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Lesson 1-1 A Plan for Problem Solving
Lesson 1-2 Variables, Expressions, and Properties
Lesson 1-3 Integers and Absolute Value
Lesson 1-4 Adding Integers
Lesson 1-5 Subtracting Integers
Lesson 1-6 Multiplying and Dividing Integers
Lesson 1-7 Writing Equations
Lesson 1-8 Problem-Solving Investigation: Work Backward
Lesson 1-9 Solving Addition and Subtraction Equations
Lesson 1-10 Solving Multiplication and Division Equations
Five-Minute Check
Main Idea and Vocabulary
Targeted TEKS
Example 1: Use the Four-Step Plan
Example 2: Use the Four-Step Plan
• Solve problems by using the six-step plan.
• Conjecture
– An educated guess
The Six Step Problem Solving Process
EXPLORE
1 – Begin with the end in mind – WHAT ARE THEY
ASKING FOR?
2 – What do I know? – WHAT AM I GIVEN IN THE
PROBLEM?
PLAN
3 – What do I NEED to know? – WHAT AM I NOT GIVEN IN
THE PROBLEM?
4 – How am I going to get it? – Frequently, this is the
formula.
5 – SOLVE the problem
6 – CHECK IT – DOES THE ANSWER MAKE
SENSE?
Use the Six-Step Plan
HOME IMPROVEMENT The Vorhees family plans to
paint the wall in their family room. They need to
cover 512 square feet with two coats of paint. If a 1gallon can of paint covers 220 square feet, how
many 1-gallon cans of paint should they purchase?
Begin w/ the end in mind – Asking for # of gal. of paint
What do I know?
Using two coats of paint, so we must double
the area to be painted.
1 can covers 220 sq. ft
Need to know? Total number of sq. ft to be covered.
How am I going to get it? They will be covering 512 × 2
square feet or 1,024 square feet.
Use the Six-Step Plan
Solve
Divide 1,024 by 220 to determine how many
cans of paint are needed.
1,024 ÷ 220 ≈ 4.7 cans
Check
Since they will purchase a whole number of
cans of paint, round 4.7 to 5.
Answer: They will need to purchase 5 cans of paint.
HOME IMPROVEMENT Jocelyn plans to paint her
bedroom. She needs to cover 400 square feet with
three coats of paint. If a 1-gallon can of paint covers
350 square feet, how many 1-gallon cans of paint
does she need?
A. 2
B. 3
0%
D
A
B
0%
C
D
C
0%
A
D. 5
A.
B.
0%
C.
D.
B
C. 4
Use the Six-Step Plan
GEOGRAPHY Study the table. The five largest
states in total area, which includes land and water,
are shown. Of the five states shown, which one has
the smallest area of water?
Use the Six-Step Plan
Explore Begin with the end in mind
You need to find the water area.
What do you know?
You are given the total area and the land
area for five states.
Plan
What do I need to know?
Total water area.
How am I going to get it?
Subtract the land area from the total area for
each state.
Use the Six-Step Plan
Solve
Alaska = 615,230 – 570,374 = 44,856
Texas = 267,277 – 261,914 = 5,363
California = 158,869 – 155,973 = 2,896
Montana = 147,046 – 145,556 = 1,490
New Mexico = 121,598 – 121,364 = 234
Check
Compare the water area for each state to
determine which state has the least water
area.
Answer: New Mexico has the smallest area of water
with 234 square miles.
GEOGRAPHY Study the table.
The five smallest states in total
area, which includes land and
water, are shown. Of the five
states shown, which one has
the smallest area of water?
A.
B.
C.
D.
Connecticut
Delaware
Hawaii
New Jersey
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
Five-Minute Check (over Lesson 1-1)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Order of Operations
Example 1: Evaluate Algebraic Expressions
Example 2: Evaluate Algebraic Expressions
Example 3: Evaluate Algebraic Fractions
Example 4: Identify Properties
Example 5: Find a Counterexample
• Evaluate expressions and identify properties.
• Variable
• A letter that
represents a number
• Algebra
• Expressions with
variables
• algebraic expression
• Contains a variable,
an operator, and a #
• numerical expression
• Contains ONLY
numbers and
operators - NO
VARIABLES!
• Evaluate
• Replace variables
with numbers and
“do the math”
• Order of Operations
• Process of “doing the math”
• Powers
• Repeated Multiplication
• Property
• Something that is ALWAYS true!
• Counterexample
• An example that shows something is NOT true
NOTES
Four Properties
1. Commutative
 Addition – a + b = b + a
 Multiplication – a * b = b * a
2.
Associative
 Add – (a + b) + c = a + (b + c)
 Mult - (a * b) * c = a * (b * c)
3. Distributive – MOST IMPORTANT!!
 a (b + c) = ab + ac
4. Identity
 Add = a + 0 = a
 Mult = a * 1 = a
BrainPops:
The Associative Property
The Commutative Property
The Distributive Property
Order of Operations
Please Excuse My Dear Aunt Sally
1) Parenthesis
2) Exponents
3) Multiply and Divide – IN ORDER from LEFT TO
RIGHT
4) Add and Subtract - IN ORDER from LEFT TO RIGHT
Evaluate Algebraic Expressions
Evaluate 3r + 2s – 4 if r = 6 and s = 3.
3r + 2s – 4 = 3(6) + 2(3) – 4
Replace r with 6 and s
with 3.
= 18 + 6 – 4
Do all multiplications first.
= 24 – 4
Add and subtract in order
from left to right.
= 20
Answer: 20
Evaluate 5p – 3s + 2 if p = 2 and s = 1.
A. –4
B. –1
C. 5
D. 9
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Evaluate Algebraic Expressions
Evaluate q2 – 4r – 1 if q = 5 and r = 6.
q2 + 4r – 1 = (5)2 – 4(6) – 1
= 25 – 4(6) – 1
Evaluate powers before
other operations.
= 25 – 24 – 1
Multiply.
=1–1
Add and subtract in order
from left to right.
=0
Answer: 0
Replace q with 5 and r
with 6.
Evaluate the expression b2 + 3c – 5 if b = 4 and c = 2.
A. 9
B. 17
0%
C. 20
D. 22
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Evaluate Algebraic Fractions
Evaluate the expression
Replace q with 5 and s with 3.
Do all multiplications first.
Divide.
Answer: 2
Evaluate the expression
A. 0
0%
B. 1
C. 2
D. 4
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Identify Properties
Name the property shown by 12 ● 1 = 12.
Multiplying by 1 does not change the number.
Answer: This is the Identity Property of Multiplication.
BrainPops:
The Associative Property
The Commutative Property
The Distributive Property
Name the property shown by the statement
3 ● 2 = 2 ● 3.
A. Associative Property of
Multiplication
B. Commutative Property of
Addition
D. Distributive Property
0%
D
A
B
0%
C
D
C
A
0%
A.
B.
0%
C.
D.
B
C. Commutative Property of
Multiplication
Find a Counterexample
State whether the following conjecture is true or
false. If false, provide a counterexample.
The sum of an odd number and an even number is
always odd.
Answer: The conjecture is true.
State whether the following conjecture is true or
false. If false, provide a counterexample.
Division of whole numbers is associative.
A. true
1.
2.
A
B
B. false;
15 ÷ (6 ÷ 2) ≠ (15 ÷ 6) ÷ 2
0%
B
A
0%
Five-Minute Check (over Lesson 1-2)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Compare Integers
Example 2: Compare Integers
Example 3: Expressions with Absolute Value
Example 4: Expressions with Absolute Value
Example 5: Expressions with Absolute Value
• Compare and order integers and find absolute
value.
• Coordinate
• Negative number
• Less than 0
• positive number
• Greater than 0
• Integer
• ALL – and + whole
numbers
• A number that
corresponds to a
point
• Inequality
• “Mathlish sentence”
that compares 2
numbers
• absolute value
• DISTANCE FROM
ZERO!
NOTES
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
•Numbers to the LEFT of zero are NEGATIVE
•Numbers to the RIGHT of zero are POSITIVE
•Numbers to the RIGHT are always GREATER than
numbers to the left.
•INTEGERS –
– Whole numbers on a number line.
– Include EVERY positive and negative number!!
Number Lines, Integers, and Inequalities - CONT
-5 -4 -3 -2 -1 0 1 2 3 4
•INEQUALITY SYMBOLS
5 6
“<“ – “Less than”
“>” – “Greater than”
“≠” – “Not equal to”
“≤” – “Less than or equal to”
“≥” – “Greater than or equal to”
•REMEMBER
– THE ALLIGATOR ALWAYS EATS THE BIGGEST
NUMBER!
ABSOLUTE VALUE
-5 -4 -3 -2 -1 0 1 2 3 4
•Absolute value
– ALWAYS positive
•Symbol is two vertical lines
– |x|
– Treated like Parenthesis!!!!
•Examples
|4|=4
|-5| = 5
|0| = 0
5 6
Compare Integers
Replace ● with < or > to make –2 ● –1 a true
sentence. Use the integers graphed on the number
line below.
–2 is less than –1, since it lies to the left of –1.
Answer: –2 < –1
Replace ● with <, >, or = to make –2 ● 2 a true
sentence. Use the integers graphed on the number
line below.
A. –2 < 2
B. –2 > 2
C. –2 = 2
D. None of the above.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Compare Integers
FOOTBALL The table below shows the number of
yards rushing for several players on a football team
during one game. Order these statistics from least
to greatest.
Compare Integers
Graph each integer on a number line.
Write the numbers as they appear from left to right.
–19, –10, 4, 5, 8
Answer: The number of yards rushing are –19, –10, 4,
5, and 8 from least to greatest.
WEATHER The table below shows the temperatures
for several cities on January 25, 2006. Order these
statistics from least to greatest.
0%
A. –24, 26, 84, 75
B. –24, 26, 75, 84
C. –24, 75, 84, 26
D. –24, 84, 75, 26
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Expressions with Absolute Value
Evaluate |5|.
The graph of 5 is 5 units from 0 on the number line.
Answer: |5| = 5
Evaluate |–3|.
A. –9
B. –3
C. 3
D. 9
1.
2.
3.
4.
A
B
C
D
Expressions with Absolute Value
Evaluate |6| – |–5|.
|6| – |–5| = 6 – |–5|
The absolute value of 6 is 6.
=6–5
The absolute value of –5 is 5.
=1
Simplify.
Answer: 1
Evaluate |9| – |–6|.
A. –3
B. 3
C. 6
D. 15
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Expressions with Absolute Value
Evaluate |x| + 13 if x = –4.
|x| + 13 = |–4| + 13
Replace x with –4.
= 4 + 13
|–4| = 4
= 17
Simplify.
Answer: 17
Evaluate |x| + 7 if x = –2.
A. 5
B. 7
C. 9
D. 12
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 1-3)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Add Integers with the Same Sign
Key Concept: Add Integers with the Same Sign
Example 2: Add Integers with the Same Sign
Example 3: Add Integers with Different Signs
Key Concept: Add integers with Different Signs
Example 4: Add Integers with Different Signs
Key Concept: Additive Inverse Property
Example 5: Add Three or More Integers
Example 6: Use Integers to Solve a Problem
• Add integers.
• Opposites
• Same number, but different signs
• additive inverse
• An integer AND its opposite
• ALWAYS add to zero
Adding Integers with the SAME sign
• ADD the numbers together
• Keep the SAME sign as the addends
• Examples
5 + 5 = 10
-5 + (-5) = -10
Adding Integers with DIFFERENT signs
•SUBTRACT the numbers from each other
• Sign of the answer has SAME sign as the addend with the
LARGEST ABSOLUTE VALUE
• Examples
-5 + 4 = -1
-8 + 10 = 2
Add Integers with the Same Sign
Find –8 + (–4).
Start at zero.
Move 8 units to the left.
From there, move 4 units left.
Answer: So, –8 + (–4) = –12.
Find –3 + (–6).
A. –9
B. –3
C. 3
D. 9
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Add Integers with the Same Sign
Find –21 + (–5).
–21 + (–5) = –26
Add |–21| and |–5|.
Both number are negative, so the
sum is negative.
Answer: –26
Find –13 + (–12).
A. 25
B. –25
C. 1
D. –1
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Add Integers with Different Signs
Find 4 + (–6).
Start at zero.
Move 4 units to
the right.
From there,
move 6 units
left.
Answer: So, 4 + (–6) = –2.
Find 3 + (–5).
A. –2
B. 2
0%
C. 7
D. 8
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Add Integers with Different Signs
Find –5 + 9.
Start at zero.
Move 5 units
to left.
From there,
move 9 units
right.
Answer: So, –5 + 9 = 4.
Find –6 + 8.
A. –2
0%
B. 0
C. 2
D. 4
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Interactive Lab:
Adding Positive and Negative Integers
Add Three or More Integers
Find 2 + (–5) + (–3).
2 + (–5) + (–3) = 2 + [ –5 + (–3)]
= 2 + (–8) or –6
Answer: –6
Associative Property
Simplify.
Find 3 + (–6) + (–2).
A. –9
B. –5
C. –1
D. 4
0%
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Use Integers to Solve a
Problem
STOCKS An investor owns 50 shares in a video
game manufacturer. A broker purchases 30 shares
more for the client on Tuesday. On Friday, the
investor asks the broker to sell 65 shares. How
many shares of this stock will the client own after
these trades are completed?
Selling a stock decreases the number of shares, so the
integer for selling is –65. Purchasing new stock
increases the number of shares, so the integer for
buying is +30. Add these integers to the starting
number of shares to find the new number of shares.
Use Integers to Solve a
Problem
50 + 30 + (–65) = (50 + 30) + (–65) Associative Property
= 80 + (–65)
50 + 30 = 80
= 15
Simplify.
Answer: The number of shares is 15.
MONEY Jaime gets an allowance of $5. She spends
$2 on video games and $1 on lunch. Her best friend
repays a $2 loan and she buys a $3 pair of socks.
How much money does Jaime have left?
A. $1
B. $2
C. $3
D. $4
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 1-4)
Main Idea
Targeted TEKS
Key Concept: Subtract Integers
Example 1: Subtract a Positive Integer
Example 2: Subtract a Positive Integer
Example 3: Subtract a Negative Integer
Example 4: Subtract a Negative Integer
Example 5: Evaluate Algebraic Expressions
Example 6: Evaluate Algebraic Expressions
• Subtract integers.
NOTES
A “-” sign means BOTH(!!) SUBTRACTION and a
NEGATIVE sign.
 If you see only ONE “-” sign
1) Subtract the numbers
2) Keep sign of largest absolute value
 If you see MORE THAN one “-” sign, remember
“ADD a Line and CHANGE the SIGN”
1 ) Change the subtraction to an ADDition
2) CHANGE the SIGN of the second number.
BrainPop:
Adding and Subtracting Integers
Subtract a Positive Integer
Find 2 – 6.
2 – 6 = 2 + (–6)
= –4
Answer: –4
To subtract 6, add (–6).
Add.
Find 3 – 7.
A. –6
B. –4
C. –1
D. 3
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Subtract a Positive Integer
Find –7 – 5.
–7 – 5 = –7 + (– 5)
= –12
Answer: –12
To subtract 5, add (–5).
Add.
Find –6 – 2.
A. 4
B. 2
0%
C. –4
D. –8
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Subtract a Negative Integer
Find 11 – (– 8).
11 – (– 8) = 11 + 8
= 19
Answer: 19
To subtract –8, add 8.
Add.
Find 15 – (– 3).
A. 9
0%
B. 12
C. 18
D. 21
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Subtract a Negative Integer
WEATHER If the overnight temperature at a
research station in Antarctica was –13° C, but the
temperature rose to 2° C during the day, what was
the difference between the temperatures?
2 – (–13) = 15
Find the difference between
the two temperatures.
Answer: The difference between the two temperatures
is 15° C.
Find –7 – (–11).
A. –18
B. –4
C. 4
D. 18
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Evaluate Algebraic Expressions
Evaluate 12 – r if p = 6, q = –3, and r = –7.
12 – r = 12 – (–7)
Replace r with –7.
= 12 + 7
To subtract –7 add 7.
= 19
Add.
Answer: 19
Evaluate 10 – c if a = 3, b = –6, and c = –2.
A. 7
B. 12
C. 14
D. 16
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Evaluate Algebraic Expressions
Evaluate q – p if p = 6, q = –3, and r = –7.
q – p = –3 – 6
Replace q with –3 and p with 6.
= –3 + (–6)
To subtract 6, add (–6).
= –9
Add.
Answer: –9
Evaluate b – a if a = 3, b = –6, and c = –2.
A. –9
B. –7
C. –1
D. 3
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Five-Minute Check (over Lesson 1-5)
Main Idea
Targeted TEKS
Key Concept: Multiply Integers with Different Signs
Example 1: Multiply Integers with Different Signs
Example 2: Multiply Integers with Different Signs
Key Concept: Multiply Integers with the Same Sign
Example 3: Multiply Integers with the Same Sign
Example 4: Multiply More than Two Integers
Key Concept: Divide Integers
Example 5: Divide Integers
Example 6: Divide Integers
Example 7: Evaluate Algebraic Expressions
Example 8: Find the Mean of a Set of Integers
Concept Summary: Multiplying and Dividing Integers
• Multiply and divide integers.
Multiplying and Dividing Integers
SAME RULES APPLY FOR MULTIPLYING AND
DIVIDING INTEGERS!
If two numbers have the SAME sign, answer is
POSITIVE!
Examples:
5 * 5 = 25 and -5 * -5 = 25
4 / 2 = 2 and (-4)/(-2) = 2
If two numbers have DIFFERENT signs, answer is
NEGATIVE!
Examples:
5 * -5 = -25 and -4 * 4 = -16
(-4) / 2 = -2 and 4 / (-2) = -2
Multiply Integers with Different Signs
Find 8(–4).
8(–4) = –32
Answer: –32
The factors have different signs. The
product is negative.
Find 6(–3).
A. –18
B. –9
C. 3
D. 6
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Multiply Integers with Different Signs
Find –5(7).
–5(7) = –35
Answer: –35
The factors have different signs. The
product is negative.
Find –2(6).
A. 4
B. –2
0%
C. –8
D. –12
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Multiply Integers with the Same Sign
Find –12(–12).
–12(–12) = 144
Answer: 144
The factors have the same sign. The
product is positive.
Find –8(–8).
A. –16
0%
B. 32
C. 64
D. 72
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Multiply More than Two Integers
Find 6(–2)(–4).
6(–2)(–4) = [6(–2) ](–4)
Associative Property
= –12(–4)
6(–2) = –12
= 48
–12(–4) = 48
Answer: 48
Find 5(–3)(–2).
A. 36
0%
B. 30
C. –18
D. –28
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Divide Integers
Find 30 ÷ –5.
30 ÷ –5 = –6
Answer: –6
The dividend and the divisor have
different signs. The quotient is
negative.
36 ÷ (–6).
A. –6
0%
B. –4
C. 6
D. 9
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Divide Integers
Find
=3
Answer: 3
The dividend and the divisor have the
same sign. The quotient is positive.
Find
A. –35
0%
B. –25
C. 6
D. 7
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Evaluate Algebraic Expressions
Evaluate 3x – (–4y) if x = –10 and y = –4.
3x – (–4y) = 3(–10) – [–4(–4)]
Replace x with –10 and
y with –4.
= –30 – 16
The product of 3 and
–10 is negative, and the
product of –4 and –4 is
positive.
= –30 + (–16)
To subtract 16, add –16.
= –46
Add.
Answer: –46
Evaluate 2a – (–3b) if a = –6 and b = –4.
A. 12
0%
B. 0
C. –12
D. –24
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Find the Mean of a Set of
Integers
WEATHER The table
shows the low temperature
for each month in McGrath,
Alaska. Find the mean
(average) of all 12
temperatures.
Find the Mean of a Set of
Integers
To find the mean of a set of numbers, find the sum of
the numbers. Then divide the result by how many
numbers there are in the set.
Answer: McGrath, Alaska has an average low
temperature of –9°C for the year.
WEATHER The table shows the record
low temperature for each month in
Brook Park, Ohio. Find the mean
(average) of all 12 temperatures.
A. about 11.6° F
B. about 12.2° F
C. about 12.9° F
D. about 13.5° F
A.
B.
C.
D.
A
B
C
D
Five-Minute Check (over Lesson 1-6)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Write an Algebraic Equation
Example 2: Write an Equation to Solve a Problem
Example 3: Test Example
• Write algebraic equations from verbal sentences
and problem situations.
• Equation
• Mathlish sentence with an EQUALS sign
• Define a variable
• Assign a letter to an unknown quantity
NOTES - CONVERTING ENGLISH
SENTENCES TO MATHLISH
SENTENCES!
There are 3 steps to follow to do this:
1) READ problem and highlight KEY
words.
2) DEFINE variable (“What will change”
or “What do I not know?”)
3) WRITE Math sentence USUALLY
from left to right (Be careful with
subtraction and division!!).
NOTES - Continued
Looks for the words like:
•
More than, increased, greater than, plus
•
•
ADDITION
Less than, decreased, reduced,
•
•
SUBTRACTION - BE CAREFUL!
Times, Of
•
•
MULTIPLICATION
Divided, spread over, “per”
•
•
DIVISION
is, was, total
•
EQUALS
Write an Algebraic Equation
CONSUMER ISSUES The cost of a book purchased
online plus $5 shipping and handling comes to a
total of $29. Write an equation to model this
situation.
READ
Cost of book plus cost of shipping is equal
to total cost.
DEFINE
Let b represent the cost of the book.
WRITE
b + 5 = 29
Write the price of a toy plus $6 shipping is $35 as an
algebraic equation.
A. p – 6 = 35
B. p + 6 = 35
C. p + 35 = 6
D. p – 35 = 6
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Write an Equation to Solve a
Problem
NUTRITION A box of oatmeal contains 10 individual
packages. If the box contains 30 grams of fiber, write
an equation to find the amount of fiber in one
package of oatmeal.
READ
Ten packages of oatmeal contain 30 grams of
fiber.
DEFINE
Let f represent the grams of fiber per package.
WRITE
Ten packages contain
of oatmeal
10f
=
30 grams
of fiber.
30
Write an Equation to Solve a
Problem
Answer: The equation is 10f = 30.
NUTRITION A particular box of cookies contains 10
servings. If the box contains 1,200 Calories, write an
equation to find the number of Calories in one
serving of cookies.
A. 10c = 1,200
0%
B. c ÷ 10 = 1,200
C. 1,200c = 10
D. c ÷ 1,200 = 10
1.
2.
3.
4.
A
B
C
D
A
B
C
D
The eighth grade has $35 less in its treasury than the
seventh grade has. Given s, the number of dollars in
the seventh grade treasury, which equation can be
used to find e, the number of dollars in the eighth
grade treasury?
A. e = 35 – s
B. e = s – 35
C. e = s ÷ 35
D. e = 35 ● s
Read the Test Item
The phrase $35 less in its treasury than indicates
subtraction. So you can eliminate C and D.
Solve the Test Item
Eighth grade treasury
is
$35 less than
seventh
treasury
=
s – 35
grade
e
Answer: The solution is B.
The high temperature on Friday was 6 degrees less
than the high temperature on Thursday. Given t, the
high temperature on Thursday, which equation can
be used to find f, the high temperature on Friday?
A. f = t – 6
B. f = t ÷ 6
C. f = 6 ● t
D. f = 6 – t
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Five-Minute Check (over Lesson 1-7)
Main Idea
Targeted TEKS
Example 1: Use the Work Backward Strategy
• Solve problems by working backward.
NOTES
 Some math problems can only be solved by
Working Backwards.
Similar to taking apart a model after putting it
together.
 This is a 3-step process that will usually work.
1. Start at the beginning and write timeline
2. Go to the END of the timeline
3. UNDO everything that was done.
Use the Work Backward Strategy
SCHEDULING Wendie is meeting some friends for
a movie and dinner. She needs to be finished with
dinner by 7:30 P.M. to make it home by 8:00 P.M.
The movie runs for 90 minutes, and she wants to
have at least 1 hour for dinner. If it takes 20 minutes
to get from the theater to the restaurant, what is the
latest starting time she can choose for the movie
she wants to see?
Explore
You know what time Wendie needs to head
home. You know the time it takes for each
event. You need to determine the time
Wendie should see the movie.
Use the Work Backward Strategy
Plan
Start with the ending time and work backward.
Solve
Finish dinner by 7:30 P.M.
Go back 1 hour for dinner.
Go back 20 minutes for travel.
Go back 90 minutes for the movie.
Check
Assume the movie starts at 4:40 P.M. Work
forward, adding the time for each event.
Answer: The latest starting time for the movie
is 4:40 P.M.
7:30 P.M.
6:30 P.M.
6:10 P.M.
4:40 P.M.
SHOPPING Mia spent $9.50 at a fruit stand, then
spent three times that amount at the grocery store.
She had $7.80 left. How much money did she have
initially?
A. $44.20
B. $45.80
C. $46.50
0%
0%
D
0%
C
A
0%
B
D. $48.30
A.
B.
C.
D.
A
B
C
D
Five-Minute Check (over Lesson 1-8)
Main Idea and Vocabulary
Targeted TEKS
Key Concept: Subtraction Property of Equality
Example 1: Solve an Addition Equation
Key Concept: Addition Property of Equality
Example 2: Solve an Addition Equation
Example 3: Solve a Subtraction Equation
• Solve equations using the Subtraction and Addition
Properties of Equality.
• Solve
• Find the value of a variable
• Solution
• The value that makes an equation true
• Inverse operations
• Operators that are opposites
Primary Goal of Solving Algebra Equations is:
GET THE VARIABLE BY ITSELF
Remember:
1) Addition And Subtraction are OPPOSITES
2) Multiplication and Division are OPPOSITES
3) If I do something to ONE SIDE of the equals sign,
I must do EXACTLY the same thing to the other
side!
Solve an Addition Equation
Solve 7 = 15 + c. Check your solution.
Method 1 Vertical Method
7 = 15 + c
Write the equation.
7 = 15 + c
–15 –15
–8 =
Subtract 15 from each side.
c
Solve an Addition Equation
Method 2 Horizontal Method
7 = 15 + c
7 – 15 = 15 – 15 + c
–8 = c
Write the equation.
Subtract 15 from each side.
Solve an Addition Equation
Check
7 = 15 + c
7 = 15 + (–8)
Write the original equation.
Replace c with –8. Is this
sentence true?
7 =7
Answer: The solution is –8.
Solve 6 = 11 + a. Check your solution.
A. –5
B. –3
C. 13
D. 17
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Solve an Addition Equation
OCEANOGRAPHY At high tide, the top of a coral
formation is 2 feet above the surface of the water.
This represents a change of –6 feet from the height
of the coral at low tide. Write and solve an equation
to determine h, the height of the coral at low tide.
Words
The height of the coral at low tide plus (–6)
feet is 2 feet.
Variable
Let h represent the height of the coral at low
tide.
Equation h + (–6) = 2
Solve an Addition Equation
h + (–6) = 2
Write the equation.
h + (–6) + 6 = 2 + 6
Add 6 to each side.
h=8
Answer: The height of the coral at low tide is 8 feet.
If Carlos makes a withdrawal of $15 from his savings
account, the amount in the account will be $47.
Write and solve an equation to find the balance of
the account before the withdrawal.
A. $65
0%
B. $45
C. $62
D. $32
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Solve a Subtraction Equation
Solve –5 = z – 16.
Method 1 Vertical Method
–5 = z – 16
–5 = z – 16
+16
+16
11 = z
Write the equation.
Add 16 to each side.
Solve a Subtraction Equation
Method 2 Horizontal Method
–5
= z – 16
–5 + 16 = z – 16 + 16
Write the equation.
Add 16 to each side.
z = 11
Answer: The solution is 11.
Solve –6 = x –12.
A. –6
0%
B. –3
C. 6
D. 9
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Five-Minute Check (over Lesson 1-9)
Main Idea
Targeted TEKS
Example 1: Solve a Multiplication Equation
Key Concept: Division Property of Equality
Key Concept: Multiplication Property of Equality
Example 2: Solve a Division Equation
Example 3: Real-World Example
• Solve equations by using the Division and
Multiplication Properties of Equality.
Primary Goal of Solving Algebra Equations is:
GET THE VARIABLE BY ITSELF
Remember:
1) Addition And Subtraction are OPPOSITES
2) Multiplication and Division are OPPOSITES
3) If I do something to ONE SIDE of the equals sign,
I must do EXACTLY the same thing to the other
side!
Solve a Multiplication Equation
Solve 7z = –49.
Write the equation.
Divide each side of the equation by 7.
7 ÷ 7 = 1 and –49 ÷ 7 = –7
Identity Property; 1z = z
Answer: The solution is –7.
Solve 8a = –64.
A. –8
B. –6
C. 4
D. 8
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Solve a Division Equation
Solve
Write the equation.
Multiply each side by 9.
–6(9) = –54
Answer: The solution is –54.
Solve
.
A. 50
B. 2
0%
C. –2
D. –50
1.
2.
3.
4.
A
B
C
D
A
B
C
D
SURVEYING English mathematician Edmund Gunter
lived around 1600. He invented the chain, which was
used as a unit of measure for land and deeds. One
chain equals 66 feet. If the south side of a property
measures 330 feet, how many chains long is it?
Words
One chain equals 66 feet.
Variable
Let c = the number of chains in 330 feet.
Equation 330 = 66c
Write the equation.
Divide each side by 66.
330 ÷ 66 = 5.
Answer: The number of chains in 330 feet is 5.
HORSES Most horses are measured in hands. One
hand equals 4 inches. If a horse measures 60 inches,
how many hands is it?
A. 12 hands
0%
B. 15 hands
C. 225 hands
D. 240 hands
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Five-Minute Checks
Image Bank
Math Tools
Adding Positive and Negative Integers
BrainPop Menu
Lesson 1-1
Lesson 1-2
(over Lesson 1-1)
Lesson 1-3
(over Lesson 1-2)
Lesson 1-4
(over Lesson 1-3)
Lesson 1-5
(over Lesson 1-4)
Lesson 1-6
(over Lesson 1-5)
Lesson 1-7
(over Lesson 1-6)
Lesson 1-8
(over Lesson 1-7)
Lesson 1-9
(over Lesson 1-8)
Lesson 1-10
(over Lesson 1-9)
To use the images that are on the
following three slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
The Associative Property
The Commutative Property
The Distributive Property
Adding and Subtracting Integers
Determine whether 29 is a prime or composite
number.
A. composite
1.
2.
A
B
B. prime
0%
B
A
0%
Determine whether 36 is a prime or composite
number.
A. composite
1.
2.
A
B
B. prime
0%
B
A
0%
Determine whether 97 is a prime or composite
number.
A. composite
1.
2.
A
B
B. prime
0%
B
A
0%
Write 13 percent as a fraction in simplest form.
A.
B.
C.
D.
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
A company’s sales increased
percent. Write
this percent as a fraction in simplest form.
A.
0%
B.
C.
1.
2.
3.
4.
A
B
C
D
A
D.
B
C
D
The original price of a DVD was $30. The sale price
is $24. What is the percent of decrease?
A. 10 percent
0%
B. 15 percent
1.
2.
3.
4.
C. 20 percent
D. 25 percent
A
B
A
B
C
D
C
D
(over Lesson 1-1)
D
C
B
A
At the local grocery store, a pound of potatoes costs
$0.29, and a pound of bananas costs $0.30. What
combination of potatoes and bananas costs $0.39?
What combination of potatoes and bananas could
you buy for exactly $1.38? Use the four-step plan to
solve the problem.
A. 1 pound of potatoes and 1
pound of bananas
B. 1 pound of potatoes and 2
A. A
pounds of bananas
B. B
C. 2 pounds of potatoes and 2
0%
C. 0% C0% 0%
pounds of bananas
D. D
D. 4 pound of potatoes and 3
pounds of bananas
(over Lesson 1-1)
A basketball player scored 27 points in the first
game, 19 points in the second game, and 32 points
in the third game. Estimate the total number of
points the basketball player scored.
A. 55
0%
B. 60
C. 75
D. 80
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-1)
A basketball player scored 27 points in the first
game, 19 points in the second game, and 32 points
in the third game. About how many more points did
he score in the first two games than in the third
game?
A. 15
B. 20
C. 30
0%
1.
2.
3.
4.
A
D. 40
A
B
C
D
B
C
D
(over Lesson 1-1)
A basketball player scored 27 points in the first
game, 19 points in the second game, and 32 points
in the third game. About how many more points did
he score in the last two games than in the first
game?
A. 20
D. 35
0%
D
A
B
0%
C
D
C
0%
A
C. 30
A.
B.
0%
C.
D.
B
B. 25
(over Lesson 1-1)
What is the next figure in the pattern shown?
0%
A.
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-2)
Evaluate
.
A.
B. 5
C. 8
D. 12
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-2)
Evaluate
A. 6
B. 9
C. 14
D. 15
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-2)
Evaluate
A. 48
0%
B. 34
1.
2.
3.
4.
C. 14
A
B
C
D
D. 6
A
B
C
D
(over Lesson 1-2)
Evaluate
.
A. 0
B. 3
C. 24
D. 72
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-2)
Evaluate
if a = 2, b = 6, and c = 8.
A. 9
B. 4
C. 3
D. 2
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-2)
Which property is shown by the expression
(2 + 5) + 19 = 2 + (5 + 19)?
A. Identity
0%
B. Distributive
1.
2.
3.
4.
C. Associative
D. Commutative
A
B
A
B
C
D
C
D
(over Lesson 1-3)
Write an integer for the situation. A gain of 5 pounds.
A. –5
B. –0.5
C. 0.5
D. 5
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-3)
Write an integer for the situation. 5 degrees below
zero.
A. –5
B. –0.5
C. 0.5
D. 5
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-3)
Use <, > or = in 6 ____ –2 to make a true sentence.
A. <
B. >
1.
2.
3.
A
B
C
C. =
0%
C
0%
B
A
0%
(over Lesson 1-3)
Order the set of integers {36, –94, –122, 23, 56} from
least to greatest.
A. {–122, 56, 36, 23, –94}
B. {56, 36, 23, –94 , –122}
C. {–94, –122, 23, 36, 56}
D. {–122, –94, 23, 36, 56}
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-3)
Evaluate the expression |–9| + |–23|.
A. 32
B. 16
C. –16
D. –32
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-3)
The following temperatures were recorded: 5
degrees above zero, 20 degrees below zero, 15
degrees below zero, and 10 degrees above zero.
What would be the order of the temperatures from
least to greatest?
0%
A. {5, 10, –15, –20}
B. {–15, –20, 5, 10}
C. {–20, –15, 5, 10}
D. {–20, –15, 10, 5}
1.
2.
3.
4.
A
A
B
C
D
B
C
D
(over Lesson 1-4)
Add: –3 + (–5).
A. 8
B. 2
C. –2
D. –8
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-4)
Add: 28 + (–12).
A. 40
B. 16
C. –16
D. –40
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-4)
Add: –13 + 20.
A. –33
0%
B. –7
1.
2.
3.
4.
C. 7
A
B
C
D
D. 33
A
B
C
D
(over Lesson 1-4)
Add: 17 + (–5).
A. 22
B. 12
C. –12
D. –22
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-4)
Evaluate the expression | a + c | – b if a = –2, b = –5,
and c = –3.
A. 10
0%
B. 0
C. –4
D. –10
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-4)
If the outside temperature was –6° F, and then
dropped by 10°, what would be the temperature?
A. 4° F
0%
1.
2.
3.
4.
B. –4° F
C. –16° F
A
D. 16° F
B
A
B
C
D
C
D
(over Lesson 1-5)
Subtract: 4 – 9.
A. 13
B. 5
C. –5
D. –13
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-5)
Subtract: –2 – (–6).
A. 8
B. 4
C. –4
D. –8
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-5)
Subtract: |–3| – |–7|.
A. 10
0%
B. 4
1.
2.
3.
4.
C. –4
A
B
C
D
D. –10
A
B
C
D
(over Lesson 1-5)
Subtract: –21 – (–10).
A. –31
B. –11
C. 11
D. 31
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-5)
Evaluate the expression | a | + c – b if a = –1, b = 3,
and c = –5.
A. 1
B. 3
C. –7
D. –8
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-5)
The balance in Ed’s checking account was $45. After
writing a check, the balance was –$14. What was the
amount of the check?
A. $14
0%
B. $31
1.
2.
3.
4.
C. $45
A
B
C
D
D. $59
A
B
C
D
(over Lesson 1-6)
Multiply: 3(–4).
A. 12
B. 7
C. –1
D. –12
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-6)
Multiply: –6(–2).
A. 12
B. 4
C. –8
D. –12
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-6)
Divide:
A. 55
0%
B. 6
1.
2.
3.
4.
C. –5
D. –6
A
B
A
B
C
D
C
D
(over Lesson 1-6)
Divide:
A. –9
B. –8
C. 9
D. 64
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-6)
Find the mean of the following set of integers.
3, –6, –8, –10, –4
A. –25
B. –13
C. –5
D. –1
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-6)
What is the value of ab – c, if a = –3, b = 4, and
c = –2?
A. –14
0%
B. –10
1.
2.
3.
4.
C. 10
D. 12
A
B
A
B
C
D
C
D
(over Lesson 1-7)
Write the verbal phrase ‘$4.75 tax added to the total’
as an algebraic expression.
A. b – $4.75
B. $4.75 + b
C. $4.75 – b
D. $4.75 × b
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-7)
Write the verbal phrase ‘a number divided by –13’ as
an algebraic expression.
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-7)
Write the verbal phrase ‘5 years younger than Mary’
as an algebraic expression.
A. x + 5
0%
B. 5 – x
1.
2.
3.
4.
C. x – 5
D. x ● 5
A
B
A
B
C
D
C
D
(over Lesson 1-7)
Write the verbal phrase ‘half of Sylvia’s money’ as an
algebraic expression.
A.
2●x
B.
C.
D.
x–2
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-7)
If x is your age, write an expression for your age
seven years from now.
A. 7 ● x
B. x – 7
C. 7 – x
D. x + 7
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-7)
The Huey P. Long Bridge is one of the most
frequently traveled bridges in Louisiana, but it is not
the longest. The Causeway Bridge is approximately
15 miles longer. The Causeway Bridge is 22 miles
long. Which equation represents the length of the
Huey P. Long Bridge?
A.
B. x + 15 = 22
C. x – 22 = 15
D. x = 22(17)
1.
2.
3.
4.
A
B
C
D
(over Lesson 1-8)
Alicia arrived home at 7:45 P.M. from the restaurant.
She spent 45 minutes waiting in the restaurant lobby
and one and a half hours eating dinner. If it took her
20 minutes to drive home, what time did she arrive at
the restaurant?
A. 6:30 P.M.
B. 5:30 P.M.
C. 5:10 P.M.
D. 6:10 P.M.
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-8)
Marcus has $6 in change left after his trip to the
movie theatre. If his movie ticket cost $5.50 and he
purchased a drink for $3.00, a bag of popcorn for
$3.50, and a box of candy for $2.00, how much
money did he originally take to the movie theatre?
A. $10
B. $15
C. $18
1.
2.
3.
4.
A
B
C
D
A
D. $20
0%
B
C
D
(over Lesson 1-8)
Candace’s quiz scores are 86, 98, 85, 94, and 89.
What is the minimum score she can make on her
next quiz to maintain a quiz average of at least 90?
A. 82
0%
1.
2.
3.
4.
B. 88
C. 91
A
D. 95
B
A
B
C
D
C
D
(over Lesson 1-8)
At nine months of age, a baby elephant can weigh
700 pounds. If this is 4 times the baby elephant’s
birth weight, how many pounds did the elephant
weigh at birth?
0%
A. 2800 pounds
1.
2.
3.
4.
B. 1400 pounds
C. 233 pounds
D. 175 pounds
A
B
A
B
C
D
C
D
(over Lesson 1-9)
A. 10
B. 4
C. –4
D. –10
A.
B.
C.
D.
A
B
C
D
(over Lesson 1-9)
A. 15
B. 11
C. –11
D. –15
0%
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-9)
A. 13
0%
B. 5
1.
2.
3.
4.
C. –5
A
B
C
D
D. –13
A
B
C
D
(over Lesson 1-9)
A. –39
B. –17
C. 17
D. 39
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
(over Lesson 1-9)
If you increase a number by 9, the result is 26.
Write and solve an equation to find the number.
A.
0%
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
B
C
D
(over Lesson 1-9)
Pam opened a checking account with $200. Then
she wrote a check for $125. What is the current
balance in Pam’s checking account?
A. –$33
0%
1.
2.
3.
4.
B. $75
C. $83
A
D. $325
B
A
B
C
D
C
D
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