By the end of this unit, students are expected to:
Develop understanding of variables and how they are related.
Explore problem situations that involve variables and relationships
Identify the dependent and independent variable and describe how they are related in a situation
Interpret the ‘stories’ told by patterns in tables and coordinate graphs of numeric (x, y) data;
Represent the pattern of change between two variables in words, data tables, graphs, and equations
Investigate situations that change over time
Examine increasing and decreasing patterns of change
Compare linear and non-linear patterns of change by using tables or graphs
Use tables, graphs and equations to find the value of a variable given the value of the associated variable
Explore relationships to become familiar with graphing in all in four quadrants
Describe advantages and disadvantages of using words, tables, graphs and equations to represent patterns of change between two variables and make connections across those representations
Write an equation to express the relationship between two variables in one and two operations: y = mx, y = b + x, and y = b + mx
Calculate average speed and show how it is reflected in a table or graph and vice versa.
Recognize and express direct proportionality relationships with a unit rate (y = mx) and represent these relationships in rate tables and graphs
Solve problems that involve variables
Develop understanding of expressions and equations.
Use properties of operations, including the Distributive Property and the Order of Operations, to write equivalent expressions for the dependent variable in terms of the independent variable
Use tables, graph or properties of numbers such as the Distributive Property to show that two expressions are equivalent
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity
Interpret and evaluate expressions in which letters stand for numbers and apply the Order of Operations as needed
Recognize that equations are statements of equivalence between two expressions
Solve linear equations of the form, y = ax, y = b + x, and y = b + ax using numeric guess and check, tables of (x, y) values, graphs or fact families
Write an inequality and associate it with an equation to find solutions and graph the solutions on a number line