June 2015

To the Students Taking 7th grade Pre-AP/GT Math at Baines for the 2015-2016 School Year: Next year will be an exciting and challenging year as you take 7th grade Math at the Pre-AP/GT level. The Pre-AP/GT curriculum in math has been designed to prepare students to take high school credit Honors Algebra in 8th grade. In short, you will be learning 4 years of math in 3 years. In order to accomplish this, several 7th grade concepts are taught in the 6th grade GT classes and the non-algebra 8th grade concepts are integrated into the 7th grade Pre-AP/GT classes. The purpose of this packet is to make sure you are as ready to begin the 7th grade portion of this experience as possible. Some of the important skills you need to have in order to be ready for 7th grade Pre-AP math include: comparing and ordering fractions, decimals, percents and integers, fraction operations, decimal operations, adding and subtracting integers with models, squares and square roots, order of operations with exponents, measurement concepts of area and composite area, and using Venn diagrams. This packet has been put together with those skills in mind. To help you strengthen and keep your math skills over the summer, we would like you to complete this packet. If you work one to two pages each week, you'll have the packet completed by the beginning of the school year. This packet will be your first grade in math class. It is due the first full week of school and will be followed with a test over the content in this packet. If you feel you need extra practice beyond that provided in this packet there are several resources available online or in the public library. In order to receive credit for this packet, you must show all work. Though graphing calculators will be used in class, the intent of this packet is to reinforce proficiency in basic skills. No calculators may be used in completing this packet unless otherwise stated. Answers with no work will receive no credit! We hope you have an enjoyable summer. We look forward to meeting you next year.

Sincerely,

Baines Middle School Math Teachers

Show ALL work where applicable. Complete your work on separate notebook paper if you need additional space. Be sure to label each problem with the page and problem number and write your final answer in the packet. No calculators may be used in completing this packet unless there is a calculator symbol at the top of the page. Answers with no work will receive no credit! If you need to reprint any portion of this packet, go to www.baines7thmath.weebly.com. and click on Pre-AP, Summer packet, and then Pre-AP/GT summer packet. Additional textbook support can be found in the 7th grade online textbook. To access the online textbook, go to www.baines7thmath.weebly.com and click on Resources, Websites, and then textbook. You must enter username-max2tx07 and password: lonestar. If you have any questions during June or August, feel free to contact Renell Green, Pre-AP seventh grade math teacher, at 281-634-6949 or renell.green@fortbendisd.com (email will have a better response time).

1

Objective: Converting fractions, decimals, and percents.

• To write a decimal as a fraction, divide the numerator of the fraction by the denominator. • To change a decimal to a fraction, read the fraction mathematically correct identifying the

place value. Decimals and fractions that have a denominator that is a power of 10 (10, 100, 1000, etc.) are read exactly the same.

o 10031310 =. are equivalent and are both read “thirty-one hundredths.”

• To write a fraction as a percent, find an equivalent fraction with a denominator of 100. Instead of writing the denominator of 100, write the value in the numerator with a percent sign.

o %1610016

254

== • To write a percent as a fraction, write the percent (without the percent sign) as the

numerator and 100 as the denominator. Percent means “per 100.” • To write a percent as a decimal, divide the percent by 100 and remove the percent sign.

• To write a decimal as a percent, multiply the decimal by 100 and add the percent symbol.

Convert each of the following values to fractions in simplest form.

1. 0.8 2. 0.52

3. 0.86

4. 2.25 5. 15% 6. 95%

7. 70% 8. 135% 9. 1%

Convert each of the following values to decimals.

10. 21% 11.

2019

12. 10

21 %

13. 851

14. 7%

15.

543

16. 5023

17. 734%

18. 0.5%

Convert each of the following values to percents.

19. 0.06 20.

107

21. 0.66

22. 207

23. 0.247

24. 5017

25. 0.7601

26. 81

27. 5.91

Glencoe Grade 7 online textbook – reference chapter 5, sections 5, 6, and 7 and chapter 7, section 7. 2

Objective: Compare and Order fractions, decimals, percents, and integers

• To compare fractions, decimals, percents and integers, rewrite all numbers so that they are in the same form. For example, if the values are decimals and fractions, rewrite all of the values as decimals and compare.

• To compare fractions, rewrite them so they have common denominators.

• Another way to compare fractions is to express them as decimals. Then compare the

decimals. Fill in each blank with <, >, or = to make a true sentence.

1. 54 ____

45

2. 23

523 .____

3.

25250 ____%

4. 33030 .____. 5. -3 ____ -

27

6. 36% ____

83

Order each set of values from least to greatest.

7. 0.48, 0.46, 209

8.

41 , 23%, 0.4, 0.2,

5013

9. 99%, 89 , 0.89,

87 , 1.1

10. 15°F, -7°F, 32°F, -15°F, -2°F, -27°F

11. The following depths or heights are relative to sea level. List the order of the locations from highest to lowest.

Location Depth or Height (m) Calipatria, California -56

Mount Everest 8,848 Mariana Trench -10,916

Mount McKinley, Alaska 6,194 Lake Superior -406

Glencoe online textbook – reference chapter 5, section 9 and chapter 2, section 2. 3

Objective: Add and Subtract Fractions

• Like fractions are fractions that have the same denominator. To add or subtract like fractions, add or subtract the numerators and write the result over the denominator.

• Simplify if necessary. • To add or subtract unlike fractions, rename the fractions with a least common

denominator. Then add or subtract as with like fractions.

• To add or subtract mixed numbers: o Add or subtract the fractions. Rename using common denominators if necessary. o Add or subtract the whole numbers. o Simplify if necessary.

Example: Find .

851221 −

Add or subtract. Write in simplest form.

1. 103

109+

2.

92

95−

3.

51

158−

4.

121

94−

5.

32

97+

6.

103

125−

7. a + b if 65

=a and .83

=b

8. a – b if

65

=a and .83

=b

9. b−

109 if .

83

=b

10.

512

539 −

11.

435

433 +

12.

517

3215 −

13. 1672

1274 −

14.

523

438 +

15.

5238 −

16.

876

977 +

17.

12117

8310 +

18. 914

151312 −

Glencoe online textbook – reference chapter 6, sections 2 and 3. 4

Objective: Multiply fractions and mixed numbers.

Multiply. Write in simplest form. Include the model for #s 1, 2, 4, and 8.1.

54

21×

2. 53

91×

3.

203

2415

×

4.

51

71×

5.

1514

75×

6.

95

109•

7. 83

114•

8. 97

32∗

9. 2726

139∗

10. 5

94∗

11.

727×

12.

31

214 ∗

13. 12

435 •

14. 73214 ∗

15. 731

532 ×

16. 31

542 ∗

17.

742

941 •

18.

836

655 •

19.

414

9710 ×

20.

437

979 ×

21. 742753 ×.

Glencoe online textbook – reference chapter 6, section 5. 5

Objective: Dividing fractions and mixed numbers.

Divide. Write answer in simplest form. 1.

41

32÷

2.

215 ÷

3.

213

65÷

4. 541

525 ÷

5.

732

764 ÷

6. 65

52÷

7. 10

85÷

8.

21136 ÷

9. 913

326 ÷

10.

21212 ÷

11. 51

21÷

12. 2

317 ÷

13. 10

212 ÷

14. 83

412 ÷

15.

613

614 ÷

Glencoe online textbook – reference chapter 6, section 6. 6

Objective: Multiplying Decimals

Multiply. 1. 714 ×. 2. 923 .∗ 3. 786 ×. 4. 30153 .. ∗ 5. 4218 ×.

6. 14760 .. ∗ 7. 6721 ×. 8. 481340 .. ∗ 9. 910466 .. × 10. 071932 .. ∗

11. 234210 .. × 12. 110236 .. ∗ 13. 381651 .. × 14. 014510 .. ∗ 15. 6325712 .. ×

Glencoe online textbook – reference chapter 3, section 2 7

Objective: Dividing Decimals

Divide. Round the answer to three decimal places if necessary. 1. 329 ÷. 2. 97318 ÷. 3. 4070 ÷. 4. 69721 ÷. 5. 2046 ÷.

6. 8211 ÷. 7. 74380 ÷. 8. 1156217 ÷. 9. 30325 ÷. 10. 8385 ÷.

11. 60910 ÷. 12. 86115 ÷. 13. 3230 ÷. 14. 9698 ÷. 15. 598320 ÷.

Glencoe online textbook – reference chapter 3, section 4 8

Objective: Exponents, Squares, and Square Roots

• The exponent tells you how many times the base is used as a factor.

o To write 63 as a product of the same factor, 6 is used as a factor 3 times. 66663 ••=

o To evaluate 54, find the product of 5555 ••• . So, 54 = 625. o To write 444444 ••••• in exponential form, write the base and count the common

factors. The number of common factors is the exponent. So, 444444 ••••• = 46.

• The product of a number and itself is the square of the number. o The square of 5 is 25 because 5 * 5 = 25.

• The factors multiplied to form perfect squares are called square roots.

o Both 77∗ and ))(( 77 −− equal 49. So 49 has two square roots, 7 and -7. o A radical sign, √, is the symbol used to indicate the positive square root of a

number. So .749 = Write each power as a product of the same factor. 1. 25 2. 16

3. 174 4. 37

5. 73 6. 86

Evaluate each expression. 7. 26 8. 62

9. 47 10. 19

11. 104 12. 34

Write each product in exponential form. 13. 1212 • 14. 101010 ••

15. 4444 ••• 16. 9999999 ••••••

17. 1515151515 •••• 18. 66666666 •••••••

Find the square of each number. 19. 3 20. 22

21. 25 22. 40

23. 9 24. 14

Find each square root. 25. 25 26. 100

27. 441 28. 900

29. 6003, 30. 81

31. What is the square of -37? 32. Find both square roots of 64. 33. Square 7.2. 34. Square 4.5.

Glencoe online textbook – reference chapter 1, sections 2 and 3. 9

Objective: Order of Operations Use the order of operations to evaluate numerical expressions.

1. Do all operations within grouping symbols ( ) first. 2. Evaluate all powers before other operations. 3. Multiply and divide in order from lest to right. 4. Add and subtract in order from left to right.

Example: Evaluate .)( 4518 2 ÷++ 468 2 ÷+ First, add 1 and 5 inside the parenthesis (grouping symbols.) 4368 ÷+ Find the value of 62 98 + Divide 36 by 4. 17 Add 8 and 9. Evaluate each expression. 1. 9 – 3 + 4 2. 5412 +÷ 3. 7225 −× 4. )(2936 ÷ 5. )( 2736 −+ 6. 25263 +× . 7. 3111 2 ÷+ )( 8. 242415 •÷−

9. )()( 4724 +•+ 10. )()( 92183 •÷• 11. 24624 +÷ 12. 37983 )( −−× 13. 43899 )( +−+ 14. 82423 2 ÷+× 15. 39315 2 ÷+÷ )( 16. 35452 +÷ )(

17. 2345 2 ×−× 18. 55613 )( −− 19. 210411 ÷−• )( 20. )( 34210 −×÷ 21. 510821 ×. 22. 42735 −×÷ 23. )( 19725 −+ 24. )( 131612 +÷+

Glencoe online textbook – reference chapter 1, section 4 10

Objective: Adding Integers with Models To add integers, it is helpful to use a model.

• When using counters, first draw circles or squares to represent the problem. o To represent a positive unit, draw a small un-shaded circle or square. o To represent a negative unit, draw a small shaded circle or square.

• Line up negatives and positives so that you can circle “zero pairs.” o (+1) + (-1) = 0. We call a positive tile + a negative tile a zero pair.

• “Remove” all zero pairs by either drawing an “X” through them or drawing an arrow. • The remaining tiles are the answer.

Draw counters or a number line to find the sum of each expression. 1. 5 + (-8) 2. -3 + 3 3. -3 + (-8)

4. -7 + (-7) 5. -8 + 10 6. -7 + 13

7. 15 + (-10) 8. -11 + (-12) 9. -14 + (-13)

Evaluate each expression if a = -8 and b = -4. Draw counters or a number line to find the sum of each expression. 10. 5 + a 11. b + (-9)

12. a + b 13. 12 + b

14. a + (-7) 15. a + 0

Glencoe online textbook – reference chapter 2, section 4. 11

Objective: Subtracting Integers with Models • When using counters to subtract, first draw circles or squares to represent the first

number in the subtraction problem. o To represent a positive unit, draw a small un-shaded circle or square. o To represent a negative unit, draw a small shaded circle or square.

• Look at the second number and “take away” that many tiles by circling the tiles and drawing an arrow.

• IF there are not enough tiles, you must add zero pairs until you have enough of the tiles you need to take away. By adding zero pairs, you are not changing the value of the original number.

• The remaining tiles are the answer. Example 1: Find -5 – (-2). Example 2: Find -3 – 2.

1. Draw 5 negative tiles. 1. Draw 3 negative tiles. 2. Circle and “take away” 2 negative tiles. 2. You can not remove 2 positive tiles so

add two zero pairs. 3. Now you can remove 2 positive tiles. 3. There are 3 negative tiles left,

so -5 – (-2) = -3 There are 5 negative tiles left so -3 – 2 = -5 Subtract. Draw counters to find the difference of each expression. 1. 5 – 2 2. 6 – (-7) 3. 3 – (-2)

4. 8 – 13 5. -7 – (-7) 6. 6 – 11

7. -3 – 8 8. 10 – 12 9. -8 – (-3)

Evaluate each expression if r = -4 and s = 10 and t = -7. 10. r – 7 11. t – s

12. s – (-8) 13. t – r

14. s – t 15. r – s

Glencoe online textbook – reference Chapter 2, section 5 12

13

14

Objective: Measurement – Area and Composite Area • Complex figures are made of two-dimensional figures. • To find the area of a complex figure, separate it into figures whose areas you know how to

find, and then add the areas. A formula chart can be found at the following link by clicking on Grade 7 Mathematics Chart. http://tea.texas.gov/student.assessment/staar/math/

• If a piece appears to be “missing,” you would subtract the area of that piece.

Find the area of each figure. Use ..143≈π Round the answer to the nearest tenths place if necessary. Be sure to label your answers with appropriate units.

Find the perimeter of #1, 2, 4, and 5. For #1 and #5, use .

722

≈π Round all answers to the

nearest tenths place if necessary. Be sure to label units. 1. ______________ 2. ______________ 4. ______________ 5. ______________

Glencoe online textbook – reference chapter 12, section 6.

6.7 mm

13.5 in.

15

Objective: Statistics – Venn Diagrams A Venn diagram is an arrangement of overlapping circles used to show how sets of data are related.

Draw a Venn diagram to show how the sets of data are related. 1.

2.

3. 4.

Glencoe online textbook – reference chapter 9, section 5 16