Activities Tools 

The table lists the names of all the activities and a brief description of each.

Representations of linear functions

The relations between various representations of a function. Effect of changes in one representation on other representations.

Rate of change of linear functions

Expressing the rate of change of processes in various representations of a function.

Transformations of graphs

Operations that change a function by changing its graph. Constructing families of functions.

Addition and subtraction of linear functions

Arithmetic operations performed on functions. Addition and subtraction of functions. Relations between the attributes of a pair of functions and those of the function that results from an arithmetic operation between them.

Equivalent expressions of functions

Writing different correspondence rules for the same function. Three ways of writing a correspondence rule for a linear function.

Functions defined on intervals

Functions that behave linearly within each interval. Phenomena that can be described using functions defined on intervals.

Equivalent quadratic expressions

Switching between various forms of correspondence rules describing quadratic functions: the vertex, polynomial, and product forms.

Graph transformations: the vertex form

Operations that change a function by changing its graph. Constructing families of functions. The vertex form of quadratic functions.

Adding functions: the polynomial form

Addition of functions. Construction of quadratic functions as the sum of the basic components: ax², bx, and c.

Products of linear functions

Relations between the attributes of multiplied linear functions and of the result function.

Quadratic growth

Quadratic functions viewed as functions representing a change that changes at a constant rate.

Economic decisions

Decision making problems in various economic contexts. Constructing functions to examine the dependencies between various parameters. Description and analysis of possibilities and decision making with respect to a given problem.

Motion at changing speed

Problems dealing with motion at changing speeds. Construction of functions that describe accelerating and decelerating motion.

Graphic design

Design of various printed matters. Analysis of possibilities for product planning and of constraints that follow from considerations of esthetics, effectiveness, and efficiency.

Solving equations

Quadratic functions. Finding solutions to quadratic functions. Discussion of several solutions. Problems that can be solved by constructing quadratic functions.

Comparisons of operations

Equations and inequalities: various representations and solutions. Operations allowed on comparisons.