10 questions without use of calculator
Equivalent fractions, decimals, percent
Compare fractions, decimals and percent
Multiply and divide fractions and mixed numbers
Order of operation
5 – 7 questions or 15% of SOL will be new form of questions:
Fill in blanks
Order of operation, Square Roots, Replacement values, practical problems
(+, -, x, ÷ of decimals and fractions)
estimate solutions (addition, subtraction, multiplication and division of
fractions)
Formula sheet (area, perimeter, surface area, volume, circumference)
Drag and Drop
Describe, least to greatest (fractions, decimals, percent), ratios
Properties of Quadrilaterals
Perfect squares
Volume and surface area of rectangular prism
Mean as a balance point (number line)
Hot Spot
shade fraction, decimal, percent
Sequences (arithmetic and geometric)
Absolute value
Multiple answers
Graphs
create bar/circle graphs/line graphs (compare)
plot points on a coordinate grid
Decimal/Fraction/% of probability Remember probability is between
0-1
2 or more answers
Absolute value
Square roots
Identify each number (implies that it could be more than one)
Measurements
Numbers
Wording on test to determine if there is more than one answer:
“Choose each number” - more than one
“Choose the number” - one answer
Also, look at the directions. It might tell you how many to choose.
Number and Number Sense (10 Questions)
6.1 Ratios
IXL: AA 1, 2, 3, 5
Ratio -comparison of two numbers
2
Ratio 2:3, fraction ( 3 ), colon (2:3), word to (2 to 3)
1.
Lucy buys 4 rolls of color film and 7 rolls of black and white film. What is the ratio of color film to
black and white film?
4:7
2.
What ratio describes the value of a nickel to the value of a quarter?
5:25
3.
There were 12 footballs and 30 students in gym class. Which ratio accurately compares the
number of students to the number of footballs?
30:12
4.
Which statement is true?
a.
b.
c.
d.
7
6:7 = 6 = 7 to 6
2
5 = 2 to 5 = 5:2
8
8:3 = 8 to 3 =
3
9
9 to 4 = 4:9 =
4
6.2
Fractions Part of a whole Part/total
Divide
4
5
=4÷5
5/0 = undefined
0/5 = 0
1.
At a school carnival, a group of 47 students played the Fish Pond game. Each student in the
group won a prize. A stuffed animal was won by 24 students, a rubber ball was won by 7
students, and the rest of the students won a baseball cap. What fraction of the group won a
baseball cap?
13/47
2.
A 20-gallon container is filled with 6 gallons of gasoline. What fraction of the
container is filled with gasoline?
6/20
3.
Lisa said 5 parts out of every 8 parts is blue. What is another way to express this relationship?
5:8 5 to 8 5/8
4.
Sonya, Darren, and Abby were on different sports teams last season. The number of wins for
each team is listed below.
• Sonya’s soccer team won 4 out of 5 games.
• Darren’s basketball team won 12 out of 20 games.
• Abby’s baseball team won 20 out of 25 games.
Which teams won the same proportion of their games?
Percent (Per 100)
A percent is a special ratio in which the denominator is 100
Any fraction where the denominator (the bottom number) is 100, the numerator (top number) is the
percent.
47/100 = 47%
7/100 = 7%
29/100 = 29%
1. Lani has learned 21 of the 84 songs in her piano playbook. What percent of the total number of
songs in the playbook has Lani learned?
25 %
2. Jenny picked 25 roses. She gave away 10 roses. What percent of the roses did Jenny give away?
40%
3. Mary picks 15 flowers from her garden. If 3 out of 5 of these flowers are yellow,
how many yellow flowers does Mary pick?
60%
4. Rona drove 56 miles to visit a friend. She drove 42 miles before stopping for gas.
What percent of the drive did Rona complete before stopping for gas?
49%
5. In Randi’s school, 5 out of every 7 students ride the bus to school.
What percent of students ride the bus?
71%
6. If there are 350 students in Randi’s school, approximately how many students ride
the bus?
248.5
7. A surveyed 643 skateboarders and found that 209 of them preferred wood
skateboards to plastic or aluminum skateboards. Based on the number of people
surveyed, what is the most reasonable estimation of the percent of skateboarders
who preferred wood skateboards?
33%
equivalent (=)
equivalent decimals, percents, and fractions (Graph a representation)
fractions that have denominators that are factors of 100. (1, 2, 4, 5, 10, 25, 20, 100)
1. Sue's little sister was coloring the squares on a 5  10 grid. She had colored 25 of the squares.
What percent of the squares were not yet colored?
2. What number can replace the
0
1
2
0.75
on the number line?
1
3. What is 0.06 represented as a percent and a fraction?
4. If you had 100 questions on your math exam and you got 95 of them correct, what is your
grade expressed as a fraction, as a decimal, and as a percent?
5. The school’s science fair was attended by
2
of the students. About what percent of the
3
students attended the science fair? (Round to the nearest percent.)
6. If there were 100 questions on your Science exam and you got 90 of them correct, what is
your grade, expressed as a fraction, as a decimal, and as a percent?
7. A seventh-grade class conducted a survey to find out what kinds of pets their classmates
owned. They discovered that 60% of the pets owned by the students were dogs. What
fractional part of the pets were not dogs?
8. Which of the following does NOT contain equivalent fractions, decimals, and percents?
2
a. 5 , 0.4, 40%
1
b.
, 0.25, 25%
4
3
c.
, 0.375, 37.5%
8
1
d.
, 0.05, 50%
20
9. Which of the following is NOT in order from least to greatest?
1 1 1
, ,
4 3 2
1 3 2
b. , ,
3 4 5
3 6 9
c. , ,
6 8 10
1 4 6
d. , ,
2 5 5
a.
Order and compare 3 fractions, decimals, and percent (decimals through thousandths, fractions with
denominators of 12 or less), in ascending or descending order. (Drag and drop)
Ascending order – Numbers are said to be in ascending order when they are arranged from the smallest
to the largest number.
5, 9, 13, 17 and 21 are arranged in ascending order
Descending order – Numbers are said to be in descending order when they are arranged from the
largest to the smallest number.
25, 21, 17, 13 and 9 are arranged in descending order
a. Numerator is 1, the bigger the Denominator the smaller the fraction.
Example: ½, 1/3, ¼, 1/5, 1/6
b.
Compare fraction to ½.
Example 2/4 2 is half of 4
3/6 3 is half of 6
4/8 4 is half of 8
c. Denominator is the same, then the bigger the numerator, the greater the number.
Example: 1/5, 2/5, 3/5, 4/5, 5/5
1. Which of the following statements is true?
a. 0.16 < 0.016
b. 5.065 < 5.65
c. 2.804 < 2.408
d. 5.83 < 0.583
2. What fraction could you place in the blank to make a true statement?
0.15 < ___< 85%
9
a. 10
7
b.
8
5
c.
6
6
d.
7
3. What percent is equivalent to 3/20?
4. Write the following in descending order.
16%, 1/6, .166
Write each improper fraction as a mixed number:
1)
12
8
2)
6
5
3)
33
10
4)
9
7
5)
17
8
6.3 Integers (hot spot) absolute value
IXL: C 1, 3, 4
Integers : Are whole numbers and their opposites. Integers are not fractions or decimals.
-4, -3, -2, -1, 0, 1, 2, 3, 4
Negative numbers, positive numbers, and zero
temperature (below 0)
finance (owing money)
Number line for integers and absolute value
1. What number is equivalent to |–16 | ?
2. What number is equivalent to |27| ?
3. What value is equivalent to | -14 | ?
4. Which point represents the integer of -3?
-5 P Q -2 -1 0 1 S T 4 5
A
5. What statement is true?
a. –15 < –1 < 0
b. –15 > 15 < –7
c. 0 < –6 > –20
d. –7 < –3 > 0
6. What number has the same absolute value as 5?
a. 5
1
5
b.

c.
d.
0
5.5
7. What integer is the opposite of –3?
below sea level
6.4 multiple representations of multiplication and division of fractions.
IXL: V 5, 6 W 1, 2, 3
2 3
 (part of a part.)
3 4
1
x 6 (part of the whole)
2
What does it mean to divide with fractions?
10 ÷ 2 “How many 2 make ten?” What “times” 2 is 10
1
1 2
2
 , “How many
make ?”
4 3
3
4
“How much for one?”
How many are in each group?
Multiplying Fractions:
4 x 2/3 = 2/3 + 2/3 + 2/3 + 2/3 4 groups of 2/3’s
a. 2/3 x ¾ = 6/12 or 1/2
How many acres of land does each person have if
2
acres are divided among 4 people?
5
Mr. Frazier has 36 yards of fence wire. He wants to divide the wire into strips that are
long. How many strips of wire will he be able to make?
3
yard
4
6.5 positive exponents and perfect squares (see notes in journal)
IXL: E 1, 2, 3, 9
Perfect squares
104 = 10,000
103 = 1000
102 = 100
101 = 10
10 0 =1.
If 10 is the base, the exponent will be the number of zeros.
20 = 1
50 = 1
0 0 = Undefined
1. Which exponential expression is equivalent to 8 x 8 x 8 x 8?
84
2. What is the expanded form of 93?
9x9x9
3. What does 100 equal?
1
4. The numbers 1, 4, 9, and 16 are called “perfect squares”
Find the next three numbers in the sequence.
25, 36, 49
5. Which is a model of 4²?
Computation and Estimation (9 questions)
6.6 a) (complete items without the use of a calculator) multiply and divide fractions and
mixed numbers
IXL: V 1, 2, 10, V 11, W5, X 6
3 1
÷ ?
5 3
1.
What is the solution for
2.
What is 8
3.
What is the solution to 5 x 2
4.
Find the solution for 8 ÷ 6
5.
What is
6.
Divide: 4
7.
Multiply: 2
1
1
÷ 2 ? 34/9 = 3 7/9
2
4
3 2
÷ ?
4 3
3
1
÷1
8
4
5
2
x3
8
5
1
?
2
2
.
5
𝟗
𝟓
= 1 4/5
b) estimate solutions and then solve single-step and multistep practical problems
involving addition, subtraction, multiplication and division of fractions. (fill in blank)
IXL: U 4, 7 V 4, 7, 9, 12 W 4, 6, 8
X7
¾ + ½ greater than or less than 1
1. Nan lives 13 ½ miles from the airport. Felipe lives 6 ¼ miles from the airport.
How many more miles does Nan live from the airport than Felipe?
2. Ms. Brown asked her students to simplify the expression below.
2/3 +1/4
What is the simplified version of Ms. Brown’s expression?
3. Stacy has 2 1/3 yards of fabric. She buys an additional 1 1/2yards of fabric.
How many total yards of fabric does she have?
4. At a sporting goods store, 3/10 of all the items are baseball items and 1/3 of all the
items are football items. What fraction of the total number of items in the store are baseball or
football items?
5. Mike and Frank ran in a race. Frank ran 1
1
1
miles. Mike ran 1
times as far as Frank. How
2
4
far did Mike run?
6. You have a 14-foot board and need to cut the board so that it is 11
you have to cut off?
1
feet long. How much do
4
7. The manager of a sporting good store ordered 58 boxes of athletic shoes. If each box weighs 2
7
pounds, which is the best estimate of how much all the boxes of shoes weigh?
8
1
8. Sandy practiced the clarinet a total of 9
hours in one week. The following chart gives the
4
number of hours she practiced each day, Monday through Saturday. How long did Sandy
practice on Sunday?
9. Lowanna is baking cookies. The recipe calls for 3
1
cups of sugar. She only wants half a recipe.
2
How much sugar will she need?
10. An auto mechanic tells John that labor is $47.00 per hour. If it takes the mechanic about 1
1
2
hours to fix John’s car, about how much will the labor cost?
11. A property of 12
2
acres will be split equally among 4 family members. What will be the size
3
of the property that each family member will receive?
12. What is the area of this rectangle?
5
1
1
22”
3 bags of candy that weigh 4
13. Jason has three
ounces, 2 ounces, and 6
ounces. What is
6
8
4
5 ” best estimate for total weight of all three bags of candy?
1 the
8
14. Mica and Denise are reading the same novel. Mica has read ½ of the novel, and Denise
has read 1/3 of the novel. How much more of the novel has Mica read than Denise?
15. Sandra wants to buy 2 gallons of detergent. The table shows the sale price of four different
brands of detergent.
Which of the following is the least expensive way for Sandra to buy 2 gallons of detergent?
a.
b.
c.
d.
Buying 4 bottles of Fresh All
Buying 4 bottles of Mega Wash
Buying 2 bottles of Ultra Clean
Buying 1 bottle of No More Stains
Ultra Clean
Fresh All
Mega Wash
No More Stains
1 gallon
½ gallon
½ gallon
2 gallons
$6.50
$2.00
$3.10
$12.00
16. Every week Sam saves $1.00 on Monday and $2.50 on Friday. If this is his
total weekly savings, how many weeks would it take him to save enough to
buy a $49 wireless phone?
A 7 weeks
B 14 weeks
C 46 weeks
D 52 weeks
6.7 Decimals addition, subtraction, multiplication, and division (Fill in Blank) estimation strategies
IXL: F 2, 3, 4, 5, 6, 7
J2
O5, X5
1.
Jake makes $6.05 per hour. About how many hours does he need to work to make $250?
2.
Shawn wants to purchase 3 CDs for $14.99 each, a shirt for $9.59, and a cap for $11.99. What is a
reasonable amount of money, before tax, that Shawn can expect to spend?
3.
You went shopping with $20. You bought a notebook for $3.70, 3 pencils for 30¢ each, and a drink,
fries, and burger for $2.20. Estimate the amount of money you had left.
4.
Here is a menu posted at Tom’s school.
Item
Pizza
Hamburger
Salad
Chicken Patty
Cost
$1.75
$2.35
$2.60
$1.95
If Tom buys pizza and a salad and pays with a $5.00 bill, how much change should he get back?
5.
Jordan has to buy 18 gallons of gas that cost $2.49 per gallon. How much will he pay for the gas?
6.
Kelly worked 7.25 hours on Monday and 6.5 hours on Tuesday. She earns $6.80 per hour. How
much did she earn for working these two days?
7.
Michael’s garden is shown below.
15.35 feet
11.75
feet
If Michael buys 60 feet of fencing to go around this garden, how much will he have left over?
8.
Charice’s van drove 147.5 miles and used 11.8 gallons of gas. How many miles per gallon did
Charice’s van travel?
9.
At the grocery store, Jerry spent $24.75 for 3 pounds of chicken and 3 pounds of cheese. The
cheese cost $4.50 per pound. What was the cost of the chicken per pound?
10. CANDY
Package (in ounces)
Package Price
8
$1.60
10
$1.80
12
$2.04
Candy Price
(per ounce)
Complete the table to determine which package has the lowest candy price, per ounce.
11. Bruce needs 30 five-foot pieces of rope for a school project. The hardware store
sells rope by the yard. How many yards of rope will Bruce need to purchase?
12. Eliana and her sister are comparing the prices of two brands of cereal.
Toasty Oats costs $2.25 for a 15-ounce box. Crunchy Oaties costs $3.90 for a 30-ounce bag.
a. What is the price per ounce of the Toasty Oats?
b. How much more expensive is Toasty Oats per ounce than Crunchy Oaties?
6.8 (complete items without the use of a calculator) Order of operations. Fill in blank
IXL: Q1
1. Simplify the expression below.
42 + 52
2. Simplify the expression below.
3 + 5 x 23 +32
3. Simplify the expressions below.
a.
72 - 9 + 1 3
b.
43 ÷ 22
4. Evaluate: 32 ∙ 2 +
6
2
5. Simplify this expression: 38 – 2 + 4 x 3 + 3²
6. Which is equivalent to 20 x (9 – 5) – 12 +4² ?
Measurement and Geometry (12 Questions)
IXL: Y 1, 2
6.9 The U.S. Customary System of measurement and measurements in the metric system.
Temperature
37°C is about 98°F (about normal body temperature).
22°C is about 72°F (about average room temperature).
0°C is about 32°F (water freezing temperature).
100°C is about 212°F (water boiling temperature).
Mountains
1.
If a cat weighs 20 pounds, it would weigh about how many kilograms?
2.
Richmond, VA is about 50 miles from Williamsburg, VA. About how many kilometers is that?
3.
If you need 12 quarts of lemonade for a class party, about how many liters is that?
4.
Which of the following is about the same length as 1 foot?
A
B
C
D
10 centimeters
30 centimeters
1 meter
3 meters
6.10 Area/Perimeter/circumference/volume/SA (Fill in the blank)
IXL: Z26 Z32
P 9 (4th grade)
π (pi) as the ratio of the circumference of a circle to its diameter;
The area determines the perfect square number. If it is not a perfect square, the area provides a means
for estimation.
1. David measures a side of a piece of wood. The length is 8 feet and the width is
one-half of the length. What is the area, in square feet, of the piece of wood?
2. Olivia measures the diameter of a circle. If the diameter is 32 centimeters, what is the radius, in
centimeters?
3. A circle has a radius of 18 inches. What is the circumference of the circle?
4. Gunther drew a circle. The radius of the circle is 20 inches. What is the area, in square inches, of
Gunther’s circle?
5. The diameter of Lexa’s hula hoop is 36 inches. What is the radius, in inches, of Lexa’s hula hoop?
6. Janet discovered a very interesting relationship between the diameter of the circle and the distance
around the outside of the circle.
Circle
A
B
C
Distance
around the
circle
21 cm
28 cm
36 cm
Circumference
almost 6.7 cm
almost 9 cm
almost 11.5 cm
Which statement best describes this relationship?
a. The circumference of the circle is
1
of the diameter of the circle.
3
b. The circumference of the circle is a little more than 3 times the length of the diameter.
c. The diameter of the circle is
1
of the circumference.
2
d. The diameter of the circle is twice the length of the circumference
7. What statement is true about pi ()?
a. Pi is the ratio of the diameter to the radius of a circle.
b. Pi is the ratio of the area of a circle to the circumference of the circle.
c. Pi is different for every circle.
d. Pi is the ratio of circumference of the circle to the diameter of the circle.
8. A model train set has a circular track that has a radius of 75 cm. What is the area on the inside of
the track?
9. Chris wants to build a rectangular pen enclosed by a fence for his horses. The pen will measure 45
feet long by 12 feet wide. How many feet of fencing does he need to enclose the rectangular pen?
10. Mr. Chen has a backyard in the shape of a rectangle that has a perimeter of 128 feet. If the width of
the backyard is 25 feet, what is the length?
11. A garden in the shape of a rectangle has length of 18 feet and a width of 12 feet. Covering the
garden with fertilizer will cost $1.15 per square foot. How much will it cost to fertilize the garden?
12. Carla is filling a fish aquarium with water. The aquarium has the shape of a rectangular prism that
measures 1
1
feet wide, 3 feet high, and 5 feet long. What is the volume of the aquarium?
2
13. If the length of the radius of the circle is 6, what is the area of the square?
a.
b.
c.
d.
12
48
72
144
14. A rectangle has a perimeter of 60 inches and length of 22 inches. What is the width of the
rectangle?
15. If the circumference of a circle is 16𝜫, what is the radius?
16. A circle has a circumference that measures 18 𝜫 inches. What is the radius, in inches, of
the circle?
17.
18.
19.
6.11 Graphs (Hot Spot)
IXL: Q1, 3, 6
a) identify the coordinates of a point in a coordinate plane (fill in the blank)
b) graph ordered pairs in a coordinate plane. (hot spot or graph)
Quadrants
X, Y axis
Origin
Vertical
Horizontal
Name three points on the x axis ____________, _____________, _________________
Name three points on the y axis_____________, _____________, _________________
6.12 congruence of segments, angles, and polygons
IXL: Z14
The symbol for congruency is 
Congruent – Same shape and Same size
6.13 describe and identify properties of quadrilaterals (drag and drop)
IXL: Z.9
Quadrilaterals – 4 sides
Sum of angles = 360 degrees
1.
Quadrilaterals have four angles. What is the sum of the measures of these four angles?
2.
The drawing below shows the shape of a school playground. Find the measure of Q.
P
Q
R
?
50

S
3.
The table shows the measure of three angles of a quadrilateral. What is the measure of the fourth
angle, D?
4.
Which statement is false?
A
B
C
D
A trapezoid has only one pair of parallel sides.
A rectangle is always a square.
A parallelogram is always a quadrilateral.
A square is always a rhombus.
5.
Which of the following quadrilaterals always have 90-degree angles?
A
B
C
D
square and parallelogram
square and trapezoid
square and rectangle
square and rhombus
6.
Which two quadrilaterals have four congruent right angles?
7.
Which two quadrilaterals have four congruent sides?
8.
Choose the answer that correctly identifies only the true statements from the following list.
a. A parallelogram is a quadrilateral with opposite sides congruent and parallel.
b. A rectangle is a square and a polygon.
c. A rectangle is a parallelogram with four right angles.
d. A square is a rhombus.
e. A trapezoid has three parallel sides.
9.
Which is the best description of a kite?
a.
b.
c.
d.
A kite is a rhombus with two pairs of adjacent congruent sides.
A kite is a quadrilateral with one pair of right angles.
A kite is a quadrilateral with two pairs of adjacent congruent sides.
A kite is a quadrilateral with two pairs or congruent angles.
Probability, Statistics, Patterns, Functions, and Algebra (19)
6.14 Graphs (GRAPH)
IXL: R 11, 16
– Bar graphs use categorical (discrete) data (e.g., months or eye color).
– Line graphs use continuous data (e.g., temperature and time).
– Circle graphs show a relationship of the parts to a whole.
Graphs:
Title Labels
Scale
Key
frequency distribution how often an item, a number, or range of numbers occurs. It can be used to
construct a histogram.
1.
The sixth graders at Kelly Middle school voted for their favorite sport.
Favorite Sports of Sixth Graders
Baseball
1
4
Golf
Basketball
1
2
3
20
1
10
Football
If the 180 students in sixth grade get to choose a sport to play for a special reward, about how many of
these students may choose Golf?
2.
Paul kept a record of how he spent his time for 24 hours.
Paul’s Day
inside activities
1
12
1
6
sleeping
outside
activities
1
3
1
other 12
school
1
3
How many hours did Paul spend on outside activities?
3.
Two hundred sixth grade students were asked to name their favorite sport. Here are the results of
this survey.
Favorite Sports
100
90
80
70
Number
of Votes
60
50
40
30
20
10
0
baseball
football
soccer
basketball
6.15 Central Tendency (notes in journal)
IXL: S 1, 2
a) describe mean
balance point (graph on a number line)
fair share
b) When do you use:
1. Mean
2. Median
3. Mode
1.
Justin collected data on how many miles he drove for each day for a week. This data is displayed
on this line plot.
Miles Driven This Week
x
x
21
22
x
x
23
x
24
25
26
x
27
x
28
29
What is the balance point for this set of data?
2.
3.
The list below shows the number of large bags of popcorn sold each day at a movie theater over
five days.
18 19 22 18 23
What is the mean (average) number of large bags of popcorn sold over the five days?
The list below shows the heights, in meters, of five different buildings.
180, 170, 120, 180, 160
What is the median height, in meters, of the buildings?
6.16 independent and dependent events (probability) Graph as a %, fraction, decimal on number line
IXL BB7
Probability is between (0 – 1) 0 no chance 1 always
The closer it is to (1) the stronger the chance.
Graph the probability on a number line. Probability can be represented as a percent, decimal, or a
fraction.
Independent (Replacement)
first roll of a number cube does not influence the second roll of the number cube.
flipping two coins; spinning a spinner and rolling a number cube
flipping a coin and selecting a card
choosing a card from a deck, replacing the card and selecting again.
Ex: When rolling three number cubes simultaneously, what is the probability of rolling a 3 on one
cube, a 4 on one cube, and a 5 on the third?
P(3 and 4 and 5)  P(3)  P(4)  P(5) 
1 1 1
1
  
6 6 6 216
Dependent (Without Replacement)
choosing two marbles from a bag but not replacing the first after selecting it
picking a sock out of a drawer and then picking a second sock without replacing the first
picking a card not replacing then picking a second card
Ex: You have a bag holding a blue ball, a red ball, and a yellow ball. What is the probability of picking
a blue ball out of the bag on the first pick then without replacing the blue ball in the bag, picking a
red ball on the second pick?
1 1 1
P(blue and red)  P(blue)  P(red after blue)   
3 2 6
Probability
Independent or dependent
Graph the results as a percent, decimal, and fraction.
1.
The names of 6 boys and 7 girls are written on cards and placed in a hat. You pick one card, and
without replacing it you pick another. What is the probability of picking 2 cards with girls’ names?
2.
A box of candy has 7 red pieces, 3 orange, 2 yellow, and 8 blue pieces. You get to pick two pieces
of candy. If you reach into the box without looking, what is the probability that you will pick a blue
piece and then a red piece of candy?
3.
A box contains 4 chocolate chip muffins, 2 blueberry muffins, and 1 corn muffin.
A muffin is randomly chosen from the box. What is the probability that a blueberry muffin or a
corn muffin is chosen?
4.
Mrs. Martin must select two different students to represent the class on the school float in the
parade. She puts the name of each student on a slip of paper and places them into a bag. What is
the probability that she will pick two girls’ names if there are 11 girls and 12 boys in the class?
5.
A bowl holds 4 pieces of green candy and 6 pieces of red candy. You take 1 piece of candy from the
bowl and then a second without replacing the first piece. Assuming a red candy was selected first,
what is the probability that both candies will be red?
6.
A bag has 6 red marbles and 4 blue marbles in it. You pick one, and without replacing it you pick
another. What is the probability of picking 2 blue marbles?
6.17 geometric and arithmetic sequences (Hot Spot)
arithmetic difference, called the common difference
6, 9, 12, 15, 18, 
5, 7, 9, 11, 13, .
geometric number patterns, multiplied
This multiplier is called the common ratio
2, 4, 8, 16, 32,
1, 5, 25, 125, 625
80, 20, 5, 1.25
1, 2, 4, 7, 11, 16
1.
What would be the next number in the following series?
1,
2.
1 1 1
,
, ,…
2 4 8
Sam created the following number pattern.
0, 1, 3, 6, 10, 15, ...
Troy said he believed the next number was 20. Sam said he was wrong. What is the next number in
Sam's pattern?
3.
What is the common ratio for this sequence?
120, 12, 1.2, 0.12, 0.012, …
4.
What is the common ratio of the sequence?
6, 0.6, 0.06, 0.006
5.
Arithmetic or geometric?
1, 4, 9, 16
6.
What is the common ratio?
1, 10, 100, 1000, 10,000
7.
Write the next three numbers in the sequence below.
2, -8, 32, -128,
6.18 one-step linear equations in one variable involving whole number coefficients and positive rational
solutions. (fill in blank)
IXL: P5
expression contains a variable (does not have and =)
term is a number, variable, product, or quotient in an expression of sums and/or differences.
In 7x2 + 5x – 3, there are three terms
coefficient numerical factor in a term. 3xy2, 3 is the coefficient;
term z, 1 is the coefficient.
equation is a mathematical sentence stating that two expressions are equal.
variable is a symbol (placeholder) used to represent an unspecified member of a set.
1. If 8 n = 96, what value of n makes the equation true?
2. The classroom teacher wrote the equation shown below for his students to solve to
find the number of kickballs, k, they could buy with the $144, if each kickball cost $9.
144/k= 9
What is the value of k in the equation?
3. Donnie is autographing baseball items. He has a total of 320 baseball cards to sign. He has
signed 14 cards so far. The equation below can be used to determine the number of baseball
cards, c, Donnie still needs to sign.
14 + c = 320
What is the number of baseball cards Donnie still needs to sign?
4. What is the value of n in the equation below?
66 + n = 226
5. At a bakery, there are 16 packages of hamburger buns for sale. The baker placed
8 hamburger buns in each package. He uses the equation below to calculate the
total number of hamburger buns, b, for sale.
b/8= 16
What is the total number of hamburger buns for sale at the bakery?
6. He also signs 300 baseballs, which are stored in 15 boxes. Donnie uses the equation
below to determine the number of baseballs, b, in each box.
15b = 300
How many baseballs are in each box?
7. What value of x makes the equation true?
7 + x = 84
8. A sixth-grade class is having a book sale. The students earn $6 for each book they sell.
To determine how many books they need to sell to reach their goal of $144, they use
the equation below where b represents a certain number of books.
6 b = 144
What is the value of b in the equation?
9. At a bakery, there are 16 packages of hamburger buns for sale. The baker placed 8 hamburger
buns in each package. He uses the equation below to calculate the total number of hamburger
buns, b, for sale.
b/8= 16
What is the total number of hamburger buns for sale at the bakery?
10. What is the value of y?
y
= 48
6
11.
12.
13.
14.
6.19 Properties
Zero property
Identity property additive
Multiplicative Identity property
Multiplicative Inverse property
Additive Inverse Property
15. What property is shown in the equation below?
6x0=0
16. Which number completes this problem correctly?
___ x 9 = 9
17. Morgan listed these problems.
1
8x 8 =1
1
x5=1
5
2 3
x
=1
3 2
What property is Morgan using?
6.20 graph inequalities on a number line (graph)
A8
x > -6
7 > y.
00 = UNDEFINED
5/0= UNDEFINED
0/5 = 0