Download York-6_SOLReview11-12 - pams

SOL 6.1
The students will describe and compare data, using ratios, and will use appropriate notations, such as
a/b, a to b, and a:b.
HINTS & NOTES
** Make sure that you write the ratio
in the order that is asked**
Reduce all ratios!!!
PRACTICE
1. There are 20 green disks and 100 purple
disks in a bag. What is the ratio of purple
disks to green disks?
100
20
20
B.
100
120
C.
20
80
D.
100
A.
2. What is the ratio of squares to total circles?
F. 4:5
G. 5:4
H. 4:9
J. 5:9
3. What is the ratio of the number of gray
circles to black circles.
A.
B.
C.
D.
2 to 5
5 to 4
4 to 2
4 to 5
Skills Checklist
I can…
 Describe a relationship within a set by comparing part of the set to the entire set.
 Describe a relationship between two sets by comparing part of one set to a corresponding part of the
other set.
 Describe a relationship between two sets by comparing all of one set to all of the other set.
 Describe a relationship within a set by comparing one part of the set to another part of the same set.
 Represent a relationship in words that makes a comparison by using the notations a , a:b, and a to b.
 Create a relationship in words for a given ratio expressed symbolically.
Grade 6 SOL Review Packet
b
1
SOL 6.2
The students will
a) investigate and describe fractions, decimals, and percents as ratios;
b) identify a given fraction, decimal or percent from a representation;
c) demonstrate equivalent relationships among fractions, decimals, and percents; and
d) compare and order fractions, decimals, and percents.
PRACTICE
HINTS & NOTES
1. What percent of this grid is shaded?
Percent – a percent is a ratio in which the
first term is compared to 100.
To write a visual as a percent – Count!:
first write as a fraction, then convert to a
decimal. Convert the decimal to a
percent.
Remember – think of percent as per
hundred.
To change a decimal to a percent →
move the decimal to the right (→) two
places.
Example: .234 = 23.4%
To change a fraction to a percent →
divide the numerator (top number) by the
denominator (bottom number). Move the
decimal to the right (→) two places.
3
Example: =.375 = 37.5%
8
To change a fraction to a decimal →
divide the numerator (top number) by the
denominator (bottom number).
Example:
3
=.375
8
A. 40%
B. 60%
2. Of the kids in Ms. Bond’s class, 40% are boys. Which
is the decimal for the part of the class that are boys?
F. 40
G. 0.4
H. 4
J. 0.04
3. Of the students in Mr. Wright’s sixth grade class, 75%
are in art. What fraction of the class is in art?
7
9
7
B.
10
3
4
5
D.
7
A.
C.
4. Which shows these numbers in order from least to
greatest?
42.62
A.
B.
C.
D.
Grade 6 SOL Review Packet
C. 50%
D. 70%
46.2
42.8
45.48
45.48, 46.2, 42.8, 42.62
42.62, 42.8, 46.2, 45.48
42.62, 42.8, 45.48, 46.2
46.2, 45.48, 42.8, 42.62
2
HINTS & NOTES
Steps for ordering numbers:
1. Change all fractions to decimals.
2. Line up the decimals.
3. Add on zeros until the numbers are the
same length. (same number of digits)
4. Ignore the decimals and put them in
order.
**Remember to look for the order that the
questions asks.
(Least →Greatest or Greatest→Least)
=
is equal to
<
is less than
>
is greater than
≠
is not equal to
MORE PRACTICE
5. Which statement is true?
1
1
>
5
4
3
7
G.
>
4 12
2
6
>
3
7
3
6
J.
>
8 11
F.
H.
6. Which symbol makes this statement true?
3
4
A.
B.
C.
D.
5
6
>
<
=
None of the
7. Which ratio is equivalent to 4.5?
F.
H.
G.
J.
8. Which would be located between the two decimals on
the number line?
0.6
A. 0.860
B. 0.481
0.8
C. 0.062
D. 0.731
Skills Checklist
I can…
 Identify the decimal and percent equivalents for numbers written in fraction form including repeating
decimals.
 Represent fractions, decimals, and percents on a number line.
 Describe orally and in writing the equivalent relationships among decimals, percents, and fractions
that have denominators that are factors of 100.
 Represent, by shading a grid, a fraction, decimal, and percent.
 Represent in fraction, decimal, and percent form a given shaded region of a grid.
 Compare two decimals through thousandths using manipulatives, pictorial representations, number
lines, and symbols (<,≤,≥, >, =).
 Compare two fractions with denominators of 12 or less using manipulatives, pictorial representations,
number lines, and symbols (<,≤,≥, >, =).
 Compare two percents using pictorial representations and symbols (<,≤,≥, >, =).
 Order no more than 3 fractions, decimals, and percents (decimals through thousandths, fractions with
denominators of 12 or less), in ascending or descending order.
Grade 6 SOL Review Packet
3
SOL 6.3
The students will
a) identify and represent integers;
b) order and compare integers; and
c) identify and describe absolute value of integers.
HINTS & NOTES
Remember – integers include positive
whole numbers, negative whole
numbers, and zero.
It can be helpful to graph the integers on
a number line. The point furthest to the
left would have the least value and the
point furthest to the right would be the
greatest value.
Absolute value- the distance of a
number from zero on the number line.
Absolute value is represented as |−6| =
6.
PRACTICE
1. Which statement is true?
A.
B.
C.
D.
-82 > 85
4,117 < -2,654
-601 > -456
-72,643 > -81,249
2. Which integer is less than -7?
F.
G.
H.
J.
-9
-6
0
8
3. The temperatures this week were recorded in the chart
below.
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Temperature
-6
-11
-3
-9
-4
On which day was the temperature the warmest?
A.
B.
C.
D.
Monday
Tuesday
Wednesday
Friday
4. Circle all of the integers below.
-4
Grade 6 SOL Review Packet
23
-0.3
2.2
4
HINTS & NOTES cont.
**Remember**
PRACTICE cont.
5. Which list of integers is ordered from greatest to least?
A.
B.
C.
D.
-17, -16, -15
-15, -16, -17
-17, -15, -5
-16, -17, -15
6. Write an integer to represent each situation:
a)
b)
c)
d)
10 degrees above zero
a loss of 16 dollars
a gain of 5 points
8 steps backward
7. Which expression has the smallest value?
A.
B.
C.
D.
|-19|
|-34|
|11|
|47|
8. Which statement is true?
F.
G.
H.
J.
-17 < -19
-13 > -20
-11 > -9
-6 < -8
9. |-5| + |2| =
A.
B.
C.
D.
-7
-3
3
7
10. Which of the following is not an integer?
F. 9
H. 0.1
G. 0
J. -2
Skills Checklist
I can…
 Identify an integer represented by a point on a number line.
 Represent integers on a number line.
 Order and compare integers using a number line.
 Compare integers, using mathematical symbols (<, >, =).
 Identify and describe the absolute value of an integer.
Grade 6 SOL Review Packet
5
SOL 6.4
The students will demonstrate multiple representations of multiplication and division of fractions.
HINTS & NOTES
PRACTICE
Demonstrate multiplication and division
of fractions using representations.
1. Look at the model.
The model represents which product?
A.
3 5

7 6
C.
3 2

7 7
B.
3 6

5 7
D.
5 7

3 6
2. Which model represents a product equivalent to
F.
G.
H.
J.
?
Skills Checklist
I can…
 Demonstrate multiplication and division of fractions using multiple representations.
 Model algorithms for multiplying and dividing with fractions using appropriate representations.
Grade 6 SOL Review Packet
6
SOL 6.5
The students will investigate and describe concepts of positive exponents and perfect squares.
HINTS & NOTES
PRACTICE
Perfect square –the number that
results from multiplying any whole
number by itself.
1. A pattern of increasing perfect squares is
shown below.
Example: 36 = 6 × 6 = 62
36, 49, 64, ___, 100
Perfect square numbers:
1, 4, 9, 16, 25, 36, 49, 64,..
What number needs to be squared to fill the blank for the
missing term?
Any real number other than zero
raised to the zero power is 1. Zero to
the zero power (0) is undefined.
Ex: 20 = 1, 50 = 1, 30 = 1
Exponent – shows how many times a
base is used as a factor.
Ex: 53 = 5 x 5 x 5
(5 is the base, 3 is the exponent)
A.
B.
C.
D.
6
7
8
9
2. Based on the geometric pattern shown,
what is the value of 55?
51 = 5
52 = 25
53 = 225
54 = 625
F. 10
H. 3,125
G. 25
J. 15,625
3. Which is a perfect square between 64 and 100?
A.
B.
C.
D.
81
99
68
74
24 =
4.
F.
G.
H.
J.
6
16
8
32
Skills Checklist
I can…
 Recognize and describe patterns with exponents that are natural numbers, by using a calculator.
2
 Recognize and describe patterns of perfect squares not to exceed 20 , by using grid paper, square
tiles, tables, and calculators.
10 4  10, 000
 Recognize powers of ten by examining patterns in a place value chart:
103  1, 000
102  100
101  10
Grade 6 SOL Review Packet
100  1
7
SOL 6.6
The students will
a) multiple and divide fractions and mixed numbers; and
b) estimate solutions and then solve single-step and multi-step practical problems involving
addition, subtraction, multiplication, and division of fractions.
PRACTICE
HINTS & NOTES
3
1
1. Lindsay bought 2 meters of rope. She used
** Change all mixed numbers to improper
4
3
fractions before performing an operation**
of it for a tire swing. How much rope did she use
for the tire swing?
** To add or subtract fractions – you MUST
have a common denominator.
5
5
A. 2
meters
C.
meters
12
12
** When multiplying fractions – multiply the
5
11
numerators and then multiply the
B. 1 meters
D.
meters
denominators. Make sure to reduce!
7
12
Example:
1 4
4
x
=
3 5 15
**When dividing fractions – change the
division sign to multiplication and flip (write the
reciprocal) of the fraction that follows the sign.
Then multiply and reduce.
KEEP – CHANGE - FLIP
Example:
2.
1
4
1 5
5
÷
=
x
=
3 5
3 4 12
**Remember**
Sum means the result when numbers are
added.
Product means the result when numbers are
multiplied.
Quotient means the result when numbers are
divided.
1
3
+
=
6
4
4
F.
10
7
G.
12
11
12
1
J. 1
12
H.
3. Beth walked
1
5
mile yesterday and
mile today.
4
12
What was the total distance walked by Beth the last
two days?
3
miles
8
5
C.
miles
12
2
miles
3
7
D.
miles
12
A.
4.
1 2
1 
5 3
B.
=
5. Look at the circle.
The shaded part is equivalent to
%.
Grade 6 SOL Review Packet
8
PRACTICE cont.
6.
2
is equivalent to
3
F.
G.
H.
J.
0.6666….
0.6
0.5
0.66
7. Which set of numbers are equivalent?
A. 0.02 = 2% =
9. Maria cut a piece of ribbon
5
foot long. She cuts
6
3
foot off of the piece of ribbon. What is the length
4
of the remaining piece of ribbon?
1
foot
12
1
B.
foot
8
1
C.
foot
6
1
D.
foot
4
A.
3
cups of
4
B. 60% = 0.06 =
10. Grandma’s cookie recipe calls for 2
C.
= 0.25 = 25%
sugar. If grandma wants to triple the recipe, how
D.
= 0.78 = 78%
much sugar will she need?
1
8. Ryan used
a can of oil that had
2
7
8 pints in it to fill his car. About how
8
3
cups
4
1
B. 8 cups
4
A. 8
3
cups
4
1
D. 6 cups
4
C. 6
much oil did he use? Choose the best
estimate.
F. 4 pints
G. 4
1
pints
2
H. 8 pints
J. 8
1
pints
2
Skills Checklist
I can…
 Multiply and divide with fractions and mixed numbers. Answers are expressed in simplest form.
 Solve single-step and multistep practical problems that involve addition and subtraction with fractions
and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or
less. Answers are expressed in simplest form.
 Solve single-step and multistep practical problems that involve multiplication and division with
fractions and mixed numbers that include denominators of 12 or less. Answers are expressed in
simplest form.
Grade 6 SOL Review Packet
9
SOL 6.7
The students will solve single-step and multistep practical problems involving addition, subtraction,
multiplication, and division of decimals.
HINTS & NOTES
** When estimating an answer – pick
the answer choice that is closest to the
answer that you came up with (round).
Rounding – If the digit to the right of the
place to which you are rounding is:
5 or greater – round up
Less than 5 – round down
Watch out for the backwards
problems- the problems that give you
the answer and want you to find the
problem. To solve these – PLUG IN
the answer choices to find the best fit.
PRACTICE
1. Tom’s neighbor paid him $15.75 for mowing the lawn.
Tom then buys a t-shirt for $10.43. How much money does
he have left?
A. $5.00
B. $26.18
C. $25.00
D. $5.32
2. The cost of dinner for three is $20.25. Which is the best
estimate for the price per person of a meal?
F.
G.
H.
J.
When using your calculator, watch your
screen to be sure you have entered
numbers correctly.
$2.50
$5.50
$7.00
$10.25
3. The table shows the prices for CDs at different stores.
Which store has the lowest price per CD?
A.
B.
C.
D.
Budget Buy
CD City
Music Mall
Shop Smart
Skills Checklist
I can…
 Solve single-step and multistep practical problems involving addition, subtraction, multiplication and
division with decimals expressed to thousandths with no more than two operations.
Grade 6 SOL Review Packet
10
SOL 6.8
The student will evaluate whole number numerical expressions, using order of operations.
HINTS & NOTES
The Order of Operations is as
follows:
First- complete all operations inside of
the grouping symbols. ( ), [ ], { }
Second-Solve all exponents
Third-Multiply or Divide in order from
left to right.
Fourth- Add or subtract in order from
left to right.
The power of a number represents
repeated multiplication of the number
83= 8 · 8 · 8.
Any number, except 0, raised to the
zero power is 1.
20 = 1, 50 = 1, 30 = 1
PRACTICE
1. Simplify:
42 + (8 + 2) ÷ 2
A. 13
B. 21
C. 9
D. 14
2. Simplify:
F.
G.
2
H.
J.
6
4
3.
32  1
2
5
2
Evaluate:
A. 1
B. 9
C.
D.
4.
F.
G.
H.
J.
Which step would be done first to simplify
the expression? 3 x 72 + 18 ÷ 2
18 ÷ 2
72
3 x 72
72 + 18
Skills Checklist
I can…
 Simplify expressions by using the order of operations in a demonstrated step-by-step approach. The
expressions should be limited to positive values and not include braces { } or absolute value | |.
 Find the value of numerical expressions, using order of operations, mental mathematics, and
appropriate tools. Exponents are limited to positive values.
SOL 6.9
Grade 6 SOL Review Packet
11
The student will make ballpark comparisons between U.S Customary System of measurement and
measurements in the metric system.
HINTS & NOTES
Length –
12 inches = 1 foot
3 feet = 1 yard
5280 feet = 1 mile
1760 yards = 1 mile
10 millimeters = 1 centimeter
100 centimeters = 1 meter
1000 meters = 1 kilometer
Weight/mass –
16 ounces = 1 pound
2000 pounds = 1 ton
1000 grams = 1 kilogram
Liquid volume –
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
1000 milliliters = 1 liter
Conversions
1 inch ~ 2.5 cm
1 meter ~ 1 yard , meter > yard
1 mile ~ 1.5 kilometer
1 nickel ~ 5 grams
1 kilogram ~ 2 pounds
1 quart ~ 1 liter
0°C ~ 32°F water freezes
100°C ~ 212°F water boils
20°C ~ 70°F room temperature
37°C ~ 98°F body temperature
Area –
100 square millimeters = 1 square
centimeter
10000 square centimeters = 1 square
meter
PRACTICE
1. Which measurement represents the least volume?
A.
B.
C.
D.
9 quarts
35 cups
2 gallons
17 pints
2. Sam bought 324 inches of yarn. How many yards of yarn
did she buy?
F. 108 yards
H. 18 yards
G. 27 yards
J. 9 yards
3. The factory worker filled 6 one-pint jars with jelly. He had
1 cup of jelly left over. How many cups of jelly did he
have to start in all?
A.4 cups
B. 13 cups
C. 7 cups
D. 25 cups
4. Kase bought 4.3 kilograms of peanuts. How many grams
did he buy?
F.
G.
H.
J.
0.43 grams
43 grams
430 grams
4,300 grams
5. The glasses shown each hold 10 fluid ounces when full.
The shaded portions show how much water is in the
glasses.
Which is closest to the amount of water in the glasses?
A.
B.
C.
D.
34 fluid ounces
28 fluid ounces
22 fluid ounces
18 fluid ounces
Skills Checklist
I can…
 Estimate the conversion of units of length, weight/mass, volume, and temperature between the U.S.
SOL 6.10
Customary system and the metric system by using ballpark comparisons. Ex: 1 L ≈ 1qt. Ex: 4L ≈ 4
qts.
Grade
SOL Review
Packet
12
6 Estimate
measurements
by comparing the object to be measured against a benchmark.
The students will
a) define pi (π) as the ratio of the circumference of a circle to its diameter;
b) solve practical problems involving circumference and area of a circle, given the diameter or
radius;
c) solve practical problems involving area and perimeter; and
d) describe and determine the volume and surface area of a rectangular prism.
HINTS & NOTES
The radius of a circle is half the length of the
diameter.
pi (π) ≈ 3.14
Circumference of a circle C= 2πr or C =
πd
Area of a circle A = πr2
PRACTICE
1. If the diameter of a circle is 9 inches, which is
closest to the circumference?
A. 14.13 in.
B. 63.59 in.
2. Bob is trying to grow grass on the circular section
of yard below. If the diameter of the circle is 6
yards, how much seed will he need to cover the
entire area?
If the question is asking for the distance
around something, it is asking for perimeter.
If the question is asking for the amount
needed to cover or the amount of space
something takes, it is asking for area.
Formulas:
Perimeter – sum of all sides
Area of triangle –
A=
1
base x height
2
Area of rectangle –
A = length x width
Area of square –
A = side x side
*Use a piece of paper or ruler to help you
measure length*
C. 28.26 in.
D. 254.34 in.
6 yds.
F. 18.84 yds.2
G. 113.04 yds.2
H. 28.26 yds.2
J. 254.34 yds.2
3. What is closest to the area of a circle if the radius
is equal to 2.5 centimeters?
A. 7.85 sq. cm.
B. 19.63 sq. cm.
C. 15.7 sq. cm.
D. 78.5 sq. cm.
4. Which situation would you use to gather data
in order to derive pi (π)?
F. Measuring a string to wrap around a polygon.
G. Measuring the Circumference and diameter of
several circles.
H. Determining how many one-inch cubes fit into a
container.
J. Determining the number of tiles needed to
cover a surface.
5. What is the area of the large rectangle shown if
each small square is 4 inches wide and 4 inches
long?
A. 30 sq. in.
B.120 sq. in.
Grade 6 SOL Review Packet
C. 80 sq. in.
D. 480 sq. in
13
Rectangular prism – think cardboard box!
All faces and bases are rectangles.
PRACTICE cont
6. How many square inches of fabric does Kendall
need for a triangular flag with a base of 20 inches and
a height of 40 inches?
Surface Area of a rectangular prism is the
sum of the areas of all six faces
SA = 2lw + 2lh + 2wh
F. 800 in.2
G. 120 in.2
H. 400 in.2
J. 100 in.2
Volume of a rectangular prism- V= lwh
Dimensions – length x width of something
7. Robin needs to paint this entire box for her school
project.
How much surface will he need to paint?
A. 22 cm2
B. 304 cm2
C. 44 cm2
D. 320 cm
8. A rectangular prism-shaped box is pictured below.
How much sand will it hold?
F. 4,096 mm3
G. 2,048 mm3
H. 1,101 mm3
J. 5,028 mm3
9. Greg walked around a football field 45 ft long and
15 ft wide. What was the total distance that Greg
walked?
F. 60 ft
G. 600 ft
Grade 6 SOL Review Packet
H. 120 ft
J. 675 ft
14
Practice Cont.
12. Candy is covering a rectangular prism-shaped
box with cloth.
10. The area of Pam’s garden is
between 1,500 and 2,000 square
inches. Which of these choices
could be the dimensions of her
garden?
A.
B.
C.
D.
18 in. x 32 in.
40 in. x 30 in.
30 in. x 60 in.
36 in. x 72 in.
What is the minimum amount of cloth Carl
needs to cover the box?
A. 272 sq. in.
11. What is the area of a triangle with a
length of 20.7 cm and a width of 18
cm?
Area =
B. 192 sq. in.
C. 136 sq. in.
D. 96 sq. in.
Skills Checklist
I can…
 Derive an approximation for pi (3.14 or 22/7 ) by gathering data and comparing the circumference to
the diameter of various circles, using concrete materials or computer models.
 Find the circumference of a circle by substituting a value for the diameter or the radius into the
formula C = πd or C = 2πr.
 Find the area of a circle by using the formula A = πr 2.
 Apply formulas to solve practical problems involving area and perimeter of triangles and rectangles.
 Create and solve problems that involve finding the circumference and area of a circle when given the
diameter or radius.
 Solve problems that require finding the surface area of a rectangular prism, given a diagram of the
prism with the necessary dimensions labeled. Solve problems that require finding the volume of a
rectangular prism given a diagram of the prism with the necessary dimensions labeled.
Grade 6 SOL Review Packet
15
SOL 6.11
The students will
a) identify the coordinates of a point in a coordinate plane; and
b) graph ordered pairs in a coordinate plane.
HINTS & NOTES
Quadrants are named in
counterclockwise order.
PRACTICE
1. Six points are shown on the grid.
Which three points can be connected in the order shown
to form a right triangle?
signs on the ordered
pairs are: quadrant I (+,+)
quadrant II, (–,+)
quadrant III, (–, –)
quadrant IV, (+,–)
Origin-is the point at the intersection of
the x-axis and the y-axis.
A.
B.
C.
D.
Points N, P, and S.
Points N, R, and T.
Points M, N, and R.
Points M, S, and P.
2. Which point is located in Quadrant I?
F. (-1, 3)
G. (2, 1)
H. (-5, -2)
J. (4, -4)
3. Mary graphed the following two points on a grid
For all points on the x-axis,
the y-coordinate is 0.
For all points on the y-axis,
the x-coordinate is 0.
A (3, 11) and C (9, 11)
What is the length of
?
4. Using the numbers below, what two numbers could be
moved below to make an ordered pair found on the x-axis.
Name as many ordered pairs as you can find that are
found on the x-axis.
Skills Checklist
I can…
 Identify and label the axes of a coordinate plane.
 Identify and label the quadrants of a coordinate plane.
 Identify the quadrant or the axis on which a point is positioned by examining the coordinates (ordered
pair) of the point.

orderedPacket
pairs in the four quadrants and on the axes of a coordinate plane.
Grade 6Graph
SOL Review
16
 Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate
plane.
 Relate the coordinate of a point to the distance from each axis and relate the coordinates of a single
SOL 6.12
The student will determine congruence of segments, angles, and polygons.
HINTS & NOTES
Congruent polygons – same shape
and size
PRACTICE
1. Which shapes are congruent?
Congruent segments – have the exact
same length
A.
B.
Congruent angles –
have the exact same degree measure
**You can always trace a figure, line,
or angle and lay it on top of a second
figure, line, or angle to see if they are
congruent**
C.
D.
2.
3. Circle all the shapes that appear to be congruent.
Skills Checklist
I can…
 Characterize polygons as congruent and noncongruent according to the measures of their sides and
angles.
 Determine the congruence of segments, angles, and polygons given their attributes.
 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the
length of a side joining points with the same first coordinate or the same second coordinate. Apply these
techniques in the context of solving practical and mathematical problems.
Grade 6 SOL Review Packet
17
SOL 6.13
The student will describe and identify properties of quadrilaterals.
HINTS & NOTES
Quadrilaterals
Trapezoid – figure has exactly
one pair of parallel sides.
Parallel sides are called bases.
Non-parallel sides are called
legs. If the legs are congruent
then it is an isosceles trapezoid.
Parallelogram – opposite sides
are congruent and parallel
Rectangle – parallelogram with
four right angles. Diagonals
bisect each other into two equal
parts.
Rhombus – parallelogram with
four congruent sides
Square – parallelogram with four
right angles and four congruent
sides
Kite- quadrilateral with two pairs
of adjacent congruent sides. One
pair of opposite angles is
congruent.
PRACTICE
1. What is the sum of the measures of all the
interior angles of any quadrilateral?
A. 540o
B. 180o
C. 360o
D. 90o
2. Which two figures always have four right angles?
F.
G.
H.
J.
parallelogram and rectangle
square and equilateral triangle
square and rhombus
rectangle and square
3. Which shape is not a quadrilateral?
A. Trapezoid
C. pentagon
B. parallelogram
D. square
4. Which set of angles could be the angle measures of a
quadrilateral?
F.
G.
H.
J.
*sum of the measures of the interior
angles of a quadrilateral = 360o
5. What is the best name for all of the figures?
Quadrilaterals can be classified by
their sides (are they parallel?
congruent?), by the measure of their
angles (any right angles?)
A. Parallelogram
B. Square
C. Rhombus
D. Rectangle
6. Find the measure of the missing angle.
x = __________
Skills Checklist
I can…
 Sort and classify polygons as quadrilaterals, parallelograms, rectangles, trapezoids, kites, rhombi,
and squares based on their properties. Properties include number of parallel sides, angle measures
and number of congruent sides.
 Identify the sum of the measures of the angles of a quadrilateral as 360°.
Grade 6 SOL Review Packet
18
SOL 6.14
The students, given a problem situation, will
a) construct circle graphs;
b) draw conclusions and make predictions, using circle graphs; and
c) compare and contrast graphs that present information from the same data set.
HINTS & NOTES
Circle graph – compares parts to a
whole – think of a pizza! All of the
sections of a circle graph add up to
100%
PRACTICE
1. Which circle graph shows the data in the table below?
Read any title, labels, key, or categories
of a graph.
Graphs from previous years may also
show up.
Line graph – shows change over time
Stem-and-leaf plot –
displays data items in order. A leaf is
the item’s last digit.
Bar graph – displays items in bars and
is used to compare amounts
2. Which two items together make up more than half of
Karen’s budget?
F.
G.
H.
J.
Grade 6 SOL Review Packet
meat and vegetables
vegetables and dairy
bakery and meat
dairy and fruits
19
PRACTICE cont.
3. A circle graph often gives what
kind of information?
5. According to these two circle graphs, which statement is
correct?
A. comparisons
B. pictures
C. percents
D. rows
4. Which three sections of the
circle graph make up 50% of
the sports that students enjoy?
Favorite Sports of Middle
School Students
A. The same number of boys and girls play the flute.
B. The flute is played by more girls than boys.
C. The number of boys playing either the tuba or the clarinet is
the same as the number of girls playing the tuba or clarinet.
D. Fifty girls play the trumpet or trombone.
6. The students in Mr. Smith’s play a game using a fair
spinner. After Spinning, they record the following results:
Which spinner was Mr. Smith’s class probably using?
1.___________________
F.
H.
H.
J.
2.___________________
3.___________________
Skills Checklist
I can…
 Collect, organize and display data in circle graphs by depicting information as fractional.
 Draw conclusions and make predictions about data presented in a circle graph.
 Compare and contrast data presented in a circle graph with the same data represented in other
graphical forms.
Grade 6 SOL Review Packet
20
SOL 6.15
The students will
a) describe the mean as balance point; and
b) describe which measure of center is appropriate for a given purpose.
PRACTICE
HINTS and NOTES
1. For which data set is the mean the best measure of central
tendency?
Mean =
Mean as Balance Point-The mean can
also be defined as the point on a numb
er line where the data distribution is
balanced. The sum of all the distances
from the mean of all points above the
mean is equal to the sum of all the
distances from the mean of all data
below the mean.
Median – middle number in a set of
ordered data
Mode – the item that occurs most often
Measures of CenterWhen should I use mean, median, or
mode?
Mean- works well for data with no very
high or very low numbers.
Median-Use when data sets have a
couple of values that are much higher or
much lower than the other numbers.
Mode-Use when you have identical
values or when data is in a yes or no
survey.
A.
B.
C.
D.
2.
94, 96, 98, 100. 97
54, 60, 58, 3, 64
26, 29, 71, 28, 71
5, 5, 5, 301, 5
School Enrollment
Grade
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
# of Students
92
91
72
86
93
What is the median for the number of students in each
grade attending this school?
F. 72
G. 92
H. 91
J. 86
3. What is the balance point for the following data?
13, 13, 14, 18, 17, 18, 19
balance point =
4. Match each set of data on the left to the correct mode on
the right. Draw a line to connect them.
1, 2, 6, 7, 9, 1, 3, 4, 12, 52
no mode
12, 13, 6, 8, 9
mode of 1 and 4
1, 3, 4, 1, 1, 4, 4
mode of 1
Skills Checklist
I can…
 Find the mean for a set of data.
 Describe the three measures of center and a situation in which each would best represent a set of
data.
 Identify and draw a number line that demonstrates the concept of mean as balance point for a set
of data.
Grade 6 SOL Review Packet
21
SOL 6.16
The students will
a) compare and contrast dependent and independent events; and
b) determine probabilities for dependent and independent events.
HINTS & NOTES
Independent Event- the outcome of
one event has no effect on the outcome
of the other.
Dependent Event-the outcome of one
event is influenced by the outcome of
the other.
The probability of an event occurring
is a ratio between 0 and 1. A
probability of 0 means the event will
never occur. A probability of 1 means
the event will always occur.
Always write probability as a fraction
first (
), then
PRACTICE
1. Gerald has a fair number cube numbered one through six.
What is the probability that he will roll a 4 on his first roll?
A
B
1
6
4
6
1
4
5
6
C
D
2. Gretchen has a bag of candy of candy.
In the bag, there are
2 green candies
4 red candies
3 yellow candies.
If Gretchen draws a piece of candy from her bag and does
not replace it, what is the probability that she will draw a
red candy followed by a green candy?
change it to a decimal or percent if
needed
F
H
G
J
8
81
3. Choosing a marble from a bag, replacing it, and then
choosing another marble is an example of which type of
event?
A
B
C
D
independent event
dependent event
complementary event
sequential event
4. Four of 9 kittens in a litter are gray and 5 kittens are black.
What is the probability that the first and second kittens to
open their eyes will be the gray kittens?
F
1
6
G
2
9
H
4
9
J
Practice Cont.
Grade 6 SOL Review Packet
22
5. A bag contains 10 yellow counting
chips and 10 red counting chips.
What is the probability that Sara will
pick a yellow chip, keep it, and then
draw a red chip on her second draw?
A
B
1
10
11
21
C
D
7. What is the probability of spinning a 6 on the first spin
and a 5 on the second spin, if the spinner is spun twice?
A
B
5
19
5
38
C
D
6. Madeline made a spinner with
equal sections.
8. The following cards are placed in a bag and drawn at
random without replacement. What is the probability of
drawing an A, and then drawing a M?
What
is the probability of Madeline not
landing on white when the spinner is
spun?
F
0%
G
12.5%
H
50%
J
87.5 %
M
A
A.
T
H
B.
E
M
C.
A
T
I
C
S
D.
Skills Checklist
I can…
 Determine whether two events are dependent or independent.
 Compare and contrast dependent and independent events.
 Determine the probability of two dependent events.
 Determine the probability of two independent events.
Grade 6 SOL Review Packet
23
SOL 6.17
The students will identify and extend geometric and arithmetic sequences.
HINTS & NOTES
PRACTICE
1.The first four figures in a pattern are shown.
Arithmetic Sequence –
A sequence where you add the same
number to each term to get the next
term.
**The number added is called the
common difference (d).**
If the numbers are getting bigger, the
common difference is a positive number.
If the numbers are getting smaller, the
common difference is a negative
number.
Geometric Sequence –
A sequence where you multiply the
same number times each term to get the
next term.
**The number multiplied is called the
common ratio (r).
If the pattern continues to double the number of dots,
what will be the total number of dots in the 7th figure
in the pattern?
A. 256
B. 128
C. 64
D. 32
2. Kendall wrote the number pattern shown
1, 2, 4, 7, 11, …
She noticed another pattern when she found that the
differences between the numbers increased by 1 as
shown below.
If the differences continue to increase by 1, what will
be the 8th term in Kendall’s original pattern?
F.
G.
H.
J.
Grade 6 SOL Review Packet
16
22
28
29
24
PRACTICE cont.
5.
3. Which sequence has a common
ratio of 4?
A.
B.
C.
D.
Match each sequence on the left with the correct answer
from below.
4, 40, 400, 4000, …….
8, 40, 200, 1000, ……
4, 8, 16, 32, ……..
3, 12, 48, 192, …..
4. Which sequence has a common
difference of 5?
F.
G.
H.
J.
0, 5, 15, 30, 50, …..
3, 8, 13, 18, …..
55, 45, 35, 25, ……
25, 35, 55, 75, ……
6. Match each sequence on the left with the correct answer
from below.
Skills Checklist
I can…
 Investigate and apply strategies to recognize and describe the change between terms in arithmetic
patterns.
 Investigate and apply strategies to recognize and describe geometric patterns.
 Describe verbally and in writing the relationships between consecutive terms in an arithmetic or
geometric sequence.
 Extend and apply arithmetic and geometric sequences to similar situations.
 Extend arithmetic and geometric sequences in a table by using a given rule or mathematical
relationship. Compare and contrast arithmetic and geometric sequences.
 Identify the common difference for a given arithmetic sequence.
 Identify the common ratio for a given geometric sequence.
Grade 6 SOL Review Packet
25
SOL 6.18
The student will solve one-step linear equations in one variable involving whole number coefficients
and positive rational solutions.
HINTS & NOTES
Plug it in! Plug it in!
For any problem involving solving an
equation, plug in all of the answer
choices until you find the one that
works.
Remember*
To undo addition – subtract
To undo subtraction – add
To undo multiplication – divide
To undo division – multiply
PRACTICE
1. Which represents the variable in the
following number sentence?
4 + 3h = 27
A.
B.
C.
D.
2. Which method could be used to solve the number
sentence shown?
Always do the exact same things to
both sides of an equation!!!
x + 9 = 12
Variable – a letter or symbol that
represents a number
F. Add 9 to both sides of the equation
G. Subtract 9 from both sides of the
equation
H. Multiply both sides of the equation by 9
J. Subtract 12 from both sides of the
equation
Coefficient – the number in front of a
variable. In the term 7y, 7 is the
coefficient.
Term – part of an expression separated
by a + or -. In the expression 4x + 5,
both 4x and 5 are terms of the
expression
4
h
3
3h
3. What value of y makes the number sentence shown true?
4y = 20
A.
B.
C.
D.
Equation - a statement in which two
expressions are shown to be equal.
4
5
16
80
4. Look at the equation mat.
What is the value of x?
2
G. 3
F.
H. 6
Grade 6 SOL Review Packet
J. 7
26
PRACTICE cont
5. Which is an equation?
A. x +
10.
3
= 16
4
B. x
C. x +
3
4
Using the representations above, which
model best represents the following?
D. 4x < 6
2r = 18
6. How many terms are in the expression
3x + 2y + 4?
F.
G.
H.
J.
2
3
4
9
7. Circle all the terms of this problem.
8. Solve for w, write answer in box.
9. Solve for k, write answer in
box.
13k = 39
Skills Checklist
I can…
 Represent and solve a one-step equation, using a variety of concrete materials such as colored
chips, algebra tiles, or weights on a balance scale.
 Solve a one-step equation by demonstrating the steps algebraically.
 Identify and use the following algebraic terms appropriately: equation, variable, expression, term,
and coefficient.
Grade 6 SOL Review Packet
27
SOL 6.19
The students will investigate and recognize
a) the properties for addition and multiplication;
b) the multiplicative property of zero; and
c) the inverse property of multiplication.
HINTS & NOTES
1.
Multiplicative property of zero-the
product of any real number and zero
equals zero.
6+1=7
Additive Identity Property-the sum of
any real number and zero is equal to the
given real number. 5 + 0 = 5
6+0=6
6●0=0
6● 1 = 6
Which student used the additive identity property?
A.
B.
C.
D.
Multiplicative Identity Property- the
product of any real number and one is
equal to the given number.
Multiplicative Inverse Property- the
product of a number and its
multiplicative inverse (reciprocal) always
equals one.
PRACTICE
Three students wrote their work on a white board.
Lisa
Doug
Tricia
Anna
Lisa
Doug
Tricia
Anna
2.
Which is not an example of the multiplicative property
of zero?
F. 5 + (-5) = 0
G. 5 ● 0 = 0
H. 0 ● 1 = 0
J. 0(-5) = 0
3.
Which property is shown in the following number
sentence?
A.
B.
C.
D.
4.
Multiplicative Identity
Multiplicative Inverse
Additive Identity
Additive inverse
Which property was used in the following number
sentence?
6●1=6
F. Multiplicative Inverse
G. Additive Inverse
H. Multiplicative Identity
J. Additive Identity
Skills Checklist
I can…
 Identify a real number equation that represents each property of operations with real numbers, when
given several real number equations.
 Test the validity of properties by using examples of the properties of operations on real numbers.
 Identify the property of operations with real numbers that is illustrated by a real number equation.
NOTE: The commutative, associative and distributive properties are taught in previous grades.
Grade 6 SOL Review Packet
28
SOL 6.20
The students will graph inequalities on a number line.
HINTS & NOTES
PRACTICE
Inequalities – To graph < or > on a
number line, use an open circle on the
number line and a shaded line covering
the solution.
1. Graph the following inequalities.
x≥5
To graph ≤ or ≥ on a number line, use
a closed circle on the number line and a
shaded line covering the solution.
-3 < x
The solution set to an inequality is the
set of all numbers that make the
inequality true.
2. Look at the graph below.
These inequalities are equivalent
x > -6 and -6 < x
Answers should have the variable on
the left of the inequality sign. To flip the
inequality, switch the two sides and
change the inequality sign.
Which inequality describes the graph?
A.
B.
C.
D.
n<4
n>4
n≤4
n≥4
3. Which graph represents 50 > m?
F.
G.
H.
J.
Skills Checklist
I can…
 Given a simple inequality with integers, graph the relationship on a number line.
 Given the graph of a simple inequality with integers, represent the inequality two different ways
using inequality symbols (<, >, <, >).
Grade 6 SOL Review Packet
29