Pre Algebra A
Math Remediation
Unit 1 – Introduction to Algebra
Unit Objectives:
 Evaluate mathematical expressions.
 Use the order of operations to simplify expressions.
 Solve equations or inequalities.
 Write an expression, equation, or inequality for a word sentence.
 Use inverse operations to write a related equation or inequality.
 Write an equation for a word problem.
Lesson Objectives:
Lesson 1: Mathematical Expressions
 Evaluate a variable expression.
 Simplify a numerical expression.
Remediation:
 http://www.quia.com/cb/116711.html is an interactive pre-algebra game for two players. Can be used with
the Smart Board or individual laptops.
 http://www.bbc.co.uk/education/mathsfile/shockwave/games/postie.html is in interactive site that allows
students to evaluate a variable in an expression. Teacher can choose the skill level. Have students
working at their desk write down the problem and solve.
 Have students complete the activity below. This is a fun way to teach students to follow a mathematical
rule and evaluate an expression.
Lesson 2: Order of Operations
 Use the order of operations to simplify a numerical expression.
 Use the order of operations to evaluate a variable expression.
Remediation:
 http://www.tki.org.nz/r/wick_ed/maths/interactives_matho2.php . This is a great website of order of
operation activities. You can select 1, 2, 3 or 4 players. Use on the Smart Board and have students not
playing to solve equations at their desk.

http://www.funbrain.com/cgi-bin/shtml.cgi?A1=../algebra/index.html . Another website where the teacher
can choose the skill level. A review of order of operations.
Lesson 3: Equations
 Find the solutions to an equation with a given replacement set.
Remediation:
 http://www.shodor.org/interactivate/activities/WholeNumberCruncher/ is an activity where students
must find a solution set for a function. Students will also be asked to identify the function or the rule.
Lesson 4: Inequalities
 Find the solutions to an inequality with a given replacement set.
Remediation:
 The instructor may want to place the following on a poster or the wall to provide a visual cue for students.
Symbol
>
<
≥
≤
Words
greater
than
less than
greater
than or
equal to
less than
or equal to
Example
x+3>2
7x < 28
5≥x-1
2y + 1 ≤ 7
Solve 5x > 10
A:
x>2
B:
x<2
C:
x > -2
D:
x < -2
Solve the inequality 3x - 7 < 5
A:
x < -2/3
B:
x>4
C:
x<4
D:
x < -4

Help students relate how an equation or inequality can be used to represent a given situation:
A.
Post vocabulary on Word Wall. Have students look at the vocabulary and tell a partner something they know
about one of the vocabulary words.
Tell students they will need to understand inequalities before they can get a driver’s license. Show them on the
overhead or on the interactive white board the picture of a speed limit sign (below). Write words to describe the
inequality, then math symbols to represent the speed.
Other examples of inequalities in real-life can be found in advertising. Have them write words and symbols
for the home prices sign. http://www.uen.org/Lessonplan/downloadFile.cgi?file=23514-2-29497Picture_1_and_3.pdf&filename=Picture_1_and_3.pdf
Another example for an inequality is the minimum height sign at an amusement park. Discuss words and
write words and symbols for h ≥ 42”.
Have each student write the words and the inequality for a real-world situation. Then, do Mix-Freeze-Pair,
where student mix around the room until you say “Freeze”. If movement is a problem for class
management, then have students pass around their examples on index cards until you say “Freeze”, then
have students write down examples. They stop by a partner and share their inequality. Partners write the
inequalities, so that after four rounds of mixing, freezing and sharing, they will have an additional four
examples of inequalities from real-world situations.
B. Do Breathless Comparisons as follows:
Tell students they will be participating in a breath-holding contest to see how many second they can hold
their breath. Watch the clock and count the seconds as they hold their breath as long as they comfortably
can. When they release their breath, they should write the number of seconds they held their breath. Have
them take and release two deep breaths, then say “Go” and begin counting seconds.
Once all have held, released and recorded their breath. Ask the person who held their breath the longest to
state their seconds. Have students use their own initial as a variable and write an inequality comparing their
time to the winner’s time (ex. J < 90). Then, ask one student who was neither the first to release nor the last
to tell how long they held breath (ex. 30 seconds). Using a variable to represent that students time, have
students write an inequality comparing their breath to that student=s (35>x).
Next, have them ask a person sitting by them how long that person held their breath and write an inequality
using their initial as the variable to represent their time and comparing to the number of seconds for the
other person. Have several students tell how their inequality statement represents this information.
Then ask, “What if we added 10 seconds to our own time and compared that to the winner’s time? How
might we write that expression (ex. L + 6 < or > 90)? Would our inequality symbol be the same as it was the
first time we compared? What if you doubled your time and subtracted 15 seconds from it? What would the
inequality comparing your time to the winner’s time look like (ex. 2J – 15 < or > 90)?”
Tell them you will solve an inequality to find a reasonable time for someone. Use one of their inequalities
and solve it. Ask, who has a time that would be reasonable as a solution for the inequality you modeled
solving (ex. 2j – 15 > 90, so j > 52.5). Who has a solution that would be reasonable here?
Name That Number (Writing and Graphing Inequalities)
Divide the class into two teams. Tell them you have stored a number you want them to guess. The number
is between -25 and 25 (or choose any range appropriate for the class). Have each team bid for the number
of questions they will need to ask you in order to guess the number (ex. “We can name that number in 5
questions!). The team, who bids the lowest, begins asking questions. Questions must be in the form of an
inequality such as, “Is x less than 0?” As the question is asked, you write an inequality for that question such
as x < 0. The team continues to ask all the questions for their bid. Then, they must accurately guess the
number. If they are able to guess the number correctly after their last question, they earn a point. If not, the
opposing team gets to ask the number of additional questions to reach their bid, then, guesses the number.
Have students write inequalities for each guess so that the inequality symbol shows the correct response.
For example, if a team asked, “Is x less than 0?", and that was not true, the class would write 0 ≤ x ≤ 25.
Begin by having them write -25 < x < 25. Type the question into the calculator and press enter to check for
yes (1) or no (0). Have them write a new inequality for each guess.
TIC TAC TOE Game Practice. Have students sketch a large 3x3 table on their paper, or copy the attached
handout. The cells in the table must have space to write a problem, solve, and graph the solution. Have
them copy the following problems into the cells in any order. They should work with a partner or team to
solve all the problems. Then, read the answers out of order and have students put a big C each time they
see a correct answer in their Tic Tac Toe. Read until several people have three in a row. This may be
assigned as homework, and reviewed at the beginning of the next class.
2n + (-7) ≥ 1 (n ≥ 4)
14 < 5p − (-9) (1 < p)
4m + 2 < 14 (m < 3)
3 > b/2 − 5 (3 > 16)
3w ≤ 12 (w ≤ 4)
-2r + 1 > 5 ( r > -2)
6 < -2s ( -3 > s )
W + 4 ≤ 10 ( w ≤ 6 )
x/-3 < 9 (x > -3)
* If the above inequalities are too difficult, include an easier skill level. You may opt not to graph.
Lesson 5: Inverse Operations, Part 1
 Use inverse operations to write a related equation.
 Use inverse operations to solve an equation.
Remediation:
 http://www.aaamath.com/g723-evaluate-1variable.html is an interactive activity where students must
evaluate expression for one variable.
 Use the slide below as a small group activity or independent activity. Delete answers on the student copy.
5-Minute Check
Solve each equation using the inverse operation.
1. 5 + r = 12
7
2. 34 = 2s
17
3. 7 = g/12
84
4. 4.37 = y – 9.32 13.69
5. Astronomers keep track of about 7000 objects. One out of every ten
of these is a satellite. The rest are “space trash.” About how many
satellites are astronomers tracking?
a. Define a variable.
s = satellites
b. Write an equation.
10s = 7000
c. Solve for the number of satellites. 700
d. Check your solution.
Lesson 6: Inverse Operations, Part 2
 Use inverse operations to write a related inequality.
 Use inverse operations to solve an equation.
 Use inverse operations to solve an inequality.
Remediation:

Use the slide below as a small group activity or independent activity. Delete answers on the student copy.
Inequalities
For the given value, state whether each inequality is true
or false.
a. x – 7 > 16, x = 15
15 – 7 > 16
8 > 16
This sentence is false.
b. 16  2h/12 + 11, h = 24
16  2*24/12 + 11
16  4 + 11
16  15
This sentence is true.

Use the activity below to solve in small groups. If students have trouble solving, have students identify
which inverse operation would be used to solve. Print out several copies and laminate. Keep in a manila
envelope to be used as a math station activity
Some of the equations below have the number 5 as their solution. If
5 is a solution to an equation, write the variable used in that
equation in one of the boxes below. When you have investigated
each equation, rearrange the letters in the boxes to form the twoword message.
©Glencoe/McGraw-Hill Pre-Algebra
Lesson 8: Writing Expressions for Word Phrases
 Write a variable expression for a word phrase.
Remediation:
 Use the following worksheet at a math station or in a small group. Print out and make copies. An
electronic copy can be found at
http://www.phschool.com/atschool/phmath/pdfs/puzzles/phsbm024.pdf .
Lesson 9: Equations and Inequalities for Word Sentences
 Write an equation for a word sentence.
 Write an inequality for a word sentence.
Remediation:
 Use the following worksheet in a small group. Electronic copy found at
http://www.phschool.com/atschool/phmath/pdfs/puzzles/phsbm056.pdf .
Lesson 10: Problem-Solving Strategies
 Write an equation for a word problem.
 Use the five-step plan to solve a simple word problem.
Remediation:
 Have student write the symbols above the number sentence as they work. Then have then put the
symbols together to make their equation. Remember to tell students that “a number” is the variable-that’s
where they put the “x”! Also, remind students that where the “is” is in the number sentence is where the
equal sign will go! Practice! This skill may take students several lessons to master. Be patient and keep
practicing!
Ex:
“X”
+
9 = 15
A number increased by nine is fifteen.

Use the following in small groups or as an independent activity. Activities increase in skill level. Delete
answers on the student’s copy.
Write an equation:
Sentence
Algebraic Equation
A number increased by nine is fifteen.
y + 9 = 15
Twice a number is eighteen.
2n = 18
Four less than a number is twenty.
x - 4 = 20
A number divided by six is eight.
k/6 = 8
Write an equation:
Sentence
Algebraic Equation
Twice a number, decreased by twenty-nine, is seven.
2t - 29 = 7
Thirty-two is twice a number increased by eight.
32 = 2a + 8
The quotient of fifty and five more than a number is ten.
Twelve is sixteen less than four times a number.
12 = 4x - 16
Write an equation:
Sentence
Algebraic
Equation
Elena is x years old. In thirteen years she will be
twenty-four years old.
x + 13 = 24
Each piece of candy costs 25 cents. The price of
h pieces of candy is $2.00.
25h = 200 or
Suzanne made a withdrawal of d dollars from her
savings account. Her old balance was $350, and
her new balance is $280.
350 - d = 280
A large pizza pie with 15 slices is shared among
p students so that each student's share is 3
slices.
.25h = 2.00
Have students take this short quiz at the end of the lesson:
Twice a number is twenty-eight.
x + 2 = 28
2x = 28
None of the above.
The quotient of thirty-nine and a number is three.
39w = 3
39 - w = 3
None of the above.
Five less than three times a number is forty-six.
5 - 3t = 46
3t - 5 = 46
None of the above.
Three is twenty-one, divided by the sum of a number
and five.
3(m+21) = 5
3m + 5 = 21
None of the above
Eric had $197 in his savings account before he was
paid his weekly salary. His current savings balance is
$429. How much money does Eric earn each week?
197 + 429 = n
197 + n = 429
197n = 429
None of the above.

Use the puzzle below to review the unit’s vocabulary and terms. Go to
http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=adj&wcsuffi
x=0151 for an electronic version of this puzzle. Print out several copies and have students complete in
small groups.