unit 1: number and operations: practice activity...

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CD-1582

Mark Twain Media/Carson-Dellosa Publishing LLC

Mark Twain Media/Carson-Dellosa Publishing LLC

CD-1582

• NCTM Standards based• Multiple grade-appropriate opportunities• Practice targeting each skill• Assessment/standardized- test format

Printed in the USA

Math Engagement: Grade 8

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Name: Date:

1582-EB © Mark Twain Media, Inc., Publishers

Skill: .Understanding .numbers, .ways .of .representing .numbers, .relationships .among .num -bers, .and.number.systems

Unit 1: Number and Operations: Practice Activity 1Name the place of the number in bold.

..1.. 75,861,298 . ..6. 6.257

..2.. 742,681,075 . ..7. 0.1046

..3.. 25,468 . ..8. 25.68

..4.. 289,726,488 . ..9. 9.0462.

..5. 12,945 . 10. 0.309

Write each number in word form.

11.. 79,643,741

12.. 2,786,581

13.. 300,000,000

14.. 278,001

15. 34.952

Write each number in standard form.

16.. eighteen million, four hundred seventy-nine

17.. six billion, eight million, nine hundred thousand, one

18.. twenty-nine thousand, six hundred fifty-four

19.. five hundred thousand, eight hundred fifteen

20. four hundred seventy-six and eighty-nine hundredths

Unit 1: Number and Operations: Practice Activity 1


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Put the decimals in order from least to greatest.

..1.. 0.74, 0.0074, 7.4, 0.072, 0.081

..2.. 2.4, 0.24, 0.024, 0.0024, 0.009

..3.. 0.58, 0.058, 0.051, 0.078, 0.091, 0.221

..4.. 0.64, 6.4, 0.246, 0.028, 2.86, 0.064

..5.. 0.89, 0.089, 0.913, 9.34, 0.227, 0.335

Put the decimals in order from greatest to least.

..6.. 0.325, 3.25, 2.41, 0.241, 0.375

..7.. 0.789, 78.9, 0.069, 0.54, 0.003

..8.. 0.221, 0.021, 278.0, 42.7, 0.076, 0.085

..9.. 0.29, 0.045, 7.89, 0.681, 0.742, 0.86

10.. 27.1, 0.271, 0.00271, 0.224, 0.004

Just. a.Tip: It is usually easier to compare decimals than to compare fractions, so you might want to consider converting fractions to decimals when you are putting fractions in order from least to greatest or from greatest to least.

Put the fractions in order from least to greatest.

11.. , , , 12.. , , ,

Put the fractions in order from greatest to least.

13.. , , , 14.. , , ,

15.. , , ,



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Write each decimal in number form.

..1.. one and nine tenths

..2.. seventeen hundredths

..3.. eleven hundredths

..4.. six and eight tenths

..5.. seventy-nine hundredths

Just. a.Tip: You can divide the numerator by the denominator to find each fraction in decimal form.

Find a decimal equal to each fraction.

..6..

.7.

..8..

..9..

10..

WAKE-UP.WORD.PROBl EM: Janice saves $789.65 during summer vacation. Her older sister, Tammy, saves about twice as much money. Her younger sister, Sue, saves about one-third as much as Tammy. How much money does Tammy save? How much money does Sue save?



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Just. a.Tip: In a number such as 52, the 5 is the base and the 2 is the exponent . The exponent indicates how many times the base is to be multiplied. For example, in 52, the 2 tells you to multiply the 5 two times. 52 = 5 x 5 = 25. When a base number has an exponent, the base number is said to be raised to the indicated power, so 52 is read as “5 to the second power.” Any base raised to the zero power equals one. 30 = 1, 100 = 1 Any base raised to the first power equals the base. 31 = 3, 101 = 10

Scientific. notation is a way to write large numbers in a smaller space using exponents to indicate the powers of 10. First, move the decimal point just to the right of the number in the farthest left place. Then, you multiply that number by 10 raised to the number of decimal places you moved over.

Example: 3,829 Move the decimal point to 3.829. The number can now be written as 3.829 x 103. You can check the number by multiplying 3.829 x (10 x 10 x 10) = 3.829 x 1,000 = 3,829. If you have a number like 700, you can drop the zeros when writing scientific notation. 700 = 7 x 102


Raise each base to the indicated power.

..1. 103

..2. 25

..3. 73

..4. 82

..5. 104

..6. 91

..7. 102

..8. 120

..9. 105

10. 111

Rewrite each number in scientific notation.

11.. 700,000

12.. 48,000,000

13.. 324.8

14.. 2,475.9

15.. 7,897,987

16.. 64.8

17.. 185,500,000

18.. 187,000

19.. 13,765.8

20.. 58,500,000


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Unit 1: Number and Operations: Assessment 1

Name the place of each number in bold.

..1.. 279,643,281 ❍ A. ten thousands ❍ B. hundred thousands ❍ C. ten millions ❍ D. hundred millions

..2.. 38,271,290 ❍ A. millions ❍ B. ten millions ❍ C. hundred thousands ❍ D. billions

Mark the answer that shows each number in word form.

..3.. 5,287,649 ❍ A. five million, two hundred seven thousand, six hundred forty-nine ❍ B. five million, two hundred eighty-seven, six hundred forty-nine ❍ C. five hundred thousand, two hundred eighty-seven thousand, six hundred forty-nine ❍ D. five million, two hundred eighty-seven thousand, six hundred forty-nine

..4.. 51,687,208 ❍ A. fifty-one million, six hundred eighty-seven thousand, two hundred eighteen ❍ B. fifty million, six hundred eighty-seven thousand, two hundred eight ❍ C. fifty-one million, six hundred eighty-seven thousand, two hundred eight ❍ D. fifty-one billion, six hundred eighty-seven thousand, two hundred eight

Mark the answer that shows each number in standard form.

..5.. two hundred eighty-five million, four hun-dred thousand, three hundred two

❍ A. 2,854,302 ❍ B. 285,400,320 ❍ C. 285,400,302 ❍ D. 285,402,300

..6.. five hundred fifteen thousand, six hundred eighty-nine

❍ A. 515,609 ❍ B. 515,689 ❍ C. 5,156,890 ❍ D. 551,689

Mark the answer that puts the decimals in order from least to greatest.

..7.. 0.071, 0.71, 0.081, 8.01, 0.17 ❍ A. 8.01, 0.71, 0.17, 0.081, 0.071 ❍ B. 0.081, 0.071, 0.17, 0.71, 8.01 ❍ C. 0.071, 0.081, 0.71, 0.17, 8.01 ❍ D. 0.071, 0.081, 0.17, 0.71, 8.01

Mark the answer that puts the decimals in order from greatest to least.

..8.. 0.21, 0.025, 0.79, 0.068, 2.40 ❍ A. 2.40, 0.79, 0.21, 0.025, 0.068 ❍ B. 0.025, 0.068, 0.21, 0.79, 2.40 ❍ C. 2.40, 0.21, 0.79, 0.068, 0.025 ❍ D. 2.40, 0.79, 0.21, 0.068, 0.025



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Mark the answer that puts the fractions in order from least to greatest.

..9.. , , , ,

❍ A. , , , ,

❍ B. , , , ,

❍ C. , , , ,

❍ D. , , , ,

Mark the answer that puts the fractions in order from greatest to least.

10.. , , , ,

❍ A. , , , ,

❍ B. , , , ,

❍ C. , , , ,

❍ D. , , , ,

Unit 1: Number and Operations: Assessment 1 (cont.)

Mark the answer that shows each decimal in number form.

11.. one and seventy-eight hundredths ❍ A. 1.78 ❍ B. 17.8 ❍ C. 0.178 ❍ D. 0.1078

12.. sixteen and eighty-seven hundredths ❍ A. 16.787 ❍ B. 0.1687 ❍ C. 16.087 ❍ D. 16.87

Mark the decimal that is equivalent to each fraction.


13.. ❍ A. 0.57 ❍ B. 0.56 ❍ C. 0.059 ❍ D. 5.6

15.. ❍ A. 0.25 ❍ B. 0.55 ❍ C. 0.075 ❍ D. 2.50

14.. ❍ A. 0.088 ❍ B. 0.8 ❍ C. 8.0 ❍ D. 0.18


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Skill: .Understanding.meanings.of.operations.and.how.they.relate.to.each.other


Just. a.Tip: It is important to know the order in which you should perform arith-metic operations. First, perform any exponentiation, and do any operations in parentheses. Next, perform multiplication and division from left to right. Finally, perform addition and subtraction from left to right.

Evaluate each expression. Do not use a calculator.

..1.. 180 ÷ 6 ÷ 2 =

..2.. 104 - 36 =

..3.. 14 + 0.06 ÷ 2 =

..4.. 12 • 12 ÷ 16 =

..5.. 58 - 17 - 21 =

..6.. 10 • 62 - 12 =

..7.. 35 + 44 =

..8.. 95 - 22 • 8 =

..9.. 45 - 8 • 5 =

10.. 94 • 26 =

11.. 60 ÷ 6 ÷ 2 =

12.. - 4 • 8 =

Extension. Activity: Write a problem. Solve the problem, and then write two to four complete sentences beneath the problem explaining how you solved it.



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Just. a.Tip: .Variables are letters that represent certain values. Sometimes the values are given, and sometimes the values are unknown. Remember to substi-tute the correct value for each variable. The value. of. each. expression will be the value of the entire number sentence, with the correct values substituted for each variable.

Evaluate each algebraic expression if b = 4, c = 6, d = 8. Remember to use the correct order of operations.

..1.. 3c + d 2 - 4 =

..2.. 1/b - • 9d =

..3.. 8c - 4d ÷ b =

..4.. 14 + 32/d ÷ 2 =

..5.. 24b • 3c ÷ 0.02 =

..6.. 2d - 2b • 18 =

..7.. c + =

..8.. 3bc2 - 8d =

..9.. bc2 ÷ 4 =

10.. 28 + c/8 =

11.. 5b + c4 - 2d =

12.. c /d - • 12d =

13. c 3 + 9b =

14. dc ÷ b =

15. 11bd =


4d 2


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Use the order of operations to evaluate each expression. Remember to work inside the paren-theses before doing anything else.

..1.. 36 + 8(14 - 4) =

..2.. (64 - 8)12 =

..3.. (34 + 16) - 21=

..4.. (82 + 2)8 =

..5.. 32(15 - 3) + 8 + 4(21 - 3) =

..6.. (122 + 6(21 - 7)) - (80 - 65) =

..7.. (93 + 8(15 - 3)) - (40 - 5) =

..8.. 40(6 • 6) - 22 =

..9.. 28(9 - 3) + 50 =

10.. (85 + 12(18 - 6))5 =

11. 2(82 - 5) + 64 =

12. (9 - 6)2 + 7(10 - 3) =

13. (4 + (8 • 7)) ÷ (15 - 9) =

14. 95 ÷ (52 - 20) =

15. 32 + (83 - 11) =

WAKE-UP.WORD.PROBlEM: Marissa has $218.75 in her savings account. During a six-month period, she earns 4% interest on the money in her savings account. How much interest does Marissa earn on her money?



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Just. a.Tip: .The radical sign over a number called the radicand means you are to find the square root of the radicand. The square. root is the number that, when squared (multiplied by itself), equals the radicand.

Example: 36 = 6 6 x 6 = 36

Simplify each square root without using a calculator.

..1.. 81

..2.. 64

..3.. 0.49

..4.. 62

..5.. 225

..6.. 16

..7.. 121

..8.. 0.36

..9..

10.. 32

Give the square root of each number.

11.. 49

12.. 100

13. 25

14. 9

15. 144


unit 1: number and operations: practice activity...

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