# Algebra Teacher's Activities Kit, Grades 6-12: 150 Ready-to-Use Activities with Real-World Applications

Algebra Teacher’s Activities Kit is a unique resource that provides 150 ready-to-use algebra activities designed to help students in grades 6—12 master pre-algebra and Algebra I. The book covers the skills typically included in an algebra curriculum. Developed to motivate and challenge students, many of the activities focus on real-life applications.

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## Overview

Algebra Teacher’s Activities Kit is a unique resource that provides 150 ready-to-use algebra activities designed to help students in grades 6—12 master pre-algebra and Algebra I. The book covers the skills typically included in an algebra curriculum. Developed to motivate and challenge students, many of the activities focus on real-life applications. Each of the book’s ten sections contains teaching suggestions that provide teachers with strategies for implementing activities and are accompanied by helpful answer keys. The activities supply students with quick feedback, and many of the answers are self-correcting.

Each activity stands alone and can be applied in the manner that best fits your particular teaching program. Algebra Teacher’s Activities Kit can be used as a supplement to your instructional program, to reinforce skills and concepts you’ve previously taught, for extra credit assignments, or to assist substitute teachers.

For quick access and easy use, the activities are printed in a big 8 1/2" x 11" format for photocopying and are organized into ten sections.

• THE LANGUAGE OF ALGEBRA (USING WHOLE NUMBERS) provides 15 activities, such as Using Square Numbers . . . Writing Phrases as Algebraic Expressions . . . Evaluating Expressions Using Exponents.
• INTEGERS, VARIABLES, AND EXPRESSIONS offers 15 activities, such as Using a Number Line to Graph Integers . . . Comparing Sums and Differences . . . Solving Word Problems with Integers.
• LINEAR EQUATIONS AND INEQUALITIES includes 24 exercises, such as Creating Word Problems . . . Solving Simple Percent Problems . . . Adding and Subtracting Matrices.
• GRAPHING LINEAR EQUATIONS AND INEQUALITIES is packed with 15 activities, including Graphing Points on the Coordinate Plane . . . Finding the Slope of a Line . . . Solving Systems of Equations by Graphing.
• BASIC OPERATIONS WITH MONOMIALS AND POLYNOMIALS offers 12 activities, such as Using the Terms of Polynomials . . . Finding Powers of Monomials . . . Finding Cubes of Binomials.
• FACTORS OF MONOMIALS AND POLYNOMIALS features 12 exercises, such as Finding the Missing Factor . . . Factoring Trinomials . . . Factoring the Sum and Difference of Cubes.
• FUNCTIONS AND RELATIONS provides 12 activities, including Identifying Functions . . . Finding the Domain of a Function . . . Evaluating the Greatest Integer Function.
• COMPLEX NUMBERS offers 12 activities, such as Simplifying Square Roots . . . Multiplying and Dividing Radicals . . . Using Complex Numbers to Simplify Expressions.
• POLYNOMIAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS gives you 13 exercises, including Solving Quadratic Equations by Factoring . . . Finding the Zeroes of Polynomial Functions . . . Borrowing and Repaying Money (with Interest).
• POTPOURRI offers you 20 exercises such as Cracking a Code . . . Building an Algebra Vocabulary Chain . . . Famous Mathematicians and Algebra.

## Product Details

ISBN-13:
9780787965983
Publisher:
Wiley
Publication date:
07/25/2003
Series:
J-B Ed: Activities Series, #10
Edition description:
First Edition
Pages:
348
Sales rank:
1,307,290
Product dimensions:
8.50(w) x 11.06(h) x 0.94(d)

## Algebra Teacher's Activities Kit

150 Ready-to-Use Activities with Real-World Applications

By Judith A. Muschla Gary Robert Muschla

#### John Wiley & Sons

Judith A. Muschla
All right reserved.

ISBN: 0-7879-6598-7

### Chapter One

The Language of Algebra
(Using Whole Numbers)

Every discipline has its own language. Soccer has its goals, figure
skating has its triple axels, and geometry has its polygons. Specialized
terminology makes it possible to understand the discipline.
How could someone describe baseball without mentioning the words
"innings," "strikes," and "outs"?

The fifteen activities of this section focus on the basic terminology
understand numerical relationships, describe operations, and reason
algebraically. By becoming fluent in the language of algebra, your students
will be prepared to move on to more advanced skills and concepts.

Teaching Suggestions for the Activities

1-1
Using the Order of Operations I

This activity requires your students to simplify an expression. The
expressions of the activity focus on the four basic operations-addition,
subtraction, multiplication, and division. No grouping symbols or exponents
are included. All numerical values are positive wholenumbers. The
symbols · and x are used to denote multiplication.

Introduce this activity by discussing the rules for the Order of Operations,
which are noted on the worksheet. Go over the example on the
worksheet together, noting the steps that are taken to arrive at the
numerical value.

Review the instructions on the worksheet with your students.
Explain that the first column lists the expression and the second column
the steps necessary to simplify an expression. Point out that each step
on the right can be paired with only one expression on the left and that
each step can be used only once. Remind your students to include the
numerical values of the expressions in their answers.

1-2 Using the Order of Operations II

This activity builds upon the skills addressed in Activity 1-1 and pro-vides
more practice with the Order of Operations. It includes the use of
grouping symbols.

Begin the activity by reviewing the Order of Operations with your
students. Emphasize that parentheses, braces, brackets, and the fraction
bar are all considered to be grouping symbols. Operations within these
symbols must be done first. Remind your students that a number
directly to the left of a grouping symbol implies multiplication.

Go over the instructions for the activity with your students. Note
that, along with identifying the incorrect answer, they are to explain why

1-3 Using the Order of Operations III

For this activity your students are to simplify various expressions using
the Order of Operations. Grouping symbols, exponents, and fractions
appear in the expressions. Unless your students are experienced with
simplifying expressions, you should assign Activities 1-1 and 1-2 before
assigning this one.

Start the activity by reviewing the Order of Operations. You should
also explain the concept of a base and an exponent. For example, in the
expression [2.sup.3] , 2 is called the base and 3 is the exponent. The exponent
means that 2 is used as a factor three times. Thus, [2.sup.3] means 2 x 2 x 2 or
8. Point out that a common error students make when working with
exponents is to multiply the base times the exponent, for example, in this
case, 2 x 3, obtaining the incorrect answer of 6.

Depending on the abilities and backgrounds of your students, you
may also wish to introduce the concept of a square number, which is a
number raised to the second power. For example, [5.sup.2] = 25 shows that 25
is a square number. Some other examples of square numbers are 9, 16,
36, 49, 64, and 81.

Make sure your students understand the instructions for the activity.
Remind them to follow the directions closely when placing their

1-4 Using Square Numbers

The purpose of this activity is to familiarize your students with square
numbers. Review the examples of square numbers included on the worksheet.
Depending on the needs of your students, you may wish to expand
the list.

Start this activity by drawing squares on the board or an overhead
projector. Draw: a 1 x 1-inch square, a 2 x 2-inch square, a 3 x 3-inch
square, and a 4 x 4-inch square. Emphasize to your students that the
number that represents the area in each square is a square number.

Next, explain the Square Number Theorem, referring to the examples
on the worksheet. Remind your students to find the square numbers
first, then add. You might mention that this procedure is the same as following
the Order of Operations.

Go over the instructions on the worksheet, and emphasize that the
last five problems require students to find the four square numbers that
add up to the number. This is the opposite of what they have to do in
problems 1 through 10. Suggest that guess and check is a good strategy
to use in solving the last four problems.

1-5 Translating Algebraic Expressions into Phrases

This activity requires students to complete a crossword puzzle with a
word omitted from a phrase. It provides practice in writing expressions.

Introduce the activity by explaining that an algebraic expression is
a combination of a variable (or variables) and a number (or numbers).
Note the examples on the worksheet. Emphasize that order matters
when subtracting and dividing. For instance, n - 3 means 3 less than a
number and not 3 minus a number. Incorrect order is a common mistake
when writing expressions.

Review the instructions on the worksheet with your students.
Remind them that this is a crossword puzzle, and encourage them to
focus their attention on the clues.

1-6 Writing Phrases as Algebraic Expressions I

This activity is a follow-up to Activity 1-5. For this activity, your students
are given a phrase containing an expression. They are to determine if
the expression is stated correctly. If it is incorrect, they are to correct the
expression.

Note the common errors that many students make with these types
of expressions. For example, they may overlook order. n - 8 is not the
same as 8 - n. They may also overlook grouping symbols. For example,
three times the sum of a number and 10 is 3(n + 10) or 3(10 + n), but not
3n + 10.

Review the instructions on the worksheet with your students.
Remind them that half of the problems on the worksheet are correct.
Students must correct the incorrect problems.

1-7 Writing Phrases as Algebraic Expressions II

This activity provides your students with more practice using algebraic
expressions. In each problem of this activity, your students are to think of
a number, do a series of numerical operations, and obtain an answer that
the teacher can predict. Your students, with the aid of algebra, are to
explain these problems as well as create problems of their own. To complete
this activity successfully, your students must be able to translate
phrases into algebraic expressions.

Start this activity by reviewing the Distributive Property. Go over
the instructions on the worksheet, then do the first problem as a class
exercise. Instruct your students to write the number they begin with in
the blank in Column I, recording each successive number in the blanks
provided. (You may wish to suggest that for problems 1 through 3 students
choose a number between 1 and 9 to keep the math simple.) Complete Column
II (for the first problem) as a class. The steps are n, which represents
the first number the students record, [n.sup.2] , [n.sup.2] - 4, [2n.sup.2] - 8, [2n.sup.2] , n. Point out
that in this problem your students end with the number with which they
started.

Note that your students should use a variable to represent a number
in Column II. If they are asked to use another number, they should
choose a different variable.

1-8 Simplifying Expressions by Combining Like Terms

This activity is designed to provide an introduction to combining similar
terms. Begin the activity by explaining basic notation: 3 x 4n can also be
written as 3 · 4n or 3(4n), all of which equal 12n. Also, n can be written
as 1n. 0 xn equals 0. Review the vocabulary on the worksheet and make
sure that your students understand the Distributive Property.

Go over the instructions on the worksheet. Remind your students to
simplify each expression completely.

1-9 Simplifying and Evaluating Expressions

In this activity your students will simplify expressions by combining like
terms and then evaluate the expressions. The problems on the worksheet
do not contain negative numbers or exponents.

Begin the activity by reviewing how to simplify expressions.
Depending on the abilities of your students, you may also find it helpful
to discuss the Distributive Property. Remind your students that expressions
such as 2a can be expressed as 2 x a and that b can be expressed
as 1 x b. Note that to substitute a number for a variable, your students
should write the number in place of the variable. For example, if a = 3,
then 2a = 2 x 3 or 6.

Go over the instructions on the worksheet with your students. Caution
them to pay close attention to grouping symbols and remind them
to always multiply before adding or subtracting.

1-10 Evaluating Expressions Using Exponents

This activity requires your students to evaluate expressions using exponents.
The answers will be positive whole numbers.

Begin this activity by discussing 0 and 1 as exponents. Note that [x.sup.1]
= x and that [x.sup.0] = 1. Depending on the background and abilities of your
students, you may also find it useful to review grouping symbols.

Go over the instructions with your students and discuss the examples
on the worksheet. Remind your students to be sure to follow the
Order of Operations where necessary.

1-11 Writing Equations

In this activity your students are provided with information that they
are to express in terms of an equation. Although they are not required
to solve the equation, they may be curious to find the solution. The equations
and their solutions are provided in the Answer Key.

Begin this activity by writing some equations on the board or an
overhead projector. Two examples are P = 4s, for finding the perimeter
of a square, and A = l x w, for finding the area of a rectangle. Explain that
the equal sign means that the number on the left of the equation has the
same value as the number on the right. Encourage your students to volunteer
examples of other equations, which you may list on the board or
an overhead projector. As you do, emphasize the equality and the meaning
of the variables. Also review key words such as "variable," "more
than," and "product."

Go over the instructions on the worksheet with your students. Caution
them to be as accurate as possible in writing equations.

1-12 Writing Equations and Inequalities I

For this activity your students must recall, find, research, and synthesize
various facts. (Most facts fall within the category of general knowledge.)
Your students are then required to compare numbers and write
an equation or inequality.

Since your students may need to conduct minor research to find
some of the information necessary to complete this activity successfully,
you may prefer to assign this activity as homework. If you have
there. Another option is to reserve time in your school's library
so that students may use reference sources. This is a nice approach,
because it provides an example to students of how math is linked to
other areas.

Start this activity by reviewing the meaning of an equation. Note
that the values on both sides of an equal sign are the same, and emphasize
that in an inequality the numbers are not equal. If necessary,
explain the meanings of the symbols > and <, which appear on the worksheet.

Review the instructions on the worksheet with your students.
Encourage them to concentrate on the phrases as they work to complete
the activity.

1-13 Writing Equations and Inequalities II

This activity builds on the skills covered in Activity 1-12 and provides
more practice with equations and inequalities. Along with the symbols
> and <, the symbols [Greater than or equal to] and [less than or equal to] are used in many of the equations.

Start the activity by discussing the symbols on the worksheet, then
go over the instructions. Depending on the abilities of your students, you
may find it helpful to do the first problem together. Remind students to
read each problem carefully before writing an equation.

1-14 Identifying the Solution of an Equation

In this activity your students are required to match solutions to equations.
They are to substitute a given value and determine whether or not
it is a solution to the equation. Obtaining the correct answers will enable
them to complete a statement at the bottom of the worksheet.

Begin the activity by reviewing the Order of Operations. Because
there are no grouping symbols, your students should substitute, then
multiply and divide in order from left to right, then add and subtract.

Go over the instructions on the worksheet. Note that of the five possible
solutions above the four equations, only one is not a solution for any
of the equations. Your students are to write the letter of each solution in
the blank before the equation. After determining the correct solutions,
they are to write the letters in order to complete the statement at the
bottom of the worksheet.

1-15 Determining the Solutions of Equations and Inequalities

This activity builds on the skills covered in Activity 1-14. For this activity
your students are given twenty equations and inequalities for which
they are to choose the solutions.

Begin the activity by reviewing the meaning of the equal sign and
the four inequality symbols: >, <, [greater than or equal to] and [less than or equal to] Go over the
instructions with your students. Emphasize that they are to record the letter of every solution.
Some problems have more than one. If no solution is given, they are
to record the letter that precedes "none."

1-1. 1. 8 - 6 + 5 = 7 2. 3 + 8 + 4 = 15 3. 3 + 2 + 4 = 9 4. 21 - 14 + 6 = 13
5. 2 + 9 - 1 = 10 6. 48 + 2 - 7 = 43 7. 3 + 25 - 2 = 26 8. 4 + 12 - 16 =
0 9. 5 + 2 - 4 = 3 10. 60 - 60 + 2 = 2 11. 6 + 18 + 4 = 28 12. 1 + 6 -
2 = 5

1-2. 1. 15 - 2 x 3 = 39 is incorrect. Subtraction was done first, then multiplication
was done. 2. 16 + 8 ÷ 2 = 12 is incorrect. Addition was done first,
then division was done. 3. 3[2 + 4] = 10 is incorrect. Grouping symbols
were ignored; multiplication was done first, then 4 was added. 4. 50 ÷
(5 x10) = 100 is incorrect. Grouping symbols were ignored; division was
done, then multiplication was done. 5.

Continues...

Excerpted from Algebra Teacher's Activities Kit
by Judith A. Muschla Gary Robert Muschla
Excerpted by permission.
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