Entering 7th Grade Math Summer Packet - Doral ... FL522263_Gr6_Mth_TB 5/18/10 1:02 PM Page 5 Pythagorean theorem c a 2 b 2 b a Simple interest formula c 2 I prt where p principal,

Math Summer Packet For

Students Entering 7

Math Summer Packet For

Students Entering 7th Grade

Doral Academy Prep School Math Department

Dear Parents and Students,

We are assigning this work in an effort to prepare our students for a successful school year,

and to provide them with an appropriate way to assist them retaining basic mathematical knowledge

needed for the 7th grade.

This work is not intended to be completed in one sitting. It is intended to be completed at a

steady pace throughout the summer. It will be the first grade to be entered in the grade book upon

returning to school. All exercises have space to show calculations, and calculator answers will not be

accepted. All work must be shown to receive the credit.

The students may be assisted, and we encourage you use the Glossary included in the

school’s website, on Mrs. Linette Prats’ page. Additionally, each section begins with examples to be

followed, and you may refer to the provided FCAT 2.0 Reference Sheet.

Remember that the educational process is a team effort and we all play vital roles- teachers,

parents, and students.

Your partners in education,

Doral Academy’s Math Department Team

Grades 6–8 FCAT 2.0 Mathematics Reference Sheet

KEY

Area

Volume/Capacity

Rectangle A bh

Parallelogram A bh

Triangle A 1 2 bh

Trapezoid A 1 2 h (b1 b2)

b

d

h

r

w

base

diameter

height

radius

width

S.A. surface area

A area B area of base C circumference

volumeV P perimeter of base

slant height

Use 3.14 or for π. 22 7

Circumference C πd or C 2πr

Circle A π r2

Total Surface Area

Rectangular Prism V V

bwh or Bh

orS A bh bw hw . . = + +2 2 2 S A Ph B. . = + 2

Right Circular Cylinder

V V Bh

orπr2h S.A. 2πrh 2B S.A. or2πrh 2πr2

Right Square Pyramid

V 1 3 Bh BPS.A. 1 2

Right Circular Cone V

V

or 1 3 πr 2 h

1 3 Bh

S A r B. . ( )= +2�1 2

Sum of the measures of the interior angles of a polygon = 180(n − 2)

Measure of an interior angle of a regular polygon = 180(n 2) n where:

n represents the number of sides

Florida Department of Education

FL522263_Gr6_Mth_TB 5/18/10 1:02 PM Page 4

FL522263_Gr6_Mth_TB 5/18/10 1:02 PM Page 5

Pythagorean theorem

a2 b2c

b

a

Simple interest formula

c2 I prt

where p principal, r rate, t time

Slope-intercept form of a linear equation

Distance, rate, time formula

d rty mx b

where m slope and b y-intercept where d distance, r rate, t time

Conversions within a System of Measure 1 yard 3 feet 1 mile 1,760 yards 5,280 feet 1 acre 43,560 square feet

1 cup 8 fluid ounces 1 pint 2 cups 1 quart 2 pints 1 gallon 4 quarts 1 pound 16 ounces 1 ton 2,000 pounds

1 meter 100 centimeters 1000 millimeters 1 kilometer 1000 meters

1 liter 1000 milliliters 1000 cubic centimeters 1 gram 1000 milligrams 1 kilogram 1000 grams

1 minute 60 seconds 1 hour 60 minutes 1 year 52 weeks 365 days

Conversions between Systems of Measure

1 inch 2.54 centimeters 1 foot 0.305 meter 1 mile 1.61 kilometers

When converting from Customary to Metric, use these approximations. 1 cup 0.24 liter 1 gallon 3.785 liters 1 ounce 28.35 grams 1 pound 0.454 kilogram

1 centimeter 0.39 inch 1 meter 3.28 feet 1 kilometer 0.62 mile

°C (°F 32) 1.8 °F (°C 1.8) 32

When converting from Metric to Customary, use these approximations. 1 liter 4.23 cups 1 liter 0.264 gallon 1 gram 0.0352 ounce 1 kilogram 2.204 pounds

Temperature conversions between Celsius and Fahrenheit

Grades 6–8 FCAT 2.0 Mathematics Reference Sheet

Florida Department of Education

Big Idea 1: BIG IDEA 1

Develop an understanding of and apply proportionality, including similarity.

1.) It is recommended that for every 8 surface, a pond should have 2 fish. A p surface of 72 square feet should contain

3.) 9 is what percent of 30?

5.) Kristen and Melissa spent 35% of t tickets. How much money did they spe

Develop an understanding of and apply proportionality, including similarity.

square feet of pond that has a in how many fish?

2.) An 8-ounce glass of Oran milligrams of vitamin C. How milligrams of vitamin C?

4.) What percent of 56 is 1

their $32.00 on movie pend?

6.) Jake’s club has 35 mem 60% of them must be presen many members must be pre

Develop an understanding of and apply proportionality, including similarity.

ange juice contains 72 w much juice contains 36

14?

mbers. Its rules require that nt for any vote. At least how

esent to have a vote?

Objective: Determine rate of increase and Examples:

A percent of change is a ratio that is increased, it is a PERCENT OF DECREASE.

1.) Determine the percent of change. R nearest whole percent if necessary. Stat percent of change is an INCREASE or D Original: 250 New: 100

3.) Determine the percent of change. R nearest whole percent if necessary. Stat percent of change is an INCREASE or D

Original: $84 New: $100

5.) Alicia planted 45 tulip bulbs last yea plans to plant 65 bulbs. Determine the in the number of tulip bulbs to the neare

nd decrease, discounts, simple interest, commission

compares the change in quantity to the original am INCREASE. If the original quantity is decreased,

Round to the ate whether the DECREASE.

2.) Determine the sale price

$39.00 jeans 40% off

Round to the ate whether the DECREASE.

4.) Justin is buying a cell p $149. The cell phone is on price. What will be the sale

ear. This year she percent of increase

est tenth.

**6.) You want to buy a ne was $48 dollars. The sale p percent of discount to the n

on, sales tax.

amount. If the original quantity it is a PERCENT OF

rice to the nearest cent.

phone that has a regular price of n sale for 15% off the regular le price?

ew sweater. The regular price price was $34. What was the

nearest percent.

Objective: Determine the surface area of geometric solids using rectangular prisms.

The sum of the areas of all the surfaces, or faces, of a three-dimensional figure is the surface area. The surface area S of a

rectangular prism with length l, width w, and height h is found using the following formula:

S = 2lw + 2lh + 2wh

Example: Find the surface area of the rectangular prism.

You can use the net of the rectangular prism to find its surface area. There are 3 pairs of congruent faces on a rectangular prism:

top and bottom

front and back

two sides Faces Area top and bottom (4 • 3) + (4 • 3) = 24 front and back (4 • 2) _ (4 • 2) =16 two sides (2 • 3) + (2 • 3) = 12 Sum of the areas 24 + 16 + 12 = 52

Alternatively, replace l with 4, w with 3, and h with 2 in the formula for surface area. S = 2lw + 2lh + 2wh S = 2 • 4 • 3 + 2 • 4 • 2 + 2 • 3 • 2 Follow order of operations. S = 24 + 16 + 12 S = 52 So, the surface area of the rectangular prism is 52 square meters.

Find the surface area of the rectangular prisms below. Round to the nearest tenth, if necessary.

1.) 2.)

3.) 4.)

5.) A packaging company needs to know how much cardboard will be required to make boxes 18 inches long,

12 inches wide, and 10 inches high. How much cardboard will be

needed for each box if there is no overlap in the construction?

6.) Oscar is making a play block for his baby sister by

gluing fabric over the entire surface of a foam block. How

much fabric will Oscar need?

Big Idea 2: BIG IDEA 2

Develop an understanding of and use formulas to determine surface areas and volumes of three- dimensional shapes.

Big Idea 3: BIG IDEA 3

Develop an understanding of operations on all rational numbers and solving linear equations.

Objective: Add, subtract, and multiply positive fractions and mixed numbers.

Examples: To add unlike fractions (fractions with different denominators), rename the fractions so there is a common denominator.

Add: 1 + 2 1 = 1x5 = 5 2 = 2x6 = 12 5 + 12 =17

6 5 6 6x5 30 5 5x6 30 30 30 30

Add: 12 1 +

8 2

12 1 =

12 1x3 =

12 3

8 2 =

8 2x2 =

8 4

2 3 2 2x3 6 3 3x2 6

12 3 +

8 4 =

20 7 7

is improper so we must change it to proper. 7 divided by 6 = 1 1

6 6 6 6 6

20 + 1 1 =

21 1

6 6

1.) Add: 1 + 1

3 9 2.) Add: 7

4 + 10

2

9 9

3.) Add: 1 5 +

4 1

9 6 4.) Add: 2

1 + 2

2

2 3

5.) A quiche recipe calls for 2 3

cups of grated cheese. 4

A recipe for quesadillas requires 1 1

cups of grated 3

cheese. What is the total amount of grated cheese needed for both recipes?

6.) You want to make a scarf and matching hat. The

pattern calls for 1 7

yards of fabric for the scarf and 8

2 1