- Explores
the mathematics of linear function.
- 5-week
course, consisting of 4 Sessons, plus an assessment in the
final week.
- Sessons
feature interactive "e-manipulatives" and guiding
questions.
- Is
conducted primarily through a bulletin board—a threaded
discussion list, but may include a discussion group and
"live" office hours.
Linear Functions Outline
This
workshop covers the following aspects of linear function:
- Different problem contexts that can be solved
with linear functions.
- Representations of linear functions: equations,
tables and graphs.
- The relationship between context and representations.
- Slope, y intercept and other related terms.
- Connections to other areas of mathematics.
Introduction
Session 1 Linear functions and finance
Linear functions are commonly used in finance to represent
income and expenses, as well as profit and loss. In this
session, you will
- Solve a typical finance problem.
- Compare solutions and the representations
used: tables, equations, and graphs.
- Consider the meaning of the parts of a
linear equation.
1.1 The printing booklets problem
1.2 Compare solutions
1.3 Representations—tables, graphs and equations
1.4 y=mx+b. What is b? What is m?
1.5 FYI: In the world of finance
Session 2 Running Races
In this session, you will work with speed;
in this case, meters per second.
You will:
- Model and solve running problems
using linear functions.
- Consider slope and y intercept and their
meaning in this
- problem context.
- Investigate and describe slope patterns.
2.1 The racing problem
2.2 Rates and slope
2.3 Properties of slope
2.4 FYI: Why do we care about contexts?
Session 3 Meeting multiple constraints
A model that leads to the general form: ax+by=c,
where a, b and c are real number constants.
In this session you will
- Model sets of constraints with linear
functions
- Solve problems using the functions in graph
or equation form.
- Assign meaning to the constants in general
and slope/intercept forms of the equations.
- Pose and solve problems in everyday contexts,
compare those contexts to the ones already studied.
3.1 Juicy problem
3.2 Comparing contexts
3.3 Posing problems
3.4 FYI: More about meeting constraints
Session 4 Comparing units for temperature
This session focuses on coversion equations
as linear functions. You will
- Create an F vs. C converter, using representations
of linear functions.
- Consider the meaning of slope and y-intercept
in this context.
- Consider the graphs of an equation when
the equation is written in two different forms.
4.1 The converter problem
4.2 Comparing converters
4.3 Exploring the function and formulas
4.4 FYI: Conversion on the web
Assessment
|
Overview