1. 7th Grade Form B
Summer Math Review Packet
2012
(For students entering 7th grade)
Name _________________________
6th Grade Math Teacher ________________

2. Objectives for the Math Summer Packet
Grade 7
2011-2012
I. Exponents (Problems 1 to 5)
• Apply the definition of exponents.
• Use expanded form to express exponents.
• Evaluate exponential expressions.
II. Order of Operations (Problems 6 to 10)
• Review the correct order of operations.
• Evaluate and simplify algebraic expressions using the correct order of
operations.
III. Rounding and Estimating (Problems 11 to 15)
• Round whole numbers to specific place values.
• Real world applications of estimating monetary values.
• Estimating quotients.
IV. Decimals (Problems 16 to 20)
• Add, subtract, multiply, and divide decimals.
V. Fractions and Decimals (Problems 21 to 25)
• Understanding that a fraction and decimal represent the same value.
• Convert a fraction to a decimal.
• Convert a decimal to a fraction.
• Real life application of converting a decimal to a fraction.
VI. Triangles (Problem 26 to 30)
• Identify the different types of triangles.
• Sketch triangles.
• Find the missing angle measures of triangles.

3. VII. Perimeter (Problems 31 to 35)
• Find the perimeter of various polygons.
• Apply algebraic applications to perimeter.
• Find the dimensions of a polygon, given the perimeter.
VIII. Area (Problems 36 to 40)
• Find the area of various polygons using their formulas
• Sketch a square and find its area
IX. Mean, Mode, and Median (Problems 41 to 45)
• Analyze and interpret data
• Find the mean, mode, and median of a given set of data.
X. Sequences (Problems 46 to 50)
• Discover the difference between an arithmetic and geometric
sequence.
• Find the missing terms of a given sequence.
• Create a sequence.

4. Directions: Complete each problem showing all work. You must show
work in order to receive credit for the answer.
EXPONENTS
Question Hint
1. Write 4●4●4●4●4 using exponents 3 4 = 3●3●3●3
2. Write 6 3 in expanded form. 8 2 = 8 ●8
3. Evaluate 22 + 61 Evaluate means to
simplify the exponents
4. Evaluate (3 2 ) 2 Add up the exponents
then take 3 to that power
5. Evaluate 7● 8 − 15 Follow PEMDAS

5. ORDER OF OPERATIONS
Question Hint
6. 4 + 8●2 Follow PEMDAS.
Parenthesis, exponents,
multiplication, division,
addition, and subtraction
7. 12 ÷3 + 9 Follow PEMDAS
8. (3 + 1) + (2 + 10) Follow PEMDAS
9. 2 ● 10 ÷ 5 Multiply and divide
from left to right
10. 18 + 2 – 8 + 1 – 7 Add and subtract
from left to right

6. ROUNDING AND ESTIMATING
Question Hint
11. Round 213,789 to the nearest hundred. Underline the place value
and then look at the digit
to the right to decide if
you round up or down.
12. Round $45.275 to the nearest cent. Cent is the same as the
hundredths place.
13. Tom went shopping at the food store. First, round each item
In his cart were the following items, a to the nearest dollar.
2-liter bottle of soda for $2.97, one bag Then add.
of chips for $1.29, and a hoagie for $4.89.
Estimate the total amount of money that
Tom will spend.
14. Diego wanted to find the 7% sales tax Round to the nearest cent
on purchases that total $15.99. On his
calculator the display showed $1.1193
as the tax. How much sales tax will
Diego pay?
15. Estimate 41.79 divided by 7.23 Round first, then divide.

7. DECIMALS
Question Hint
16. 15.62 + 35.7 = Line up the decimal point.
17. 7.3 + 18 + 0.49 = The decimal is behind a whole
number.
18. 18 – 6.89 = Add in a decimal point and zeroes.
19. 0.45 X 0.003 = Multiply the numbers and then count
decimal spaces.
20. 0.462 ÷ 0.3 = The number after the ÷ is the divisor.
The divisor must be a whole
number.

8. FRACTION AND DECIMALS
Question Hint
Change the following fraction
to a decimal.
3
21. Numerator ÷ denominator
8
2
22. If it is a repeating decimal,
3
use the bar notation
0.4444… = 0.4
Change the following decimals
to fractions:
23. 0.3 The way you read it is the way
you write it.
24. 0.64 Simplify your fraction
Divide out any common factors
25. The tooth fairy left Emily $0.95
under her pillow. Write Emily’s
money as a fraction, in simplest form.

9. TRIANGLES
Question Hint
26. Find a ruler and accurately An equilateral triangle
draw an equilateral triangle. has 3 congruent sides.
Label the lengths of each side.
27. Name an object in your house A right Triangle has only
that contains the shape of a one right angle
Right triangle.
28. Name and sketch a pattern in your
house that contains triangles.
29. The measure of the angles of a The sum of three angles
triangle are 52°, 37°, and x °. of a triangle equals 180°.
Find the measure of “x”.
30. Each angle in an equilateral All three angles in an
equilateral triangle are
triangle = ___________° congruent.

10. PERIMETER
Question Hint
31. Find the perimeter of a triangle Perimeter is the
with sides of 4.8 cm, 9.6 cm and distance around an
5.3 cm. object.
32. Find the perimeter of a regular Regular means all
hexagon with sides of 0.75 m. sides congruent.
33. Farmer Fred’s field is a rectangle Find the length first.
32 yd wide. The length of the Opposite sides of a
field is twice the width. How rectangle are congruent.
much fencing does he need Sketch the rectangle.
to go around it?
34. The perimeter of a “STOP” sign A stop sign is an
is 112 inches. What is the length octagon.
of each side?
35. The frame around a square poster A square has 4 congruent
is 96 inches long. How long is sides.
each side of the poster?

11. AREA
Question Hint
Find the area of the shapes below.
36. Rectangle
A = lw
4cm
12cm
37. Triangle
A = ½ bh
10ft.
15ft.
38. 12 miles Square
A = s2
s - side
39. Circle
A = π r2
Diameter = 10m radius = half of a diameter
π ≈ 3.14
40. Find something that is a Square
square in your house. Measure A = s2
it and find its area.
Item_________________ Length of side____________ Area___________

12. MEAN, MODE, AND MEDIAN
Question Hint
Use the data below to answer questions 41 to 43.
17, 14, 17, 11, 21, 20, 19
41. Find the mean To find the mean, add up
the numbers and divide by the
number of items in your data
set
42. Find the mode Mode occurs most often
43. Find the median Median is the middle
number when the data is in
numerical order
44. If your grades for the quarter Mean = average
are 85, 93, 90, and 88, what is
your mean for the quarter?
45. What is the median of the If there are 2 numbers in
following data: 0, 3, 3, 5, 7, 9, 10, 11 the middle, then you have to
find the average of those 2
numbers

13. SEQUENCES
Question Hint
46. Name the next 3 numbers in Arithmetic sequences-
the arithmetic sequence below same number is added to
and describe the pattern. find the pattern
25, 29, 33, 37, …
47. Name the next 3 numbers in Geometric sequence -
the geometric sequence below multiply by a common
and describe the pattern. ratio to get the next term
2, 10, 50, …
48. Create a sequence using the rule Multiply by .5 is the
below. Provide 4 terms same as dividing by 2
start with 84; multiply by .5
49. Find the missing terms in the Find the pattern of
sequence the numbers to find
the missing terms
12, 15, _____, 21, 24, ______
50. Name the next 3 numbers in the Find the pattern of
sequence below and describe the the numbers given
pattern.
4, 14, 12, 22, 20, 30,…