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:

  1. Complex fraction:  a fraction which contains one or more fractions in the numerator, the denominator or both.
  2. Equation: a mathematical sentence containing an “equals sign”, i.e., “=”
  3. Proportion: a comparison of two ratios
  4. Quantity:  a number representing “how much” or “how many” of something
  5. Rate:  a ratio of two measurements having different units
  6. Ratio:  a comparison of two quantities
  7. 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 multi-digit 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

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:

  1. Absolute value:  the numerical distance a number is from zero on a number line
  2. Denominator: the number or expression written below the fraction bar
  3. Equivalent fractions: two or more fractions with the same value but different names
  4. Factor: a whole number that can be divided evenly into a given number
  5. Fraction:  A way of representing a part of a whole
  6. Improper fraction:  A fraction that has a numerator greater than the denominator
  7. Integers:  the set of natural numbers, their opposites and zero
  8. Irrational number: a number  that cannot be written as a ratio
  9. Like fractions: two or more fractions with the same denominators
  10. Negative number:  a real number less than zero
  11. Numerator: the number or expression written above the fraction bar
  12. Opposites:  two numbers on a numberline on opposite sides of zero, the same distance from zero
  13. Positive number:  a real number greater than zero
  14. Quotient:  The answer to a division problem
  15. Rational number:  A number that can be written as a ratio
  16. Real number:  any number represented on the number line
  17. Repeating decimal:  a division that results in a quotient that ends in a pattern of digits that repeat indefinitely
  18. Terminating decimal:  a division that results in a quotient that ends
  19. 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 one-variable 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 one-step linear equations in one variable involving non-negative 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

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 y-intercept 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:

  1. Algebraic expression: a mathematical phrase containing numbers, variables and operation symbols
  2. Equation:  a mathematical sentence that contains an equals sign, =
  3. Equivalent expressions:  expressions that can be simplified to the same value, term, or combination of terms
  4. Inequality:  a mathematical sentence that contains <, >, ≠, ≤, or ≥
  5. Inverse operations:  two “opposite” arithmetic operations that undo each other
  6. Like terms:  terms that contain the same variable and the same exponent
  7. Numerical expression: a mathematical phrase containing numbers and operation symbols
  8. One-step equation: an equation that contains one operation, and can be solved in one step
  9. Operation:  a mathematical process such as addition, subtraction, multiplication, or division
  10. Solution:  a value for the variable that makes an equation true
  11. Term:  each number or variable in a mathematical expression, equatiion, or sequence
  12. Two-step equation:  an equation that can be solved in two step, e.g., contains two operations
  13. Variable:  a symbol, usually, a letter, used to represent an unknown number
  14. 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 two-dimensional 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 two-dimensional figures are congruent if a series of rigid transformations can be performed to ma the pre-image to the image.

  • I can describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

  • I can understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image 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 three-dimensional 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

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

  1. Function: A relation in which exactly one element of the range is paired with each element of the domain
  2. Domain: The set of the first numbers or abscissas of the ordered pairs in a relation
  3. Range: The set of second numbers in the ordered pairs of a relation

 

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