Project
This project introduces the idea of a mathematical
group. Since the properties that define a group are
familiar to your students, this can be an accessible
project even though it resembles an introduction
to abstract algebra. If you want to discus
6
Cumulative Review
Cumulative Review
Assessment Resources
Multiple Choice
For Exercises 6 and 7, determine which equation
describes the given transformation.
1. Simplify the following expression.
x 25y 29
x 211y 27
216
A. x 216
B.
y
6
C. x 2
y
D.
y2
x6
x
4
Go
Test
For a chapter test, go to
Web Code: bfa-0453
nline
PHSchool.com
Assessment Resources
Multiple Choice
Open Response
1. Which matrix is the row-reduced echelon form
of the following matrix?
6. Solve the following system using Gaussian
Elimination.
Investigation Overview
This investigation continues the extension of the real
numbers into the complex numbers much as the
story continued historically. Mathematicians up until
the 19th century did not accept complex numbers
as having any actual usefulnes
Mathematical Reflections
5B
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you graphed exponential functions.
You wrote rules for exponential functi
Investigation Overview
In this investigation, students begin by solving
systems of two equations in two unknowns. They
review the solution techniques of substitution and
elimination that they learned in CME Project
Algebra 1. Then they extend this work to
Chapter 5
Exponential and
Logarithmic Functions
In this chapter, students extend the definition
of exponents to include rational and real-valued
exponents. They make this extension in a way that
preserves the laws of exponents. Along the way
they review p
Mathematical Reflections
5A
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you evaluated and simplied
exponents. You developed the laws of exponents
Investigation Overview
This investigation is an introduction to the power
of using matrix multiplication to model all sorts of
multivariate phenomena in a way that is conceptually
and notationally simple.
Basically, whenever you have a linear system with
Project
Project: Using Mathematical Habits
More Matrix Operations
In this chapter, you looked at several applications
of matrix algebra, including Gaussian Elimination,
matrix addition, and matrix multiplication. There
are several other operations on matr
Developing Students
Mathematical Habits
Key mathematical habits in this chapter include:
EXTENSION By making strategic choices that
preserve the laws of exponents, students extend the
set of numbers that can be used as exponents to
include all real number
2.3
Lesson Overview
Algebra With Functions
GOALS
Compose functions.
The basic rules of algebra tell you how the operations of addition and
multiplication behave. Addition and multiplication are operations that
combine numbers. In this lesson, you will le
4.13
Lesson Overview
Probability Models
GOAL
Analyze sequences of repeated probabilities.
Consider all those bugs from the Lesson 4.12 Maintain Your Skills exercises.
They all were moving around among the three corners of a triangle, named
T, L, and R. T
Chapter 4
Linear Algebra
This chapter introduces matrices both as shorthand
(to record all the information in a system of linear
equations) and as mathematical objects in their
own right. Students learn to translate between
systems of linear equations and
6
Chapter Test
Go
Test
For a chapter test,
go to Web Code: bfa-0653
nline
PHSchool.com
Assessment Resources
Chapter Test
page 1 of 2
Multiple Choice
1. Which equation describes the graph of y x 2 after a translation 3 units to
the right and 2 units up?
A.
Project Overview
This project explores the functional equation that
exponential functions satisfy: f(x 1 y) = f(x) ? f(y).
Students start with a very small set of assumptions
about this function and try to build an understanding
of how any function that s
Mathematical Reflections
6B
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you learned to write any
composition of translations and dilations as an
Investigation Overview
Throughout this chapter, students have studied
exponential functions. In the last lesson of
Investigation 5B, students proved that exponential
functions are one-to-one, so they must have
inverses. In this investigation, students stu
8.1
Lesson Overview
Getting Started
GOAL
Warm up to the ideas of the investigation.
The values of trigonometric functions are related to the coordinates of
points on a circle with radius 1 centered at the origin.
Olivia watches Paul walk around a circle.
Developing Students
Mathematical Habits
Key mathematical habits in this chapter include:
VISUALIZATION Students visualize graphs as
transformations of the basic graphs, seeing them
as translations, scalings, and reflections or as
compositions of these tra
3C
Mathematical Reflections
In this investigation, you found relationships between
magnitudes and arguments of factors and products.
You also graphed the solutions to equations in the form
x n 2 1 5 0. These exercises will help you summarize what
you have
4
Mid-Chapter Test
Go
nline
PHSchool.com
For a mid-chapter test,
go to Web Code: bfa-0452
Mid-Chapter Test
Assessment Resources
Multiple Choice
Open Response
1. What is the solution to the following system?
2x 2 5y = 1
3x 2 4y = 5
A. (27, 3)
B. (3, 1)
C.
Investigation Overview
Matrices are much more than tables. They have a
mathematical life of their own. They can be added,
subtracted, multiplied, and multiplied by scalars
(real numbers). The algebra of matrices is similar
to the algebra of numbers studen
Investigation Overview
This investigation reintroduces the laws of exponents
as defined for positive integer exponents. It asks
students to use those laws as the basis for deciding
how to extend the definition to zero, negative,
and rational exponents. As
Chapter 6
Graphs and
Transformations
In this chapter, students extend the graphing skills
they learned in CME Project Algebra 1 and Geometry
to include more kinds of graphs. They also learn to
recognize transformations of these graphs and to
connect trans
Lesson Overview
1.10 Getting Started
GOAL
Warm up to the ideas of the investigation.
You can use a table to help you rewrite a recursive denition for a function
as a closed-form denition.
For Exercises 15, make a table of the function values for inputs b
6.3
Lesson Overview
Translating Graphs
GOAL
Recall the lumping method of factoring from Chapter 2. You can also
use the lumping technique to help you graph equations.
Minds in Action
episode 24
Sasha and Derman are trying to graph the equation y = (x 2 3)
Developing Students
Mathematical Habits
These key habits are developed in this chapter.
EXTENSION Students see the decisions made in
deciding how to calculate with complex numbers as
an extension from the real numbers in such a way
as to preserve the basi
5
Mid-Chapter Test
Go
nline
PHSchool.com
For a mid-chapter test, go
to Web Code: bfa-0552
Mid-Chapter Test
Assessment Resources
Multiple Choice
7. Use the sequence below.
1. Which of the following expressions is NOT equal
to 5 12 ?
A.
A5 6B 2
C.
5 24
5 12
Mathematical Reflections
4A
EXERCISES 68 At the start of the investigation,
you may have assigned these as Questions 13 for
students to think and write about.
In this investigation, you learned how to solve a system
of three equations in three unknowns. Y