Download Name:

Math Quarter 1 Benchmark Study Guide
The 1st Quarter Math Benchmark will be on Monday, October 28, 2013
Homework Schedule:
Due: Tuesday, October 22ndIntegers and Absolute Value (pages 2-3)
Due: Wednesday, October 23rdGraphing Inequalities & Measures of Central Tendency (pages 4-6)
Due: Thursday, October 24thFractions, Decimals & Percents (pages 7-9)
Due: Friday, October 25thBasic Skills & Multi-Step Word Problems (pages 10-12)
Remember to show all work, even for multiple choice questions. Credit will not be given if
work is not shown. It is ok to show your work on a separate sheet of paper. Be sure to bring the
work paper with you!
1
Benchmark 1 Study Guide
Integers
Name:
Integers- all whole numbers and their opposites […-3, -2, -1, 0, 1, 2, 3…]
NOT a fraction, decimal, or percent
-4.5, ¾, 85%
Draw a number line to represent the integers -5 to 5
Practice
Use your knowledge of integers to answer the following questions.
1. Circle the numbers below that ARE integers.
1.3
⅜
5
-23
6.6666
0
49%
17
What makes a number NOT an integer? ____________________________________________
_____________________________________________________________________________
2. Write the following phrases numerically.
A loss of 20 yards
____________________
5 inches taller
____________________
An altitude of 3800 feet
____________________
7 units to the left of zero on
the number line
____________________
A profit of $10
____________________
A debit of $48
____________________
A credit of $65
____________________
A debt of $3
____________________
3. Draw a comparison sign to complete each number statement.
-19 ____ 5
30 ____ -25
-6 ____ -7
-15 ____ 0
20 ____ -11
-10 ____ -3
Remember positive numbers
are ALWAYS greater than
negative numbers.
When comparing two negative
numbers, the number closer to
zero is always greater.
2
Answer the following questions by looking at the number line.
E
-6
-5
F
-4
-3
-2
G
-1
0
1
2
3
H
I
4
5
6
4. At what point do you find H? _____
5. Which point represents -5? _____
Ascending- order from least to greatest
Descending- order from greatest to least
6. Put the following integer in ascending order:
1, –8, 7, -12
–4, –1, 2, -5
7. Circle the set of integers that are in descending order.
A) -6, -3, 5, 10
B) -3, 5, -6, 10
C) 10, 5, -3, -6
D) 10, -6, 5, -3
Absolute Value
Absolute Value: the number of units a number is away from zero.

–4says “the absolute value of negative four”

–2 
11
+5says “the absolute value of positive five”
7 
26
3
Graphing Inequalities
< Less than
> Greater than
≤ Less than or equal to
≥ Greater than or equal to
Open dot means < or >
“less than” or “greater than”
Closed dot means ≤ or ≥ “less than or equal to” or “greater than or equal to”
Always read the answer starting with the variable to find out which direction the arrow points.
Practice
Graph each inequality.
1.
r > -1
2.
p≤3
Name each inequality.
n
n
Measures of Central Tendency
Mean- the average (add up all of the numbers and divide by the number of items)
* Mean works well for sets of data with no very high or low numbers
Example: Test scores from the last unit test
82 95 73 100 85 79 64 88 91 76
833
10
=
83.3 %
4
Median- the middle number in a set of data
* Median is a good choice when data sets have a couple of values much higher or lower than
most of the others
Example: The number of fish in a pond
3, 6, 1, 0, 5, 3, 4
Put the numbers in order
0, 1, 3, 3, 4, 5, 6
3 is the median
Example: The number of cookies each student ate at lunch
4 1 5 2 0 8 4 3 0 6
Put numbers in order
0 0 1 2 3 4 4 5 6 8
3.5 is the median
Mode- the number that occurs most often
* There can be more than one mode or no mode at all
* If there are exactly two modes, it is called bimodal
* Mode is a good descriptor to use when the set of data has some identical values
Example: The number of points Victoria scores in each basketball game
12 5 18 10 12 9 18 12 7 15
Put numbers in order:
5 7 9 10 12 12 12 15 18 18
12 is the mode
5
Find the mean, median, and mode of the following sets of data.
Example: The number of hours kids watch TV per week
11
Mean-
5
22
=
14
8
13
6
16
Median-
Mode-
Mean as a balance point- the point on a number line where the data distribution is balanced
Find the mean as a balance point for the following set of data.
“Number of Siblings”
6
Fractions, Decimals, and Percents
Fractions- the representation of a number expressed in the form a/b
Numerator-the number above a fraction bar
3
numerator
Denominator- the number below a fraction bar
7
denominator
Decimals- the representation of a number based on tenths, hundredths, and thousandths
Place values
Percents- the representation of a number out of 100
Find the percent of each grid
_____%
_____%
_____%
Converting Fractions, Decimals, and Percents
Fraction
Decimal

if the denominator is 10 or 100, read the fraction as a decimal

reduce to simplest form and divide the numerator by the denominator
3 = 0.3
10
10 (simplify to 5/6 and do long division) = 0.833
12
7
Decimal
Percent

Dr. Pepper

move the decimal point two places to the right (multiply by 100)
.DP
0.82 = 82%
Percent
0.7 = 70%
Decimal

Revers Dr. Pepper

move the decimal point two places to the left (divide by 100)
DP.
94% = 0.94
16.2% = 0.162
Comparing Fractions, Decimals, and Percents
Fractions

find a common denominator

change both fractions into decimals or percents
Decimals

align decimal points

add zeros to even up place values

compare numbers according to their place values
Percents

compare the whole numbers
Mixed Forms

change all numbers to the same form (percents are the easiest to compare)
Compare the following numbers using a <, >, or = sign.
0.9 ____ ½
82% ____ 1.4
2/3 ____ 5/6
¼ ____ 2/7
Put the following numbers in ascending order.
0.64, 1/5, 43%, ½ ________________________________
8
Put the following numbers in descending order.
2/3, 0.09, 16%, 3/8 ________________________________
Complete the chart below.
Fraction
Decimal
Percent
1/4
2/4
3/4
1/5
2/5
3/5
4/5
1/3
2/3
1/8
2/8
3/8
4/8
5/8
6/8
7/8
9
Basic Skills
Adding and Subtracting Decimals
 Line up the decimal points
 Fill in zeros when necessary
Multiplying Decimals
 Decimals do NOT need to be lined up
 Count how many digits are after each decimal point and write it to the side of the problem
 Multiply
 Put the decimal point in the answer
Dividing Decimals
 If only one number has a decimal point, do long division and bring the decimal point straight
up into your answer
 If both numbers have a decimal point, move both decimal points to the right so the divisor
(the number at the door) becomes a whole number
Practice- Show all of your work and circle the best answer.
1. Add: $1.36 + $9.44
A
$9.08
B
$9.74
C
$9.80
D $10.80
2. Subtract:
A
B
C
D
0.298
1.072
1.928
2.928
3. Multiply:
A
B
C
D
4.298  2.37
0.23
x 1.6
1.38
0.138
3.58
0.368
10
4.
Find the quotient of: 9 6.669
A 0.0741
B 0.741
C
7.41
D
74.1
5.
Find the quotient.
0.942 ÷ 0.003
A
B
C
D
0.314
3.14
31.4
314
Multistep Word Problems
Six Step method to solving a word problem
1) The Question
2) The Facts
3) The Plan
4) The Picture
5) The Action
6) The Check
Practice- Show all of your work and circle the best answer.
1. At a trip to the grocery store, you buy 4 lbs. of bananas for $0.49 per pound, 2 boxes
of oatmeal each at $3.79 per box, and 4 yogurts advertised at 2 for $1.00. If you give
the cashier a $20.00 bill, how much change should you get back?
A $7.75
B $8.28
C $8.46
D $11.54
11
2. The sixth-grade band is raising money to help buy new instruments. They are
selling $21 magazine subscriptions. If 56 students sell one subscription each, how
much money will they raise?
A
B
C
D
$1,000
$1,076
$1,176
$1,680
3. Johanna rented a car. Rental costs were $29.00 per day plus $0.49 for each mile
driven. If she kept the car for 1 day and drove 50 miles, how much did she owe?
A $29.49
B $31.45
C $53.50
D $78.00
4.
Mr. Rico’s class decided to invite their parents to their National Hugging Day
party. Amber, Jordan, and Brian made the invitations.
Item
Cost
Package of Paper
$3.92
Package of Stickers
Box of Envelopes
$3.42
$5.13
Stamps
$0.32 each
It took one package of paper and one package of stickers to make the invitations.
They used one box of envelopes and twenty five stamps. About how much did it
cost in all to make the invitations?
12