M03.B-O.3.1.5 
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends.
When grade appropriate instruction pertaining to an eligible content should begin
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M03.B-O.3.1.5
Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations. Example 1: Observe that 4 times a number is always even. Example 2: Explain why 6 times a number can be decomposed into three equal addends.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M04.B-O.3.1.1
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule “increase the number of sides by 1” and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex.
When grade appropriate instruction pertaining to an eligible content should begin
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M04.B-O.3.1.1
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Example 1: Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms alternate between odd and even numbers. Example 2: Given the rule “increase the number of sides by 1” and starting with a triangle, observe that the tops of the shapes alternate between a side and a vertex.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M04.B-O.3.1.2
Determine the missing elements in a function table (limit to +, –, or × and to whole numbers or money).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M04.B-O.3.1.3
Determine the rule for a function given a table (limit to +, –, or × and to whole numbers).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M05.B-O.2.1.1
Generate two numerical patterns using two given rules. Example: Given the rule “add 3” and the starting number 0 and given the rule “add 6” and the starting number 0, generate terms in the resulting sequences.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M05.B-O.2.1.2
Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Example: Given two patterns in which the first pattern follows the rule “add 8” and the second pattern follows the rule “add 2,” observe that the terms in the first pattern are 4 times the size of the terms in the second pattern.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M06.B-E.3.1.2
Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation.
When grade appropriate instruction pertaining to an eligible content should begin
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M06.B-E.3.1.2
Analyze the relationship between the dependent and independent variables using graphs and tables and/or relate these to an equation.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.2.1.1
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.2.1.2
Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-E.2.1.3
Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-E.2.1.3
Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-F.1.1.1
Determine whether a relation is a function.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-F.1.1.2
Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions). Example: Given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-F.1.1.2
Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions). Example: Given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-F.1.1.3
Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-F.2.1.1
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. Interpret 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.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-F.2.1.1
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. Interpret 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.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-F.2.1.1
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. Interpret 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.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.1.2.1
Create, interpret and/or use the equation, graph or table of a linear function.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.1.2.2
Translate from one representation of a linear function to another (graph, table and equation).
When grade appropriate instruction pertaining to an eligible content should begin
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A1.2.1.2.2
Translate from one representation of a linear function to another (graph, table and equation).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.2.1.1
Identify, describe and/or use constant rates of change.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.2.1.2
Apply the concept of linear rate of change (slope) to solve problems.
When grade appropriate instruction pertaining to an eligible content should begin
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A1.2.2.1.2
Apply the concept of linear rate of change (slope) to solve problems.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.2.1.3
Write or identify a linear equation when given - the graph of the line
- 2 points on the line, or
- the slope and a point on a line,
(Linear equation may be in point-slope, standard and/or slope-intercept form).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A1.2.2.1.4
Determine the slope and/or y-intercept represented by a linear equation or graph.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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M08.B-F.2.1.2
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally.
When grade appropriate instruction pertaining to an eligible content should begin
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M08.B-F.2.1.2
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.1.1.1
Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
When grade appropriate instruction pertaining to an eligible content should begin
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A1.2.1.1.1
Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.1.1.2
Determine if a relation is a function given a set of points or a graph.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A1.2.1.1.3
Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.1.3.2.1
Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
When grade appropriate instruction pertaining to an eligible content should begin
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A2.1.3.2.1
Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
When grade appropriate instruction pertaining to an eligible content should begin
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A2.1.3.2.1
Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.2.1.1.1
Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
When grade appropriate instruction pertaining to an eligible content should begin
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A2.2.1.1.1
Analyze a set of data for the existence of a pattern and represent the pattern with a rule algebraically and/or graphically.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.2.1.1.2
Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A2.2.1.1.3
Determine the domain, range or inverse of a relation.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.2.1.1.4
Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increasing/decreasing, intercepts, zeros, and asymptotes).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.2.2.1.1
Create, interpret and/or use the equation, graph or table of a polynomial function (including quadratics).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.2.2.1.2
Create, interpret and/or use the equation, graph or table of an exponential or logarithmic function (including common and natural logarithms).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content
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A2.2.2.1.3
Determine, use and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential or logarithmic function.
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A2.2.2.1.4
Translate a polynomial, exponential or logarithmic function from one representation to another (graph, table and equation).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
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A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
When grade appropriate instruction pertaining to an eligible content should begin |
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A2.2.2.2.1
Identify or describe the effect of changing parameters within a family of functions (e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).
When students are expected to demonstrate the knowledge, skills, and abilities described by an eligible content |
