories by count.
GA.K.MDR.7.3	Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
GEOMETRIC & SPATIAL REASONING -- 2D and 3D shapes, relative locations, attributes
GA.K.GSR.8	Identify, describe, and compare basic shapes encountered in the environment, and form two-dimensional shapes and three-dimensional figures.
GA.K.GSR.8.1	Identify, sort, classify, analyze, and compare two- dimensional shapes and three-dimensional figures, in different sizes and orientations, using informal language to describe their similarities, differences, number of sides and vertices, and other attributes.
GA.K.GSR.8.2	Describe the relative location of an object using positional words.
GA.K.GSR.8.3	Use basic shapes to represent specific shapes found in the environment by creating models and drawings.
GA.K.GSR.8.4	Use two or more basic shapes to form larger shapes.

Grade 1

NUMERICAL REASONING -- counting, numbers, equality, place value, addition, subtraction
GA.1.NR.1	Extend the count sequence to 120. Read, write, and represent numerical values to 120 and compare numerical values to 100.
GA.1.NR.1.1	Count within 120, forward and backward, starting at any number. In this range, read and write numerals and represent a number of objects with a written numeral.
GA.1.NR.1.2	Explain that the two digits of a 2-digit number represent the amounts of tens and ones.
GA.1.NR.1.3	Compare and order whole numbers up to 100 using concrete models, drawings, and the symbols >, =, and <.
GA.1.NR.2	Explain the relationship between addition and subtraction and apply the properties of operations to solve real-life addition and subtraction problems within 20.
GA.1.NR.2.1	Use a variety of strategies to solve addition and subtraction problems within 20.
GA.1.NR.2.2	Use pictures, drawings, and equations to develop strategies for addition and subtraction within 20 by exploring strings of related problems.
GA.1.NR.2.3	Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve authentic problems.
GA.1.NR.2.4	Fluently add and subtract within 10 using a variety of strategies.
GA.1.NR.2.5	Use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false.
GA.1.NR.2.6	Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers.
GA.1.NR.2.7	Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.
PATTERNING & ALGEBRAIC REASONING -- repeating patterns, growing, patterns, and shrinking patterns
GA.1.PAR.3	Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns found in real-life situations.
GA.1.PAR.3.1	Investigate, create, and make predictions about repeating patterns with a core of up to 3 elements resulting from repeating an operation, as a series of shapes, or a number string.
GA.1.PAR.3.2	Identify, describe, and create growing, shrinking, and repeating patterns based on the repeated addition or subtraction of 1s, 2s, 5s, and 10s.
GEOMETRIC & SPATIAL REASONING -- shapes, attributes, partitions of circles and rectangles
GA.1.GSR.4	Compose shapes, analyze the attributes of shapes, and relate their parts to the whole.
GA.1.GSR.4.1	Identify common two- dimensional shapes and three- dimensional figures, sort and classify them by their attributes and build and draw shapes that possess defining attributes.
GA.1.GSR.4.2	Compose two-dimensional shapes (rectangles, squares, triangles, half-circles, and quarter-circles) and three- dimensional figures (cubes, rectangular prisms, cones, and cylinders) to create a shape formed of two or more common shapes and compose new shapes from the composite shape.
GA.1.GSR.4.3	Partition circles and rectangles into two and four equal shares.
NUMERICAL REASONING -- base ten structure, addition and subtraction within 100
GA.1.NR.5	Use concrete models, the base ten structure, and properties of operations to add and subtract within 100.
GA.1.NR.5.1	Use a variety of strategies to solve applicable, mathematical addition and subtraction problems with one- and two-digit whole numbers.
GA.1.NR.5.2	Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
GA.1.NR.5.3	Add and subtract multiples of 10 within 100.
MEASUREMENT & DATA REASONING -- length, time, money
GA.1.MDR.6	Use appropriate tools to measure, order, and compare intervals of length and time, as well as denominations of money to solve real-life, mathematical problems and answer relevant questions.
GA.1.MDR.6.1	Estimate, measure, and record lengths of objects using non-standard units, and compare and order up to three objects using the recorded measurements. Describe the objects compared.
GA.1.MDR.6.2	Tell and write time in hours and half-hours using analog and digital clocks, and measure elapsed time to the hour on the hour using a predetermined number line.
GA.1.MDR.6.3	Identify the value of quarters and compare the values of pennies, nickels, dimes, and quarters.
GA.1.MDR.6.4	Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to compare and order whole numbers.

Grade 2

NUMERICAL REASONING -- counting within 1000, place value, addition and subtraction, fluency to 20, developing multiplication through arrays
GA.2.NR.1	Using the place value structure, explore the count sequences to represent, read, write, and compare numerical values to 1000 and describe basic place-value relationships and structures.
GA.2.NR.1.1	Explain the value of a three- digit number using hundreds, tens, and ones in a variety of ways.
GA.2.NR.1.2	Count forward and backward by ones from any number within 1000. Count forward by fives from multiples of 5 within 1000. Count forward and backward by 10s and 100s from any number within 1000. Count forward by 25s from 0.
GA.2.NR.1.3	Represent, compare, and order whole numbers to 1000 with an emphasis on place value and equality. Use >, =, and < symbols to record the results of comparisons.
GA.2.NR.2	Apply multiple part-whole strategies, properties of operations and place value understanding to solve real-life, mathematical problems involving addition and subtraction within 1,000.
GA.2.NR.2.1	Fluently add and subtract within 20 using a variety of mental, part-whole strategies.
GA.2.NR.2.2	Find 10 more or 10 less than a given three-digit number and find 100 more or 100 less than a given three-digit number.
GA.2.NR.2.3	Solve problems involving the addition and subtraction of two-digit numbers using part- whole strategies.
GA.2.NR.2.4	Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
GA.2.NR.3	Work with equal groups to gain foundations for multiplication through real-life, mathematical problems.
GA.2.NR.3.1	Determine whether a group (up to 20) has an odd or even number of objects. Write an equation to express an even number as a sum of two equal addends.
GA.2.NR.3.2	Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
PATTERNING & ALGEBRAIC REASONING -- patterns up to 20 and addition and subtraction within 1,000
GA.2.PAR.4	Identify, describe, extend, and create repeating patterns, growing patterns, and shrinking patterns.
GA.2.PAR.4.1	Identify, describe, and create a numerical pattern resulting from repeating an operation such as addition and subtraction.
GA.2.PAR.4.2	Identify, describe, and create growing patterns and shrinking patterns involving addition and subtraction up to 20.
MEASUREMENT & DATA REASONING -- length, distance, time, and money
GA.2.MDR.5	Estimate and measure the lengths of objects and distance to solve problems found in real-life using standard units of measurement, including inches, feet, and yards.
GA.2.MDR.5.1	Construct simple measuring instruments using unit models. Compare unit models to rulers.
GA.2.MDR.5.2	Estimate and measure the length of an object or distance to the nearest whole unit using appropriate units and standard measuring tools.
GA.2.MDR.5.3	Measure to determine how much longer one object is than another and express the length difference in terms of a standard-length unit.
GA.2.MDR.5.4	Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
GA.2.MDR.5.5	Represent whole-number sums and differences within a standard unit of measurement on a number line diagram.
GA.2.MDR.6	Solve real-life problems involving time and money.
GA.2.MDR.6.1	Tell and write time from analog and digital clocks to the nearest five minutes, and estimate and measure elapsed time using a timeline, to the hour or half hour on the hour or half hour.
GA.2.MDR.6.2	Find the value of a group of coins and determine combinations of coins that equal a given amount that is less than one hundred cents, and solve problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.
GEOMETRIC & SPATIAL REASONING -- sorting shapes, lines of symmetry, partitioning circles and rectangles
GA.2.GSR.7	Draw and partition shapes and other objects with specific attributes and conduct observations of everyday items and structures to identify how shapes exist in the world.
GA.2.GSR.7.1	Describe, compare and sort 2-D shapes including polygons, triangles, quadrilaterals, pentagons, hexagons, and 3-D shapes including rectangular prisms and cones, given a set of attributes.
GA.2.GSR.7.2	Identify at least one line of symmetry in everyday objects to describe each object as a whole.
GA.2.GSR.7.3	Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (“halves,” “thirds,” “fourths”, “half of,” “third of,” “quarter of,” etc.).
GA.2.GSR.7.4	Recognize that equal shares of identical wholes may be different shapes within the same whole.

Grade 3

NUMERICAL REASONING -- base ten numerals and place value up to 10,000, and rounding up to 1,000
GA.3.NR.1	Use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers up to 1,000.
GA.3.NR.1.1	Read and write multi-digit whole numbers up to 10,000 using base-ten numerals and expanded form.
GA.3.NR.1.2	Use place value reasoning to compare multi-digit numbers up to 10,000, using >, =, and < symbols to record the results of comparisons.
GA.3.NR.1.3	Use place value understanding to round whole numbers up to 1000 to the nearest 10 or 100.
PATTERNING & ALGEBRAIC REASONING -- fluency, addition and subtraction within 10,000, multiplication and division within 100, equality, properties of operations
GA.3.PAR.2	Use part-whole strategies to represent and solve real-life problems involving addition and subtraction with whole numbers within 10,000.
GA.3.PAR.2.1	Fluently add and subtract within 1000 to solve problems.
GA.3.PAR.2.2	Apply part-whole strategies, properties of operations and place value understanding, to solve problems involving addition and subtraction within 10,000. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.
GA.3.PAR.3	Use part-whole strategies to solve real-life, mathematical problems involving multiplication and division with whole numbers within 100.
GA.3.PAR.3.1	Describe, extend, and create numeric patterns related to multiplication. Make predictions related to the patterns.
GA.3.PAR.3.2	Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.
GA.3.PAR.3.3	Apply properties of operations (i.e., commutative property, associative property, distributive property) to multiply and divide within 100.
GA.3.PAR.3.4	Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent.
GA.3.PAR.3.5	Use place value reasoning and properties of operations to multiply one-digit whole numbers by multiples of 10, in the range 10-90.
GA.3.PAR.3.6	Solve practical, relevant problems involving multiplication and division within 100 using part-whole strategies, visual representations, and/or concrete models.
GA.3.PAR.3.7	Use multiplication and division to solve problems involving whole numbers to 100. Represent these problems using equations with a letter standing for the unknown quantity. Justify solutions.
NUMERICAL REASONING -- unit fractions, equivalent fractions, fractions greater than 1
GA.3.NR.4	Represent fractions with denominators of 2, 3, 4, 6 and 8 in multiple ways within a framework using visual models.
GA.3.NR.4.1	Describe a unit fraction and explain how multiple copies of a unit fraction form a non-unit fraction. Use parts of a whole, parts of a set, points on a number line, distances on a number line and area models.
GA.3.NR.4.2	Compare two unit fractions by flexibly using a variety of tools and strategies.
GA.3.NR.4.3	Represent fractions, including fractions greater than one, in multiple ways.
GA.3.NR.4.4	Recognize and generate simple equivalent fractions.
MEASUREMENT & DATA REASONING -- elapsed time, liquid volume, mass, lengths in half and fourth of an inch, data
GA.3.MDR.5	Solve real-life, mathematical problems involving length, liquid volume, mass, and time.
GA.3.MDR.5.1	Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
GA.3.MDR.5.2	Tell and write time to the nearest minute and estimate time to the nearest fifteen minutes (quarter hour) from the analysis of an analog clock.
GA.3.MDR.5.3	Solve meaningful problems involving elapsed time, including intervals of time to the hour, half hour, and quarter hour where the times presented are only on the hour, half hour, or quarter hour within a.m. or p.m. only.
GA.3.MDR.5.4	Use rulers to measure lengths in halves and fourths (quarters) of an inch and a whole inch.
GA.3.MDR.5.5	Estimate and measure liquid volumes, lengths and masses of objects using customary units. Solve problems involving mass, length, and volume given in the same unit, and reason about the relative sizes of measurement units within the customary system.
GEOMETRIC & SPATIAL REASONING -- polygons, parallel line segments, perpendicular line segments, right angles, lines of symmetry, area, perimeter
GA.3.GSR.6	Identify the attributes of polygons, including parallel segments, perpendicular segments, right angles, and symmetry.
GA.3.GSR.6.1	Identify perpendicular line segments, parallel line segments, and right angles, identify these in polygons, and solve problems involving parallel line segments, perpendicular line segments, and right angles.
GA.3.GSR.6.2	Classify, compare, and contrast polygons, with a focus on quadrilaterals, based on properties. Analyze specific 3- dimensional figures to identify and describe quadrilaterals as faces of these figures.
GA.3.GSR.6.3	Identify lines of symmetry in polygons.
GA.3.GSR.7	Identify area as a measurable attribute of rectangles and determine the area of a rectangle presented in real-life, mathematical problems.
GA.3.GSR.7.1	Investigate area by covering the space of rectangles presented in realistic situations using multiple copies of the same unit, with no gaps or overlaps, and determine the total area (total number of units that covered the space).
GA.3.GSR.7.2	Determine the area of rectangles (or shapes composed of rectangles) presented in relevant problems by tiling and counting.
GA.3.GSR.7.3	Discover and explain how area can be found by multiplying the dimensions of a rectangle.
GA.3.GSR.8	Determine the perimeter of a polygon presented in real-life, mathematical problems.
GA.3.GSR.8.1	Determine the perimeter of a polygon and explain that the perimeter represents the distance around a polygon. Solve problems involving perimeters of polygons.
GA.3.GSR.8.2	Investigate and describe how rectangles with the same perimeter can have different areas or how rectangles with the same area can have different perimeters.

Grade 4

NUMERICAL REASONING -- place value, rounding, comparisons with multi-digit numbers, addition and subtraction, multiplicative comparisons, multiplication, and division involving whole numbers
GA.4.NR.1	Recognize patterns within the base ten place value system with quantities presented in real-life situations to compare and round multi-digit whole numbers through the hundred-thousands place.
GA.4.NR.1.1	Read and write multi-digit whole numbers to the hundred-thousands place using base-ten numerals and expanded form.
GA.4.NR.1.2	Recognize and show that a digit in one place has a value ten times greater than what it represents in the place to its right and extend this understanding to determine the value of a digit when it is shifted to the left or right, based on the relationship between multiplication and division.
GA.4.NR.1.3	Use place value reasoning to represent, compare, and order multi-digit numbers, using >, =, and < symbols to record the results of comparisons.
GA.4.NR.1.4	Use place value understanding to round multi-digit whole numbers.
GA.4.NR.2	Using part-whole strategies, solve problems involving addition and subtraction through the hundred-thousands place, as well as multiplication and division of multi-digit whole numbers presented in real-life, mathematical situations.
GA.4.NR.2.1	Fluently add and subtract multi-digit numbers to solve practical, mathematical problems using place value understanding, properties of operations, and relationships between operations.
GA.4.NR.2.2	Interpret, model, and solve problems involving multiplicative comparison.
GA.4.NR.2.3	Solve relevant problems involving multiplication of a number with up to four digits by a 1-digit whole number or involving multiplication of two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
GA.4.NR.2.4	Solve authentic division problems involving up to 4-digit dividends and 1- digit divisors (including whole number quotients with remainders) using strategies based on place-value understanding, properties of operations, and the relationships between operations.
GA.4.NR.2.5	Solve multi-step problems using addition, subtraction, multiplication, and division involving whole numbers. Use mental computation and estimation strategies to justify the reasonableness of solutions.
PATTERNING & ALGEBRAIC REASONING -- patterns, input-output tables, factors, multiples, composite numbers, prime numbers
GA.4.PAR.3	Generate and analyze patterns, including those involving shapes, input/output diagrams, factors, multiples, prime numbers, and composite numbers.
GA.4.PAR.3.1	Generate both number and shape patterns that follow a provided rule.
GA.4.PAR.3.2	Use input-output rules, tables, and charts to represent and describe patterns, find relationships, and solve problems.
GA.4.PAR.3.3	Find factor pairs in the range 1�100 and find multiples of single-digit numbers up to 100.
GA.4.PAR.3.4	Identify composite numbers and prime numbers and explain the relationship with the factor pairs.
NUMERICAL REASONING -- fraction equivalence, comparison of fractions, and addition and subtraction of fractions with like denominators
GA.4.NR.4	Solve real-life problems involving addition, subtraction, equivalence, and comparison of fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100 using part-whole strategies and visual models.
GA.4.NR.4.1	Using concrete materials, drawings, and number lines, demonstrate and explain the relationship between equivalent fractions, including fractions greater than one, and explain the identity property of multiplication as it relates to equivalent fractions. Generate equivalent fractions using these relationships.
GA.4.NR.4.2	Compare two fractions with the same numerator or the same denominator by reasoning about their size and recognize that comparisons are valid only when the two fractions refer to the same whole.
GA.4.NR.4.3	Compare two fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies and recognize that comparisons are valid only when the two fractions refer to the same whole.
GA.4.NR.4.4	Represent whole numbers and fractions as the sum of unit fractions.
GA.4.NR.4.5	Represent a fraction as a sum of fractions with the same denominator in more than one way, recording with an equation.
GA.4.NR.4.6	Add and subtract fractions and mixed numbers with like denominators using a variety of tools.
GA.4.NR.5	Solve real-life problems involving addition, equivalence, comparison of fractions with denominators of 10 and 100, and comparison of decimal numbers as tenths and hundredths using part-whole strategies and visual models.
GA.4.NR.5.1	Demonstrate and explain the concept of equivalent fractions with denominators of 10 and 100, using concrete materials and visual models. Add two fractions with denominators of 10 and 100.
GA.4.NR.5.2	Represent, read, and write fractions with denominators of 10 or 100 using decimal notation, and decimal numbers to the hundredths place as fractions, using concrete materials and drawings.
GA.4.NR.5.3	Compare two decimal numbers to the hundredths place by reasoning about their size. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
MEASUREMENT & DATA REASONING -- time, metric measurements, distance, elapsed time, liquid volume, mass, and length
GA.4.MDR.6	Measure time and objects that exist in the world to solve real-life, mathematical problems and analyze graphical displays of data to answer relevant questions.
GA.4.MDR.6.1	Use the four operations to solve problems involving elapsed time to the nearest minute, intervals of time, metric measurements of liquid volumes, lengths, distances, and masses of objects, including problems involving fractions with like denominators, and also problems that require expressing measurements given in a larger unit in terms of a smaller unit, and expressing a smaller unit in terms of a larger unit based on the idea of equivalence.
GA.4.MDR.6.2	Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
GA.4.MDR.6.3	Create dot plots to display a distribution of numerical (quantitative) measurement data.
GEOMETRIC & SPATIAL REASONING -- polygons, points, lines, line segments, rays, angles, perpendicular lines, area, perimeter
GA.4.GSR.7	Investigate the concepts of angles and angle measurement to estimate and measure angles.
GA.4.GSR.7.1	Recognize angles as geometric shapes formed when two rays share a common endpoint. Draw right, acute, and obtuse angles based on the relationship of the angle measure to 90 degrees.
GA.4.GSR.7.2	Measure angles in reference to a circle with the center at the common endpoint of two rays. Determine an angle's measure in relation to the 360 degrees in a circle through division or as a missing factor problem.
GA.4.GSR.8	Identify and draw geometric objects, classify polygons based on properties, and solve problems involving area and perimeter of rectangular figures.
GA.4.GSR.8.1	Explore, investigate, and draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular lines, parallel lines, and lines of symmetry. Identify these in two- dimensional figures.
GA.4.GSR.8.2	Classify, compare, and contrast polygons based on lines of symmetry, the presence or absence of parallel or perpendicular line segments, or the presence or absence of angles of a specified size and based on side lengths.
GA.4.GSR.8.3	Solve problems involving area and perimeter of composite rectangles involving whole numbers with known side lengths.

Grade 5

NUMERICAL REASONING -- place value, multiplying by powers of 10, multiplication and division of multi-digit numbers, fractions, decimal numbers, numerical expressions
GA.5.NR.1	Use place value understanding to solve real-life, mathematical problems.
GA.5.NR.1.1	Explain that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
GA.5.NR.1.2	Explain patterns in the placement of digits when multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10, up to 10 to the third powers.
GA.5.NR.2	Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.
GA.5.NR.2.1	Fluently multiply multi-digit (up to 3- digit by 2-digit) whole numbers to solve authentic problems.
GA.5.NR.2.2	Fluently divide multi-digit whole numbers (up to 4-digit dividends and 2-digit divisors no greater than 25) to solve practical problems.
GA.5.NR.3	Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.
GA.5.NR.3.1	Explain the meaning of a fraction as division of the numerator by the denominator ( a/b = a � b). Solve problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
GA.5.NR.3.2	Compare and order up to three fractions with different numerators and/or different denominators by flexibly using a variety of tools and strategies.
GA.5.NR.3.3	Model and solve problems involving addition and subtraction of fractions and mixed numbers with unlike denominators.
GA.5.NR.3.4	Model and solve problems involving multiplication of a fraction and a whole number.
GA.5.NR.3.5	Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.
GA.5.NR.3.6	Model and solve problems involving division of a unit fraction by a whole number and a whole number by a unit fraction.
GA.5.NR.4	Read, write, and compare decimal numbers to the thousandths place, and round and perform operations with decimal numbers to the hundredths place to solve relevant, mathematical problems.
GA.5.NR.4.1	Read and write decimal numbers to the thousandths place using base- ten numerals written in standard form and expanded form.
GA.5.NR.4.2	Represent, compare, and order decimal numbers to the thousandths place based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
GA.5.NR.4.3	Use place value understanding to round decimal numbers to the hundredths place.
GA.5.NR.4.4	Solve problems involving addition and subtraction of decimal numbers to the hundredths place using a variety of strategies.
GA.5.NR.5	Write, interpret, and evaluate numerical expressions within authentic problems.
GA.5.NR.5.1	Write, interpret, and evaluate simple numerical expressions involving whole numbers with or without grouping symbols to represent actual situations.
PATTERNING & ALGEBRAIC REASONING -- generating patterns, plotting ordered pairs in the first quadrant
GA.5.PAR.6	Solve relevant problems by creating and analyzing numerical patterns using the given rule(s).
GA.5.PAR.6.1	Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms by completing a table.
GA.5.PAR.6.2	Represent problems by plotting ordered pairs and explain coordinate values of points in the first quadrant of the coordinate plane.
MEASUREMENT & DATA REASONING -- measurements within the metric system, measurement conversions and time as a unit of measurement
GA.5.MDR.7	Solve problems involving customary measurements, metric measurements, and time and analyze graphical displays of data to answer relevant questions.
GA.5.MDR.7.1	Explore realistic problems involving different units of measurement, including distance, mass, weight, volume, and time.
GA.5.MDR.7.2	Ask questions and answer them based on gathered information, observations, and appropriate graphical displays to solve problems relevant to everyday life.
GA.5.MDR.7.3	Convert among units within the metric system and then apply these conversions to solve multi- step, practical problems.
GA.5.MDR.7.4	Convert among units within relative sizes of measurement units within the customary measurement system.
GEOMETRIC & SPATIAL REASONING -- Properties of polygons and rectangular prisms, classify polygons
GA.5.GSR.8	Examine properties of polygons and rectangular prisms, classify polygons by their properties, and discover volume of right rectangular prisms.
GA.5.GSR.8.1	Classify, compare, and contrast polygons based on properties.
GA.5.GSR.8.2	Determine, through exploration and investigation, that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category.
GA.5.GSR.8.3	Investigate volume of right rectangular prisms by packing them with unit cubes without gaps or overlaps. Then, determine the total volume to solve problems.
GA.5.GSR.8.4	Discover and explain how the volume of a right rectangular prism can be found by multiplying the area of the base times the height to solve authentic, mathematical problems.

Grade 6

NUMERICAL REASONING -- multiplication and division of whole numbers and fractions, and all four operations with decimal numbers
GA.6.NR.1	Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers.
GA.6.NR.1.1	Fluently add and subtract any combination of fractions to solve problems.
GA.6.NR.1.2	Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fractions and solve word problems.
GA.6.NR.1.3	Perform operations with multi-digit decimal numbers fluently using models and student-selected strategies.
GA.6.NR.2	Apply operations with whole numbers, fractions and decimals within relevant applications.
GA.6.NR.2.1	Describe and interpret the center of the distribution by the equal share value (mean).
GA.6.NR.2.2	Summarize categorical and quantitative (numerical) data sets in relation to the context: display the distributions of quantitative (numerical) data in plots on a number line, including dot plots, histograms, and box plots and display the distribution of categorical data using bar graphs.
GA.6.NR.2.3	Interpret numerical data to answer a statistical investigative question created. Describe the distribution of a quantitative (numerical) variable collected, including its center, variability, and overall shape.
GA.6.NR.2.4	Design simple experiments and collect data. Use data gathered from realistic scenarios and simulations to determine quantitative measures of center (median and/or mean) and variability (interquartile range and range). Use these quantities to draw conclusions about the data, compare different numerical data sets, and make predictions.
GA.6.NR.2.5	Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
GA.6.NR.2.6	Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using a dot plot or box plot to examine this impact.
GA.6.NR.3	Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mathematical situations.
GA.6.NR.3.1	Identify and compare integers and explain the meaning of zero based on multiple authentic situations.
GA.6.NR.3.2	Order and plot integers on a number line and use distance from zero to discover the connection between integers and their opposites.
GA.6.NR.3.3	Recognize and explain that opposite signs of integers indicate locations on opposite sides of zero on the number line; recognize and explain that the opposite of the opposite of a number is the number itself.
GA.6.NR.3.4	Write, interpret, and explain statements of order for rational numbers in authentic, mathematical situations. Compare rational numbers, including integers, using equality and inequality symbols.
GA.6.NR.3.5	Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative quantity in a relevant situation.
GA.6.NR.3.6	Distinguish comparisons of absolute value from
GA.6.NR.4	Solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning.
GA.6.NR.4.1	Explain the concept of a ratio, represent ratios, and use ratio language to describe a relationship between two quantities.
GA.6.NR.4.2	Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
GA.6.NR.4.3	Solve problems involving proportions using a variety of student-selected strategies.
GA.6.NR.4.4	Describe the concept of rates and unit rate in the context of a ratio relationship.
GA.6.NR.4.5	Solve unit rate problems including those involving unit pricing and constant speed.
GA.6.NR.4.6	Calculate a percent of a quantity as a rate per 100 and solve everyday problems given a percent.
GA.6.NR.4.7	Use ratios to convert within measurement systems (customary and metric) to solve authentic problems that exist in everyday life.
GEOMETRIC & SPATIAL REASONING -- area of polygons, volume of right rectangular prisms, surface area of 3-D figures
GA.6.GSR.5	Solve relevant problems involving area, surface area, and volume.
GA.6.GSR.5.1	Explore area as a measurable attribute of triangles, quadrilaterals, and other polygons conceptually by composing or decomposing into rectangles, triangles, and other shapes. Find the area of these geometric figures to solve problems.
GA.6.GSR.5.2	Given the net of three-dimensional figures with rectangular and triangular faces, determine the surface area of these figures.
GA.6.GSR.5.3	Calculate the volume of right rectangular prisms with fractional edge lengths by applying the formula, V = (area of base) x (height).
PATTERNING & ALGEBRAIC REASONING -- numerical and algebraic expressions, factors, multiples, algebraic expressions, plotting points in all four quadrants, rational numbers on a number line, polygons in the coordinate plane
GA.6.PAR.6	Identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain authentic situations.
GA.6.PAR.6.1	Write and evaluate numerical expressions involving rational bases and whole-number exponents.
GA.6.PAR.6.2	Determine greatest common factors and least common multiples using a variety of strategies to make sense of applicable problems.
GA.6.PAR.6.3	Write and read expressions that represent operations with numbers and variables in realistic situations.
GA.6.PAR.6.4	Evaluate expressions when given values for the variables, including expressions that arise in everyday situations.
GA.6.PAR.6.5	Apply the properties of operations to identify and generate equivalent expressions.
GA.6.PAR.7	Write and solve one-step equations and inequalities as mathematical models to explain authentic, realistic situations.
GA.6.PAR.7.1	Solve one-step equations and inequalities involving variables when values for the variables are given. Determine whether an equation and inequality involving a variable is true or false for a given value of the variable.
GA.6.PAR.7.2	Write one-step equations and inequalities to represent and solve problems; explain that a variable can represent an unknown number or any number in a specified set.
GA.6.PAR.7.3	Solve problems by writing and solving equations of the form x + p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
GA.6.PAR.7.4	Recognize and generate inequalities of the form x > c, x > c, x < c, or x < c to explain situations that have infinitely many solutions; represent solutions of such inequalities on a number line.
GA.6.PAR.8	Graph rational numbers as points on the coordinate plane to represent and solve contextual, mathematical problems; draw polygons using the coordinates for their vertices and find the length of a side of a polygon.
GA.6.PAR.8.1	Locate and position rational numbers on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane.
GA.6.PAR.8.2	Show and explain that signs of numbers in ordered pairs indicate locations in quadrants of the coordinate plane and determine how two ordered pairs may differ based only on the signs.
GA.6.PAR.8.3	Solve problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same x-coordinate or the same y-coordinate.
GA.6.PAR.8.4	Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same x-coordinate or the same y-coordinate.

Grade 7

NUMERICAL REASONING -- integers, percentages, fractions, decimal numbers
GA.7.NR.1	Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
GA.7.NR.1.1	Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.
GA.7.NR.1.2	Show and explain p + q as the number located a distance |q| from p, in the positive or negative direction, depending on whether q is positive or negative. Interpret sums of rational numbers by describing applicable situations.
GA.7.NR.1.3	Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.
GA.7.NR.1.4	Show and explain subtraction of rational numbers as adding the additive inverse, p � q = p + (�q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in contextual situations.
GA.7.NR.1.5	Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
GA.7.NR.1.6	Make sense of multiplication of rational numbers using realistic applications.
GA.7.NR.1.7	Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
GA.7.NR.1.8	Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
GA.7.NR.1.9	Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
GA.7.NR.1.10	Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
GA.7.NR.1.11	Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.
PATTERNING & ALGEBRAIC REASONING -- linear expressions with rational coefficients, complex unit rates, proportional relationships
GA.7.PAR.2	Use properties of operations, generate equivalent expressions and interpret the expressions to explain relevant situations.
GA.7.PAR.2.1	Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
GA.7.PAR.2.2	Rewrite an expression in different forms from a contextual problem to clarify the problem and show how the quantities in it are related.
GA.7.PAR.3	Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
GA.7.PAR.3.1	Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Interpret the solution based on the situation.
GA.7.PAR.3.2	Construct algebraic inequalities to solve problems, leading to inequalities of the form px + q > r, px + q < r, px + q ≤ r, or px + q ≥ r, where p, q, and r are specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
GA.7.PAR.4	Recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, and equations.
GA.7.PAR.4.1	Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units presented in realistic problems.
GA.7.PAR.4.2	Determine the unit rate (constant of proportionality) in tables, graphs (1, r), equations, diagrams, and verbal descriptions of proportional relationships to solve realistic problems.
GA.7.PAR.4.3	Determine whether two quantities presented in authentic problems are in a proportional relationship.
GA.7.PAR.4.4	Identify, represent, and use proportional relationships.
GA.7.PAR.4.5	Use context to explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
GA.7.PAR.4.6	Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
GA.7.PAR.4.7	Use similar triangles to explain why the slope, m, is the same between any two distinct points on a non- vertical line in the coordinate plane.
GA.7.PAR.4.8	Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
GA.7.PAR.4.9	Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.
GA.7.PAR.4.10	Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the potential limitations and scope of the sample to the population.
GA.7.PAR.4.11	Analyze sampling methods and conclude that random sampling produces and supports valid inferences.
GA.7.PAR.4.12	Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Simulate multiple samples of the same size.
GEOMETRIC & SPATIAL REASONING -- vertical, adjacent, complementary, and supplementary angles, circumference and area of circles, area and surface area, volume of cubes, right prisms, and cylinders
GA.7.GSR.5	Solve practical problems involving angle measurement, circles, area of circles, surface area of prisms and cylinders, and volume of cylinders and prisms composed of cubes and right prisms.
GA.7.GSR.5.1	Measure angles in whole non- standard units.
GA.7.GSR.5.2	Measure angles in whole number degrees using a protractor.
GA.7.GSR.5.3	Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
GA.7.GSR.5.4	Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
GA.7.GSR.5.5	Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.
GA.7.GSR.5.6	Solve realistic problems involving surface area of right prisms and cylinders.
GA.7.GSR.5.7	Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in the plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.
GA.7.GSR.5.8	Explore volume as a measurable attribute of cylinders and right prisms. Find the volume of these geometric figures using concrete problems.
PROBABILITY REASONING -- likelihood, theoretical and experimental probability
GA.7.PR.6	Using mathematical reasoning, investigate chance processes and develop, evaluate, and use probability models to find probabilities of simple events presented in authentic situations.
GA.7.PR.6.1	Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occurring. Describe that a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
GA.7.PR.6.2	Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequency will approach the theoretical probability.
GA.7.PR.6.3	Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.
GA.7.PR.6.4	Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
GA.7.PR.6.5	Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
GA.7.PR.6.6	Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (numerical) variables as probability models to draw informal inferences about two samples or populations.

Grade 8

NUMERICAL REASONING -- rational and irrational numbers, decimal expansion, integer exponents, square and cube roots, scientific notation
GA.8.NR.1	Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.
GA.8.NR.1.1	Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.
GA.8.NR.1.2	Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.
GA.8.NR.2	Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.
GA.8.NR.2.1	Apply the properties of integer exponents to generate equivalent numerical expressions.
GA.8.NR.2.2	Use square root and cube root symbols to represent solutions to equations. Recognize that x^2 = p (where p is a positive rational number and |x| ≤ 25) has two solutions and x^3 = p (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ -1000 and ≤ 1000.
GA.8.NR.2.3	Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.
GA.8.NR.2.4	Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).
PATTERNING & ALGEBRAIC REASONING -- expressions, linear equations, and inequalities
GA.8.PAR.3	Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena.
GA.8.PAR.3.1	Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors.
GA.8.PAR.3.2	Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
GA.8.PAR.3.3	Create and solve linear equations and inequalities in one variable within a relevant application.
GA.8.PAR.3.4	Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.
GA.8.PAR.3.5	Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.
GA.8.PAR.3.6	Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.
GA.8.PAR.4	Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.
GA.8.PAR.4.1	Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b.
GA.8.PAR.4.2	Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.
FUNCTIONAL & GRAPHICAL REASONING -- relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines
GA.8.FGR.5	Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.
GA.8.FGR.5.1	Show and explain that a function is a rule that assigns to each input exactly one output.
GA.8.FGR.5.2	Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
GA.8.FGR.5.3	Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
GA.8.FGR.5.4	Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
GA.8.FGR.5.5	Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y1) = m(x-x1) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
GA.8.FGR.5.6	Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
GA.8.FGR.5.7	Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.
GA.8.FGR.5.8	Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
GA.8.FGR.5.9	Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
GA.8.FGR.6	Solve practical, linear problems involving situations using bivariate quantitative data.
GA.8.FGR.6.1	Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit.
GA.8.FGR.6.2	Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.
GA.8.FGR.6.3	Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear model in the context of the data.
GA.8.FGR.6.4	Use appropriate graphical displays from data distributions involving lines of best fit to draw informal inferences and answer the statistical investigative question posed in an unbiased statistical study.
GA.8.FGR.7	Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.
GA.8.FGR.7.1	Interpret and solve relevant mathematical problems leading to two linear equations in two variables.
GA.8.FGR.7.2	Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.
GA.8.FGR.7.3	Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection.
GA.8.FGR.7.4	Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.
GA.8.FGR.7.5	Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular.
GEOMETRIC & SPATIAL REASONING -- Pythagorean theorem and volume of triangles, rectangles, cones, cylinders, and spheres
GA.8.GSR.8	Solve geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.
GA.8.GSR.8.1	Explain a proof of the Pythagorean Theorem and its converse using visual models.
GA.8.GSR.8.2	Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.
GA.8.GSR.8.3	Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.
GA.8.GSR.8.4	Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.