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Functions & Relations
Kindergarten

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.
 
1st Grade

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.
 
2nd Grade

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.
 
3rd Grade

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).
 
4th Grade

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 multi-step problems.
  • Use concrete, pictorial, and verbal representations to solve problems involving unknowns.
  • Understand and use the concept of equality.
 
5th Grade

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.
 
6th Grade

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.
 
7th Grade

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.
 
8th Grade

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.
 
Course 1 (Algebra)

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

 
Course 2 (Geometry)

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.
 


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