#### Innovative lessons for key K-8 math concepts and skills

The Minnesota K-12 Academic Standards in Mathematics are grounded in the belief that all students can and should be mathematically proficient. All students need to learn important mathematical concepts, skills, and relationships with understanding. The standards describe a connected body of mathematical knowledge students learn through the processes of problem solving, reasoning and proof, communication, connections, and representation. DreamBox lessons and reports are aligned to show standards proficiency in these strands: Number and Operation; Algebra; Geometry and Measurement; Data Analysis and Probability. You can track progress with Insight Reports that surface student performance by each standard and even create personalized assignments aligned with specific Minnesota standards.

#### Lessons by Standards

Region | Standard | Description | Level |
---|---|---|---|

Minnesota | 9.2.1.1 | Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain. | Algebra |

Minnesota | 9.2.1.4 | Obtain information and draw conclusions from graphs of functions and other relations. | Algebra |

Minnesota | 9.2.1.6 | Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function. | Algebra |

Minnesota | 9.2.1.8 | Make qualitative statements about the rate of change of a function, based on its graph or table of values. | Algebra |

Minnesota | 9.2.2.3 | Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions. | Algebra |

Minnesota | 9.2.2.4 | Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively. | Algebra |

Minnesota | 9.2.2.6 | Sketch the graphs of common non-linear functions such as ??(??)= ???, ??(??) = |??|, ??(??)= 1/??, ??(??) = ??^3, and translations of these functions, such as ??(??) = ?(??-2) + 4. Know how to use graphing technology to graph these functions. | Algebra |

Minnesota | 9.2.3.2 | Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree. | Algebra |

Minnesota | 9.2.3.3 | Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. | Algebra |

Minnesota | 9.2.3.7 | Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables. | Algebra |

Minnesota | 9.2.4.1 | Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. | Algebra |

Minnesota | 9.4.1.3 | Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions. | Algebra |

Minnesota | 1.1.1.1 | Use place value to describe whole numbers between 10 and 100 in terms of tens and ones. | Grade 1 |

Minnesota | 1.1.1.2 | Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. | Grade 1 |

Minnesota | 1.1.1.3 | Count, with and without objects, forward and backward from any given number up to 120. | Grade 1 |

Minnesota | 1.1.1.4 | Find a number that is 10 more or 10 less than a given number. | Grade 1 |

Minnesota | 1.1.1.5 | Compare and order whole numbers up to 100. | Grade 1 |

Minnesota | 1.1.1.7 | Use counting and comparison skills to create and analyze bar graphs and tally charts. | Grade 1 |

Minnesota | 1.1.2.1 | Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations. | Grade 1 |

Minnesota | 1.1.2.3 | Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s. | Grade 1 |

Minnesota | 1.2.2.1 | Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. | Grade 1 |

Minnesota | 1.2.2.2 | Determine if equations involving addition and subtraction are true. | Grade 1 |

Minnesota | 1.3.2.2 | Tell time to the hour and half-hour. | Grade 1 |

Minnesota | 2.1.1.1 | Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks. | Grade 2 |

Minnesota | 2.1.1.2 | Use place value to describe whole numbers between 10 and 1000 in terms of hundreds, tens and ones. Know that 100 is 10 tens, and 1000 is 10 hundreds. | Grade 2 |

Minnesota | 2.1.1.3 | Find 10 more or 10 less than a given three-digit number. Find 100 more or 100 less than a given three-digit number. | Grade 2 |

Minnesota | 2.1.1.5 | Compare and order whole numbers up to 1000. | Grade 2 |

Minnesota | 2.1.2.1 | Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. | Grade 2 |

Minnesota | 2.1.2.2 | Demonstrate fluency with basic addition facts and related subtraction facts. | Grade 2 |

Minnesota | 2.1.2.4 | Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. | Grade 2 |

Minnesota | 2.1.2.5 | Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits. | Grade 2 |

Minnesota | 2.1.2.6 | Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts. | Grade 2 |

Minnesota | 2.2.2.2 | Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. | Grade 2 |

Minnesota | 2.3.1.2 | Identify and name basic two- and three-dimensional shapes, such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. | Grade 2 |

Minnesota | 2.3.2.1 | Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. | Grade 2 |

Minnesota | 3.1.1.2 | Use place value to describe whole numbers between 1000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones. | Grade 3 |

Minnesota | 3.1.1.4 | Round numbers to the nearest 10,000, 1000, 100 and 10. Round up and round down to estimate sums and differences. | Grade 3 |

Minnesota | 3.1.2.1 | Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms. | Grade 3 |

Minnesota | 3.1.2.3 | Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division. | Grade 3 |

Minnesota | 3.1.2.4 | Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems. | Grade 3 |

Minnesota | 3.1.2.5 | Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. | Grade 3 |

Minnesota | 3.1.3.1 | Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. | Grade 3 |

Minnesota | 3.1.3.2 | Understand that the size of a fractional part is relative to the size of the whole. | Grade 3 |

Minnesota | 3.1.3.3 | Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator. | Grade 3 |

Minnesota | 3.3.1.1 | Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids. | Grade 3 |

Minnesota | 3.3.3.1 | Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. | Grade 3 |

Minnesota | 3.4.1.1 | Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units. | Grade 3 |

Minnesota | 4.1.1.2 | Use an understanding of place value to multiply a number by 10, 100 and 1000. | Grade 4 |

Minnesota | 4.1.1.3 | Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. | Grade 4 |

Minnesota | 4.1.1.5 | Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies, including the relationship between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 4 |

Minnesota | 4.1.1.6 | Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. | Grade 4 |

Minnesota | 4.1.2.1 | Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions. | Grade 4 |

Minnesota | 4.1.2.2 | Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. | Grade 4 |

Minnesota | 4.1.2.3 | Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators. | Grade 4 |

Minnesota | 4.1.2.5 | Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks. | Grade 4 |

Minnesota | 4.1.2.6 | Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. | Grade 4 |

Minnesota | 4.2.1.1 | Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. | Grade 4 |

Minnesota | 4.2.2.1 | Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving multiplication or division to represent number sentences. | Grade 4 |

Minnesota | 4.2.2.2 | Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. | Grade 4 |

Minnesota | 4.3.1.1 | Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. | Grade 4 |

Minnesota | 4.3.1.2 | Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. | Grade 4 |

Minnesota | 4.3.2.1 | Measure angles in geometric figures and real-world objects with a protractor or angle ruler. | Grade 4 |

Minnesota | 4.3.2.3 | Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. | Grade 4 |

Minnesota | 4.3.2.4 | Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. | Grade 4 |

Minnesota | 5.1.1.4 | Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results. | Grade 5 |

Minnesota | 5.1.2.1 | Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. | Grade 5 |

Minnesota | 5.1.2.3 | Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. | Grade 5 |

Minnesota | 5.1.3.1 | Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms. | Grade 5 |

Minnesota | 5.1.3.4 | Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. | Grade 5 |

Minnesota | 5.2.1.2 | Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system. | Grade 5 |

Minnesota | 5.2.2.1 | Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. | Grade 5 |

Minnesota | 6.1.1.1 | Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. | Grade 6 |

Minnesota | 6.1.1.2 | Compare positive rational numbers represented in various forms. Use the symbols . | Grade 6 |

Minnesota | 6.1.1.3 | Understand that percent represents parts out of 100 and ratios to 100. | Grade 6 |

Minnesota | 6.1.1.7 | Convert between equivalent representations of positive rational numbers. | Grade 6 |

Minnesota | 6.1.2.1 | Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. | Grade 6 |

Minnesota | 6.1.2.3 | Determine the rate for ratios of quantities with different units. | Grade 6 |

Minnesota | 6.1.3.1 | Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. | Grade 6 |

Minnesota | 6.1.3.4 | Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. | Grade 6 |

Minnesota | 6.2.1.1 | Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. | Grade 6 |

Minnesota | 6.2.3.1 | Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. | Grade 6 |

Minnesota | 7.1.1.2 | Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. | Grade 7 |

Minnesota | 7.1.1.3 | Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid. | Grade 7 |

Minnesota | 7.1.2.1 | Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. | Grade 7 |

Minnesota | 7.1.2.4 | Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest. | Grade 7 |

Minnesota | 7.1.2.6 | Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. | Grade 7 |

Minnesota | 7.2.1.2 | Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed. | Grade 7 |

Minnesota | 7.2.2.1 | Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. | Grade 7 |

Minnesota | 7.2.2.2 | Solve multi-step problems involving proportional relationships in numerous contexts. | Grade 7 |

Minnesota | 7.2.2.4 | Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. | Grade 7 |

Minnesota | 7.2.3.1 | Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws. | Grade 7 |

Minnesota | 7.2.3.2 | Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. | Grade 7 |

Minnesota | 7.2.3.3 | Apply understanding of order of operations and grouping symbols when using calculators and other technologies. | Grade 7 |

Minnesota | 7.2.4.1 | Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. | Grade 7 |

Minnesota | 7.3.2.1 | Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors. | Grade 7 |

Minnesota | 7.3.2.3 | Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. | Grade 7 |

Minnesota | 7.3.2.4 | Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation. | Grade 7 |

Minnesota | 8.1.1.4 | Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions. | Grade 8 |

Minnesota | 8.1.1.5 | Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved. | Grade 8 |

Minnesota | 8.2.1.1 | Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as ??(??), to represent such relationships. | Grade 8 |

Minnesota | 8.2.1.3 | Understand that a function is linear if it can be expressed in the form ??(??) = ????+?? or if its graph is a straight line. | Grade 8 |

Minnesota | 8.2.2.1 | Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. | Grade 8 |

Minnesota | 8.2.2.2 | Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the ??-intercept is zero when the function represents a proportional relationship. | Grade 8 |

Minnesota | 8.2.4.2 | Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used. | Grade 8 |

Minnesota | 8.2.4.3 | Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line. | Grade 8 |

Minnesota | 8.2.4.7 | Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically. | Grade 8 |

Minnesota | 8.2.4.8 | Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations. | Grade 8 |

Minnesota | 8.3.1.1 | Use the Pythagorean Theorem to solve problems involving right triangles. | Grade 8 |

Minnesota | 8.3.1.2 | Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system. | Grade 8 |

Minnesota | 8.4.1.1 | Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit. | Grade 8 |

Minnesota | K.1.1.2 | Read, write, and represent whole numbers from 0 to at least 31. Representations may include numerals, pictures, real objects and picture graphs, spoken words, and manipulatives such as connecting cubes. | Kindergarten |

Minnesota | K.1.1.3 | Count, with and without objects, forward and backward to at least 20. | Kindergarten |

Minnesota | K.1.1.5 | Compare and order whole numbers, with and without objects, from 0 to 20. | Kindergarten |

Minnesota | K.1.2.2 | Compose and decompose numbers up to 10 with objects and pictures. | Kindergarten |