Functions & Relations
Core Ideas
 Understand patterns and use mathematical models to represent and understand qualitative and quantitative relationships.
 Sort, classify, and order objects by size, number, and other properties.
 Recognize, describe, and extend patterns of sound, shape, or number.
 Model change qualitatively, such as students growing taller or the weather turning colder.


Core Ideas
 Understand patterns and use mathematical models to represent and understand qualitative and quantitative relationships.
 Describe and extend patterns of sound, shape, or number and translate from one representation to another.
 Describe and extend growing as well as repeating patterns.
 Use the general principles and properties of operations, such as commutativity, with specific numbers.
 Model problem situations using objects, pictures, and symbols
 Describe change qualitatively, such as students growing taller or the weather turning colder.

Core Ideas
 Understand patterns and use mathematical models to represent and understand qualitative and quantitative relationships.
 Describe, extend, and create patterns of sound, shape, and number and translate from one representation to another.
 Describe, extend, and create growing as well as repeating patterns.
 Compare principles and properties of operations, such as commutativity, between addition and subtraction.
 Use concrete, pictorial, and verbal representations to develop an understanding of symbolic notations.
 Describe change quantitatively such as a student's growing two inches in one year.

Core Ideas
 Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships.
 Describe and extend geometric and numeric patterns.
 Represent and analyze patterns using words and/or tables.
 Illustrate general principles and properties of operations, such as commutativity, using specific numbers.
 Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
 Model problem situations with objects and use representations such as graphs and tables to draw conclusions.
 Describe qualitative change (such as students growing taller).
 Describe quantitative change (such as a student's growing two inches in one year).
 Solve simple problems involving a functional relationship (two quantities which vary together, like finding the total cost of multiple items when you know the cost of one).

Core Ideas
 Understand patterns and use mathematical models to represent and to understand qualitative and quantitative relationships.
 Represent and analyze patterns and functions using words, tables, and graphs.
 Find the results of a rule for a specific value.
 Use inverse operations to solve multistep problems.
 Use concrete, pictorial, and verbal representations to solve problems involving unknowns.
 Understand and use the concept of equality.

Core Ideas
 Understand patterns and use mathematical models such as algebraic symbols and graphs to represent and understand quantitative relationships.
 Represent the idea of a variable as an unknown quantity using a letter or a symbol.
 Express mathematical relationships using equations and graph them on a coordinate grid.
 Investigate how a change in one variable relates to a change in a second variable.
 Identify and describe situations with constant and varying rates of change and compare them.
 Understand and use properties of operations, such as the distributive property of multiplication over addition.

Core Ideas
 Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change.
 Represent, analyze, and generalize a variety of relations and functions with tables, graphs, and words.
 Use symbolic algebra to represent situations and to solve linear equations.
 Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

Core Ideas
 Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change.
 Represent, analyze, and generalize a variety of functions including linear and simple exponential relationships.
 Relate and compare different forms of representation for a relationship including words, tables, graphs in the coordinate plane, and symbols.
 Express mathematical relationships using expressions and equations.
 Develop conceptual understanding of different uses of variables.
 Use symbolic algebra to represent situations to solve problems.
 Identify and describe situations with constant or varying rates of change and compare them.

Core Ideas
 Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change.
 Identify functions as linear or nonlinear, and contrast their properties from tables, graphs, or equations.
 Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
 Recognize and generate equivalent forms of simple algebraic expressions and solve linear equations.
 Model and solve contextualized problems involving inequalities.
 Use graphs to analyze the nature of changes on quantities in linear relationships
 Recognize, represent and solve contextualized problems involving polynomials and their factors.

Core Ideas
 Understand patterns, relations, and functions.
 Generalize patterns using explicitly defined functions.
 Understand relations and functions and select, convert flexibly among, and use various representations for them.
 Analyze functions of one variable by investigating local and global behavior, including slopes as rates of change, intercepts, and zeros.
MARS Tasks
Sorting Functions
Sidewalk Patterns
Functions

Core Ideas
 Understand patterns, relations, and functions.
 Understand and perform transformations on functions.
 Understand and compare the properties of classes of functions, including linear, quadratic, reciprocal, and exponential functions.
 Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships.





