

Course 1, Unit 1  Patterns of Change
Overview
The intent of this unit, which begins CorePlus Mathematics Course 1,
is to focus student attention on the variety of types of change inherent
in problem situations. This unit will provide students with a broad picture
of patterns of change. Students will explore linear, quadratic, inverse
variation, and exponential patterns of change throughout the unit. Within
this unit there is an effort to make a distinction between causeandeffect
change relationships and changeovertime relationships. In the third
unit of this course, linear functions will be analyzed as a class of
functions with a specific pattern of change. The unit should be completed
in under 4 weeks of classes that meet approximately 50 minutes each
day.
Key Ideas from Course 1, Unit 1

Linear: Linear functions have graphs that are straight lines,
rules that can be written in the form y = a + bx, and
tables of (x, y) values in which the ratio of change
in y to change in x is constant. These ideas are formally
developed in Unit 3. (See student book pages 150167.)
Exponential: Exponential functions have curved graphs showing
the dependent variable increasing at an increasing rate (for exponential
growth) and decreasing at a decreasing rate (for exponential decay)
and rules that can be written in the form y = a(b)^{x},
where b is the constant growth or decay factor. In tables of
(x, y) values for exponential functions, if successive x values
differ by 1, then the ratio of corresponding y values is b.
Ideas about exponential growth and decay will be developed more formally
in Course 1, Unit 5. (See student book pages 289303,
322331.)
Quadratic: Quadratic functions have graphs that are parabolas,
rules that can be written in the form y = ax^{2} + bx + c, and
tables of (x, y) values in which y values
change in a symmetric pattern centered at a maximum or minimum value.
For example, y = x^{2}  4.

x 
y 
3 
5 
2 
0 
1 
3 
0 
4 
1 
3 
2 
0 
3 
5 


NOWNEXT rules (pages 2633): In many problem
situations it is important to study the pattern of change in a single
variable
that
changes with passage of time. Observing values of that variable at
regular time intervals, it is natural to look for a pattern relating
each value of the variable to the next value. The NOWNEXT language
is an informal way of capturing this perspective on patterns of change.
Writing linear and exponential patterns of change in NOWNEXT form
highlights the constant additive and constant multiplicative patterns
of change that characterize those two fundamental quantitative relationships.
These ideas are developed further in Course 1, Units 3 and
5. (See student book pages 157161.) Examples:
x 
y 
0 
2 
1 
5 
2 
8 
3 
11 
4 
14 

Linear
Relationship
To get NEXT y, add 3 to the current yvalue.
Two symbolic ways to represent this pattern are
NEXT = NOW + 3, starting at
2, and y = 3x + 2. 
x 
y 
0 
2 
1 
6 
2 
18 
3 
54 
4 
162 

Exponential
Relationship
To get NEXT y, multiply the current yvalue by
3.
Two symbolic ways to represent this pattern are
NEXT = 3NOW, starting at 2, and y = 2(3^{x}). 
Examples of other patterns introduced:
y = 3/x 

y = x^{3} 

This work with NOWNEXT patterns of change is also a precursor
to work with sequences and series in future units (see Course 3,
Unit 7, Recursion and Iteration).
