This document is a summer math review packet for students entering 8th grade. It provides objectives and practice problems for key 8th grade math topics including order of operations, ratios and proportions, solving equations and inequalities, integers, fractions decimals and percents, geometry, statistics, mean median and mode, coordinate system and transformations, and GCF/LCM. The packet contains 50 total practice problems across these 10 math domains to help review and reinforce skills over the summer.

1. 8th Grade Form A
Summer Math Review Packet
2012
(For students entering 8th grade)
Name__________________________________
7th Grade Math Teacher__________________

2. Objectives for the Math Summer Packet
Grade 8
2011-2012
I. Order of operations (Problems 1 – 5)
• Use PEMDAS to evaluate numerical expressions
• Simplify numerical expressions
• Evaluate numerical expressions with exponents and
parentheses
II. Ratios and Proportions (Problems 6 – 10)
• Express ratios as fractions
• Solve proportions
• Write proportions to solve word problems
III. Solving Equations and Inequalities (Problems 11 – 15)
• Solve one step equations involving addition and
subtraction
• Solve one step equations involving multiplication and
division
• Use one step equations to solve word problems
IV. Integers
• Compare and order integers (Problems 16 – 20)
• Evaluate numerical expressions involving adding,
subtracting, multiplying and dividing integers.
V. Fractions, Decimals and Percents (Problems 21 – 25)
• Convert fractions to decimals
• Convert decimals to percents
• Convert percents to decimals
• Order numbers written in various formats
• Find percent of a number in problem solving

3. VI. Geometry (Problems 26 – 30)
• Classify types of angles
• Classify polygons
• Find the missing length in a pair of similar triangles
• Classify quadrilaterals
• Evaluate the sum of the measures of the interior angles
of a polygon
VII. Statistics: Analyze Data (Problems 31 – 34)
• Create a stem and leaf plot given a set of data
• Create a line plot given a set of a data.
• Interpret a line plot
• Interpret a box and whisker plot
VIII. Analyzing Data: Mean, Median and Mode (Problems 35 – 40)
• Determine the mean, median, mode and range of a set of
data
• Analyze data to find mode of a set of data
• Interpret the effects of changing numbers in a set of data
IX. Coordinate System and Transformations (Problems 41 – 45)
• Identify quadrants in the coordinate system
• Identify various transformations
• Graph ordered pairs on a coordinate system
X. GCF/LCM (Problems 46 – 50)
• Find the prime factorization of a composite number
• Find the greatest common factor of a pair of numbers
• Find the least common multiple of a pair of numbers
• Solve word problems involving GCF/LCM

4. Order of Operations
Directions: Simplify. SHOW ALL WORK.
1) 4 × 32 + 2 ÷ 2 - (5 + 3) Hint: Parentheses,
Exponents, Multiplication
and Division, Addition and
Subtraction
2) 12 ÷ 4 + 32 × 3 – 1 Hint: a2 = a x a
3) (3 + 6) × 10 – 8 Hint: Parentheses first!
4) 10 ÷ 5 + 52 × 3 – 2 Hint: work from left to right
5) 4 × 22 + 4 ÷ 4 - (6 + 1) Hint: PEMDAS

5. Ratios and Proportion
6. Solve for x: Hint: Use cross products to solve.
x 18
=
7 42
7. The weather records for one
month of 30 days show the Hint: Ratios must be written in the order
following: specified and in simplest form.
Sunny days - 16
Cloudy days - 10
Rainy days - 5 days
Write the following ratios.
a. Sunny days to all days
b. Cloudy days to all days
c. Cloudy days to rainy days
8. A pancake recipe calls for 2.5 Hint: Set up a proportion.
cups of pancake mix to make 10
servings. How many cups of mix
are needed to make 14 servings?
9. Mrs. Wright wanted one daffodil
plant for every 2 tulip plants in Hint: Keep similar units in the same
her garden. If she planted 20 location in both sides of the proportion.
daffodil bulbs, how many tulip
bulbs did she plant?
10. The scale on a map is 0.25 inches Hint: Keep similar units in the same
equals 8 miles. The measured distance location in both sides of the proportion.
Between 2 cities is 5 inches. What
is the actual distance in miles?

6. Solving Equations and Inequalities
11. Solve by adding or subtracting. Hint: use the inverse operation to
a. 7 + t = 12 isolate the variable.
b. h – 21 = 52
c. 15 = m + 9
12. Solve by multiplying or dividing. Hint: 8z mean 8 times z.
v
a. 8z = 160 mean v divided by 13.
3
v
b. = 52
3
c. -12q = -24
13. Solve each inequality. Hint: Inequalities are solved the
a. t – 11 < 22 same as equations.
b. 15 < y + 12
c. 16k ≥ 64
14. Two sisters, Jenny and Penny, play on Hint: Write an addition equation.
the same basketball team. Last season
they scored a combined total of 458 points.
Jenny scored 192 of the points. Write and
solve an equation to find the number of
points, p, Penny scored.
15. Gary needs to buy a suit to go to a formal dance. Hint: Write a division equation.
1
Using a coupon, he can save $60, which is of
2
the cost of the suit. Write and solve an equation
to determine the cost, c, of the suit.

7. Integers
16. After the first round of the 2005 Masters golf Hint: Negative numbers are
Tournament, scores relative to par were Tiger Woods 2, less than zero.
Vijay Singh -4, Phil Mickelson -2, and Justin Leonard 5.
List the golfers in order from the lowest score to the
Highest.
17. Compare using <, >, or =. Hint: Make a number line
a. −9 ____ 15 if necessary.
b. 13 ____ −17
c. −14 ____ 0
d. 5 ____ −5
18. Evaluate each expression: Hint: If the signs are the
a. −6 + (−12) = same, add the numbers. If
b. −15 + 8 = the signs are different, find
c. 7 + (−10) = the difference of the
numbers and use larger sign
19. Evaluate each expression: Hint: Subtracting a negative
a. −8 − (−11) = is the same as adding
b. 24 − (−27) =
c. −43 – 13 =
20. Evaluate each expression: Hint: Same signs stay
a. −3 x −7 = positive. Different signs
b. −144 ÷ 12 = are negative.
c. −42 ÷ −6 =

8. Fractions, Decimals, and Percents
21. Write the following fractions as decimals: Hint: Divide numerator by denominator.
5
a.
7
7
b.
20
10
c.
3
22. Write the following decimals as percents: Hint: Move the decimal two places
a. 0.65 to the right or multiply by 100.
b. 2.43
c. 0.08
23. Write the following percents as decimals: Hint: Move two decimal two places
a. 43% to the right or divide by 100.
b. 120%
c. 5%
13 13
24. Write 0.25%, , 0.57, and 300% Hint: Change all to decimals first.
5 5
in order from least to greatest.
25. Bags of trail mix are made from 3 Hint: The mix is made up of a total
parts peanuts to 2 parts dried fruit. of five parts. Make a fraction of the
What percent of the mix is peanuts? parts of peanuts to the whole, then
convert to a decimal then a percent.

9. Geometry
26. Classify each angle below as acute, obtuse, Hint: Look up definition of
right, or straight: each type of angle.
a. b. c.
27. Classify each polygon by the number of sides: Hint: Look up definition
(i.e. pentagon, hexagon..)
a. b. c.
28. The triangles below are similar. Find the missing side Hint: Set up a proportion.
labeled x.
x 8
5 10
29. Name each quadrilateral below: Hint: Use definition
(i.e. trapezoid, square...)
a. b. c.
30. The sum of the measures of a polygon can be Hint: In the formula, n
found using the formula (n -2)180. Find the sum represents the number of
of the measures of the angles of a decagon. sides a decagon has.

10. Statistics: Analyzing Data
31. Write the stems that would be used Hint: In the plot the leaves are
in a stem-and-leaf plot for each set the last digit and the stems are
of data. Then make a stem and leaf plot. digits in front of it.
28, 32, 38, 30, 31, 13, 18, 26, 24, 15, 32
32. Make a line plot for the data below: Hint: Draw a number line and
use an X for each time the
45, 35, 50, 40, 40, 55, 30, 35, 45, 35 number appears.
33. The line plot below shows how far in kilometers Hint: Count the number of
some students live from school. How many students X’s.
are represented in the plot?
X
X X
X X X X X X
0 1 2 3 4 5 6 7 8 9
34. This box-and-whisker plot indicates the scores on last week's science test. Which
grade represents the lower quartile? Hint: Find the median of the lower half of the data.

11. Analyzing Data – Mean, Median, Mode
Use the following Data for questions 35, 36,37, and 38:
17, 13,18, 20, 17,15,12
35.Find the mean of the above data Hint: It is the average
36. Find the median of the above data Hint: Put the numbers in
order and find the middle
number.
37. Find the mode of the above data Hint: It is the number that
occurs the most.
38. Find the range of the above data. Hint: It is the difference
between the highest and
lowest number.
39. Rachel is curious about the number of pets that people own. She surveyed her 20
classmates, asking them exactly how many pets they own. Rachel's data is shown below:
Number of Pets 0 Pets 1 Pet 2 Pets 3 Pets
Number of Classmates 7 7 2 4
What is the mode number of pets owned by Rachel's classmates? Hint: Same as #37
40. A set of data set contains 50, 100, 75, 60, 75, Hint: Think about the what
1,000, 90, 100, 125 and 75. Without calculating, each one represents and
would the mean, median or mode be most affected how each one is found.
by eliminating 1,000 from the list? Explain.

12. Coordinate System and Transformations
41. In which quadrant is the ordered pair (3,−2)? Hint: The 1st Quadrant is
at the top right and then
follow counter clockwise.
42. What type of transformation is shown in the figure below? Hint: Is it a reflection (flip),
translation (slide), or
rotation (turn)?
⊳
43. What type of transformation is shown in the figure below? Hint: Refer to #42
44. Graph and label the following ordered pairs below:
A(3,4) , B(−1,2) and C(−2, −3) Hint: (x, y) , go across then
up or down.
45. When playing chess, you can move the game Hint: Refer to #42
pieces up or down, left or right, or diagonally.
What type of transformation is used in this game?
Give reasoning for your answer.

13. GCF/LCM
46. Find the prime factorization of 18. Hint: Use a factor tree to find primes.
47. Find the GCF of 12 and 36. Hint: Think of which is the greatest factor
(a number that divides evenly) of both
numbers.
48. Find the LCM of 12 and 15. Hint: The multiples are like counting by
that number. For example, multiples of 6
would be 6, 12, 18, etc.
49. Mary has piano lessons every two weeks. Hint: Find the LCM of the weeks.
Her brother has soccer tournaments every
three weeks. Her sister has an orthodontist
appointment every four weeks. If they all
happen to fall on this Saturday, how long
until it would happen again?
50. What would be the greatest number Hint: Find the GCF of the rows.
of crayons in each row of a 6, a 10,
and a 12-crayon box if all rows have the
same number of crayons in them?