Math Progression – 68
Mathematics Missouri Learning Standards
Note: See Student/Student Resources for Video Lessons by Grade Level Expections.
RATIOS AND PROPORTIONAL RELATIONSHIPS
6th Grade

I can understand a ratio as a comparison of two quantities and represent these comparisons.

I can understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate.

I can solve problems involving ratios and rates.
7th Grade

I can compute unit rates, including those that involve complex fractions, with like or different units.

I can recognize and represent proportional relationships between quantities.

I can solve problems involving ratios, rates, percentages and proportional relationships.
Vocabulary:
 Complex fraction: a fraction which contains one or more fractions in the numerator, the denominator or both.
 Equation: a mathematical sentence containing an “equals sign”, i.e., “=”
 Proportion: a comparison of two ratios
 Quantity: a number representing “how much” or “how many” of something
 Rate: a ratio of two measurements having different units
 Ratio: a comparison of two quantities
 Unit rate: the rate for one unit of a given quantity
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NUMBER SENSE AND OPERATIONS
6th Grade

I can compute and interpret quotients of positive fractions.

I can demonstrate fluency with division of multidigit whole numbers.

I can demonstrate fluency with addition, subtraction, multiplication and division of decimals.

I can find common factors and multiples.

I can use positive and negative numbers to represent quantities,

I can locate a rational number as a point on the number line.

I can understand that the absolute value of a rational number is its distance from 0 on the number line.

I can extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3).
7th Grade

I can apply and extend previous understandings of numbers to add and subtract rational numbers.

I can apply and extend previous understandings of numbers to multiply and divide rational numbers.

I can solve problems involving the four arithmetic operations with rational numbers.
8th Grade

I can explore the real number system.

I can estimate the value and compare the size of irrational numbers and approximate their locations on a number line.
Vocabulary:
 Absolute value: the numerical distance a number is from zero on a number line
 Denominator: the number or expression written below the fraction bar
 Equivalent fractions: two or more fractions with the same value but different names
 Factor: a whole number that can be divided evenly into a given number
 Fraction: A way of representing a part of a whole
 Improper fraction: A fraction that has a numerator greater than the denominator
 Integers: the set of natural numbers, their opposites and zero
 Irrational number: a number that cannot be written as a ratio
 Like fractions: two or more fractions with the same denominators
 Negative number: a real number less than zero
 Numerator: the number or expression written above the fraction bar
 Opposites: two numbers on a numberline on opposite sides of zero, the same distance from zero
 Positive number: a real number greater than zero
 Quotient: The answer to a division problem
 Rational number: A number that can be written as a ratio
 Real number: any number represented on the number line
 Repeating decimal: a division that results in a quotient that ends in a pattern of digits that repeat indefinitely
 Terminating decimal: a division that results in a quotient that ends
 Unlike fractions: two or more fractions with the same denominators
EXPRESSIONS, EQUATIONS AND INEQUALITIES
6th Grade

I can describe the difference between an expression and an equation.

I can create and evaluate expressions involving variables and whole number exponents.

I can identify and generate equivalent algebraic expressions using a mathematical properties.

I can use substitution to determine whether a given number in a specified set makes a onevariable equation or inequality true.

I can understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true.

I can write and solve equations using variables to represent quantities, and understanding the meaning of the variable in the context of the situation.

I can solve onestep linear equations in one variable involving nonnegative rational numbers.

I can recognize that inequalities may have infinitely many solutions.

I can identify and describe relationships between two variables that change in relationship to one another.
7th Grade

I can apply properties of operations to simplify and to factor linear algebraic expressions with rational coefficients.

I can understand how to use equivalent expressions to clarify quantities in a problem.

I can solve multistep problems posed with rational numbers.

I can write and/or solve linear equations and inequalities in one variable.
8th Grade

I can know and apply the properties of integer exponents to generate equivalent expressions.

I can investigate concepts of square and cube roots.

I can express very large and very small quantities in scientific notation and approximate how many times larger one is than the other.

I can use scientific notation to solve problems.

I can graph proportional relationships.

I can apply concepts of slope and yintercept to graphs, equations and proportional relationships.

I can solve linear equations and inequalities in one variable.

I can analyze and solve systems of linear equations.
Vocabulary:
 Algebraic expression: a mathematical phrase containing numbers, variables and operation symbols
 Equation: a mathematical sentence that contains an equals sign, =
 Equivalent expressions: expressions that can be simplified to the same value, term, or combination of terms
 Inequality: a mathematical sentence that contains <, >, ≠, ≤, or ≥
 Inverse operations: two “opposite” arithmetic operations that undo each other
 Like terms: terms that contain the same variable and the same exponent
 Numerical expression: a mathematical phrase containing numbers and operation symbols
 Onestep equation: an equation that contains one operation, and can be solved in one step
 Operation: a mathematical process such as addition, subtraction, multiplication, or division
 Solution: a value for the variable that makes an equation true
 Term: each number or variable in a mathematical expression, equatiion, or sequence
 Twostep equation: an equation that can be solved in two step, e.g., contains two operations
 Variable: a symbol, usually, a letter, used to represent an unknown number
 Property: a statement or characteristic that is true for every number or object in the same classification
GEOMETRY AND MEASUREMENT
6th Grade

I can find the area of polygons by composing or decomposing the shapes into rectangles or triangles.

I can find the volume of right rectangular prisms.

I can solve problems by graphing points in all four quadrants of the Cartesian coordinate plane.

I can solve problems using nets.
7th Grade

I can solve problems involving scale drawings of real objects and geometric figures, including computing actual lengths and areas from a scale drawing and reproducing the drawing at a different scale.

I can use a variety of tools to construct geometric shapes.

I can describe twodimensional cross sections of pyramids, prisms, cones and cylinders.

I can understand the concepts of circles.

I can use angle properties to write and solve equations for an unknown angle.

I can understand the relationship between area, surface area and volume.
8th Grade

I can verify experimentally the congruence properties of rigid transformations.

I can understand that twodimensional figures are congruent if a series of rigid transformations can be performed to ma the preimage to the image.

I can describe the effect of dilations, translations, rotations and reflections on twodimensional figures using coordinates.

I can understand that twodimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the preimage to the image.

I can explore angle relationships and establish informal arguments.

I can use models to demonstrate a proof of the Pythagorean Theorem and its converse.

I can use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two and threedimensional contexts.

I can solve problems involving surface area and volume.
DATA ANALYSIS, STATISTICS AND PROBABILITY
6th Grade

I can recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

I can understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape.

I can 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 from a single number.

I can display and interpret data.

I can summarize numerical data sets in relation to the context.
7th Grade

I can understand that statistics can be used to gain information about a population by examining a sample of the population.

I can use data from multiple samples to draw inferences about a population and investigate variability in estimates of the characteristic of interest.

I can analyze different data distributions using statistical measures.

I can compare the numerical measures of center, measures of frequency and measures of variability from two random samples to draw inferences about the population.

I can investigate the probability of chance events.

I can investigate the relationship between theoretical and experimental probabilities for simple events.

I can explain possible discrepancies between a developed probability model and observed frequencies.

I can find probabilities of compound events using organized lists, tables, tree diagrams and simulations.
8th Grade

I can construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities.

I can generate and use a trend line for bivariate data, and informally assess the fit of the line.

I can interpret the parameters of a linear model of bivariate measurement data to solve problems.

I understand the patterns of association in bivariate categorical data displayed in a twoway table.
FUNCTIONS
8th Grade

I can explore the concept of functions. (The use of function notation is not required.)

I can compare characteristics of two functions each represented in a different way.

I can investigate the difference between linear and nonlinear functions.

I can use functions to model linear relationships between quantities.

I can describe the functional relationship between two quantities from a graph or a verbal description.
Vocabulary
 Function: A relation in which exactly one element of the range is paired with each element of the domain
 Domain: The set of the first numbers or abscissas of the ordered pairs in a relation
 Range: The set of second numbers in the ordered pairs of a relation