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Exploring Linear Functions: Representational Relationships

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Exploring Linear Functions: Representational Relationships

Grade Levels

10th Grade, 11th Grade, 12th Grade, 9th Grade

Course, Subject

Algebra I, Algebra II
Related Academic Standards
A1.2.2.1.2 A1.2.2.1.2
Apply the concept of linear rate of change (slope) to solve problems.
G.2.1.2.2 G.2.1.2.2
Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).
G.2.1.2.3 G.2.1.2.3
Use slope, distance and/or midpoint between 2 points on a coordinate plane to establish properties of a 2-dimensional shape.
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  • Big Ideas
    Mathematical statements can be justified through deductive and inductive reasoning and proof.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Objects can be transformed in an infinite number of ways. Transformations can be described and analyzed mathematically.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    Similarity relationships between objects are a form of proportional relationships. Congruence describes a special similarity relationship between objects and is a form of equivalence.
    Some geometric relationships can be described and explored as functional relationships.
    Some questions can be answered by collecting, representing, and analyzing data, and the question to be answered determines the data to be collected, how best to collect it, and how best to represent it.
    Spatial reasoning and visualization are ways to orient thinking about the physical world.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
    Two variable quantities are proportional if their values are in a constant ratio. The relationship between proportional quantities can be represented as a linear function.
  • Concepts
    2- and 3-dimensional figures
    Analysis of one and two variable (univariate and bivariate) data
    Analytic Geometry
    Geometric Relations: Congruence and Similarity
    Geometric Representations
    Graphing on a coordinate plane
    Proportionality: Similar figures and objects, scale factors, unit rate
    Sampling as a method of estimation and prediction
    Trigonometric Ratios
  • Competencies
    Apply a variety of strategies for proportional reasoning and use them to solve real world problems, including problems dealing with similarity and rates of change.
    Define, describe, and analyze 2- and 3-dimensional figures, their properties and relationships, including how a change in one measurement will affect other measurements of that figure.
    Extend previous understandings of the characteristics of 3d-shapes to develop an understanding of, and use formulas to determine surface areas and volumes.
    Use algebraic properties and processes in mathematical situations and apply them to solve real world problems.
    Use concepts of congruence and similarity to relate and compare 2- and 3-dimensional figures, including trigonometric ratios.
    Use coordinates and algebraic techniques to interpret, represent, and verify geometric relationships.

Description

Technology allows the linking of multiple representations of mathematical situations and the exploration of the relationships that emerge.

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Exploring Linear Functions: Representational Relationships

Content Provider

NCTM

 

The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.

 

The National Council of Teachers of Mathematics is the global leader and foremost authority in mathematics education, ensuring that all students have access to the highest quality mathematics teaching and learning. We envision a world where everyone is enthused about mathematics, sees the value and beauty of mathematics, and is empowered by the opportunities mathematics affords.

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