Required Text:
Discovering Algebra, An Investigative Approach by Jerald
Murdock, et al. Key Curriculum Press, 2007.
Course Description:
This course is designed to expose students to a variety of
algebraic concepts and applications throughout the summer session. At the end of
the program, students will have studied and applied the skills in the fol lowing
areas : statistics and probability; variation and linear models ; quadratic and
exponential models; and functions and the transformations of functions. Students
will perform daily investigations where they will be able to discover algebraic
methods and concepts . Frequently the students will carry out activities in which
they will apply the concepts they discovered though their investigations. In
addition , investigations are followed up with discussions intended to elaborate
on the real world meanings of their findings.
It is important to note the goal of this course is to
exposed students to challenging algebraic concepts, and not for them to master
these concepts. As a result the focus of the course will not be on homework
assignments or test, but rather on activities, investigations and discussions. .
In order to tie the many concepts together, chapter review problems will be
solved and presented as a class. However, the main focus of this course remains
to be on discovery, discussion, and application.
The course has been separated into three units by week. A
brief out line of the three units is as follows:
Week 1: Data Explo ration , Probability, Variation,
Graphs, and Linear Equations.
During this week students will work with data collections and statistics,
study probability, proportions, variation, and be introduced to linear
equations. Some activities will include investigating variation with a bicycle
gear, and using jellybeans to discover probability.
Week 2: Point-Slope, Systems of Equations ,
Inequalities, and Functions
This week students will work with Point-Slope form to fit data, find out
what happens when you have two linear equations on the same graph, and learn
about
functions. Week 3: Transformation, Quadratic Equations,
Geometry, and Project
Students will now move their functions around the coordinate plane, discover
how to solve and graph second-degree equations, have an introduction to Geometry
and Trigonometry , and have the opportunity to present their project .
Algebra and Its Applications
Week 1: Data Exploration, Proportions and Variation, Graphs and Linear
Equations
Monday
Data Exploration |
Morning |
Introduction, Getting to know each
other; Math Review ; Create and interpret graphical displays of data and
calculate and understand measures of central tendency; Bar graphs, dot
plots , histograms, and stem-and-leaf plots |
1.1 Pulse Rates
1.2 Intro to Central Tendency
1.3 Box Plots
1.4 Hand spans |
| Afternoon |
Collect and interpret data;
Understanding, creating, and making sense of a Cartesian square (two
variable equations ); Estimating. |
1.5 Exploring a Conjecture
1.6 Let it Roll!
1.7 Guesstimating |
| Evening |
Using Matrices to organize and
combine data |
1.8 Row x Columns Matrix
Multiplication
Chapter 1 Review |
Tuesday
Proportional Reasoning and Variation |
Morning |
Proportion: what are they? How do you
set them up? And how do I solve them? Converting measurements to solve
proportions; Working with percents; Direct Variation |
2.1 Multiply and Conquer
2.2 Fish in the Lake
2.3 Converting Centimeters into Inches
2.4 Ship Canals |
| Afternoon |
Inverse Variation, Evaluating
expressions, Order of Operations |
2.5 Speed versus Time
2.7 Number Tricks |
| Evening |
Undoing Operations |
2.7 Just Undo It! Chapter 2 Review |
Wednesday
Linear Equations and Graphs |
Morning |
Linear Equations, Recursive
Sequences, Linear Plots, Time-Distance Relationships |
3.1 Recursive Toothpick Patterns
Computer Lab
3.2 On the Road Again
3.3 Walk the Line |
| Afternoon |
Linear Equations, Slope-Intercept
Form, Rate of Change , Slope |
3.4 Working out with equations
3.5 Wind Chill |
| Evening |
Solving equations using the balancing
method |
3.6 Balancing Pennies
Chapter 3 Review |
Thursday
Fitting a Line to Data |
Morning |
A Formula for Slope; Writing a Linear
Equation to Fit Data; Point-Slope Form of a Linear Equation |
PEMDAS
4.1 Step Right Up
4.2 Beam Strength
4.3 Point-Slope Form |
| Afternoon |
Equivalent Algebraic Equations;
Writing Point-Slope Equations to Fit Data |
4.4 Equivalent Equations
4.5 Life Expectancy |
| Evening |
More on Modeling; Applications of
Modeling |
4.6 Bucket Brigade
4.7 What’s My Line |
| Friday |
Morning |
Data Collection and Modeling |
4.8 Toyland Bungee Jump
Chapter 4 Review |
| Afternoon |
Data Collection and Modeling |
Group Assessment |
