Linear Relationships:
Recognize problem situations in which two or more variables have a linear relationship to each other.Identify and describe the patterns of change between the independent and dependent variables for linear relationships represented by tables, graphs, equations, or contextual settings
Construct tables, graphs, and symbolic equations that represent linear relationships
Identify the rate of change between two variables and the x- and y-intercepts from graphs, tables, and equations that represent linear relationships
Translate information about linear relationships given in a context, a table, a graph, or an equation to one of the other forms
Write equations that represent linear relationships given specific pieces of information, and describe what information the variables and numbers represent
Make a connection between slope as a ratio of vertical distance to horizontal distance between two points on a line and the rate of change between two variables that have a linear relationship
Recognize that y = mx represents a proportional relationship
Solve problems and make decisions about linear relationships using information given in tables, graphs, and equations
Equivalence:
Understand that the equality sign indicates that two expressions are equivalent.Recognize that the equation y = mx + b represents a linear relationship and means that mx + b is an expression equivalent to y
Recognize that linear equations in one unknown, k = mx + b or y = m(t) + b, where k, t, m, and b are constant numbers, are special cases of the equation y = mx + b
Recognize that finding the missing value of one of the variables in a linear relationship,y = mx + b, is the same as finding a missing coordinate of a point (x, y) that lies on the graph of the relationship
Solve linear equations in one variable using symbolic methods, tables, and graphs
Recognize that a linear inequality in one unknown is associated with a linear equation
Solve linear inequalities using graphs or algebraic reasoning
Solve linear inequalities using graphs or algebraic reasoning
Write and interpret equivalent expressions
When your child encounters a new problem, it is a good idea to ask questions such as:
What are the variables in the problem?
Do the variables in the problem have a linear relationship to each other?
What patterns in the problem suggest that the relationship is linear?
How can the linear relationship in a situation be represented with a verbal description, a table, a graph, or an equation?
How do changes in one variable affect changes in a related variable?
How are these changes captured in a table, a graph, or an equation?
How can tables, graphs, and equations of linear relationships be used to answer questions?
Moving Straight Ahead - Explanation of Concepts for Those Helping at Home - Connected Mathematics 3 Resource