Problems of the Week 19 - NCWiseOwlmath.ncwiseowl.org/UserFiles/Servers/Server_4507209... · Problems of the Week Visual Multi-Step Data/Investigations Problem-Solving Strategies

Grade 8 • Page 55

Geometry/Measurement

19Problems of the Week

Visual

Multi-StepData/Investigations

Problem-SolvingStrategies

What Do You Say?

Construct a triangle on thegeoboard so that there is thelargest number of pegspossible inside the triangle.How many pegs are inside?

Feet on the Earth, Head in the SkyA six-foot tall person walks aroundthe earth. How much farther does theperson’s head travel than the person’sfeet?

From: Mathematical Challenges for theMiddle Grades, NCCTM, 1991, p. 24.

By what factor does the volumeincrease if the radius and theheight of a cylinder are doubled?

Materials: 1 stop watchHave students sit in rows of 5.• Begin with 1 row of students.• At the timer’s signal, the first student

stands up, waves his or her arms overheadand sits down. Then each student repeatsthe wave. After the last student sits down,the timer records the time in seconds.

• Repeat for 10, 15, 20 and 25 students.• Graph the ordered pairs on a coordinate

plane (x-axis = # of students; y-axis = time)How long would it take 35 students tocomplete the wave? 45 students? number ofstudents in the 8th grade at your school?

How many ways are there in which FarmerBrown can place his animals (a donkey, a cow, agoat, a pig, a sheep and a horse) in two fields sothat at least one animal is in each field?

Explain how you would figure the surfacearea of a cylinder.

Grade 8 • Page 56

MentalMath

19

Keeping Skills Sharp

1. 8 – (–5)

2. Change to an improper fraction: 19

10

3. Change23 to a decimal.

4. Write as a fraction: .6

5. Find the mode for following set of scores:93, 80, 77, 93, 69, 90

6. Order from least to greatest: 38

, , 12

14

7. Prime or composite? 16

8. List the factors of 27.

9. Write an expression that represents “3 less than w.”

10. Rewrite 5 × 5 × 5 × 5 × 5 as an exponential expression.

1. Solve for m: m ÷ 2 = 48 – 14

2. 3.72 × 104

3. Write as a word phrase: x – 18

4. Solve and check: x12

= 0

5. Solve and check: g – 0.75 = 4.26

6. Estimate: 1217 ÷ 31

7. Solve for c: 3 × (c + 4) = 111

8. If b = 4 and c = 7, give the value of b2 – 3c.

9. 0.0072× 0.12

10. Find the least common multiple of 4, 6, and 10.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. ___________

=

*See answer key. This section should not be duplicated for the students.

Grade 8 • Page 57

19Visual

Multi-Step

Data/Investigations


Problem-Solving Strategies

What Do You Say?To determine the surface area of a cylinder you add theareas of the two circular bases and the lateral area of thecylinder. The lateral area is the area of the rectangularregion that would correspond to a label on a can.

Mental Math1. 13

2.1910

3. 0 6.

4.35

5. 93

6.14

38

12

, ,

7. composite

8. 1, 3, 9, 27

9. w – 3

10. 55

Keeping Skills Sharp1. m = 68

2. 37,200

3. a number decreased by 18

4. x = 0

5. g = 5.01

6. 40

7. c = 33

8. -5

9. 0.000864

10. 60

Answer: 12π feet. If r = radius of earth, thenC (head) = C(earth) + x2π(r + 6) = 2πr + xx = 12π feet

Answer: 8

Field A Field B1 5 6 ways2 4 15 ways3 3 20 ways4 2 15 ways5 1 6 ways

62 ways

Eight pegs are inside the triangle.

Answers may vary.

This section provides anoral drill for sharpeningone's mental computation.Before each session givethese directions, "Numberyour paper from 1 to 10.Write your answer as thequestions are called out.Each question will berepeated one time only."

Answer Key

Grade 8 • Page 58



Visual



What Do You Say?

Mary planted three flower gardens. The area of the rosegarden is half the area of the geranium garden; thebegonia garden is twice the area of the geranium garden.The begonia garden is 8 square meters. What is the totalarea of the three gardens? Hint: Draw a picture.

A bag contains 5 orange marbles,3 green marbles and 4 purple marbles.How many green marbles must be addedso that the probability of drawing a

green marble is 34 ?

1. Students collect graphs from newspapers,magazines, and the internet.

2. Place students in groups of four. Thegroups work to find misleading facts witheach graph.

3. Groups will present their best graph withreasons to support their choice and theworst graph with reasons to support theirchoice.

Write an EquationThe Mathematics Theater has twenty-fiveseats in the first row, twenty-seven seats inthe second, twenty-nine in the third, and soon. How many seats are in the fifteen-rowtheater?

A When would you expect the median andmean to be close together? Explain youranswer.

B Your math scores are 32, 100, 75, 72 and78. Would you rather have your teacheruse the mean or median? Explain youranswer.

Find 5 rectangles with integralcentimeter dimensions 1 through 10using each value once so that youcan put them together withoutoverlapping and form a square.

Grade 8 • Page 59

MentalMath

20


1. Use < , >, or = to complete: 5

12 ___ 7

12

2. Order from least to greatest: 34

, , 23

56

3. Write using exponents: 7 • 7 • 7

4. 12 + 52

5. (10 + 2)2

6. Use < , >, or = to complete: 22.168 ____ 22.1168

7. Prime or composite? 11

8.34

= ?16

9. Simplify: 1848

10. – 10

1. Find the range, median, and mode:35¢, 10¢, 25¢, 20¢, 20¢, 20¢, 15¢

2. –85 – (–106) + 18 =

3. If x = 4 and y = –2, evaluate 4(x – 3y).

4. Combine like terms: 9y + 6y – 2 + 10 – 3y

5. Solve for a: –18 = a6

6. List all the factors of 90.

7. Write in scientific notation: 6,432,000,000

8. Simplify: 7299

9. –8 + –20 =

10. Write as an integer: 83

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. ___________


Grade 8 • Page 60

20Visual

Multi-Step

Data/InvestigationsAnswers will vary.



What Do You Say?

Mental Math1. <

2.23

, , 34

56

3. 73

4. 37

5. 144

6. >

7. prime

8. 12

9.38

10. –10

Keeping Skills Sharp1. range = 25¢

median = 20¢

mode = 20¢

2. 39

3. 40

4. 12 y + 8

5. - 108

6. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45,90

7. 6.432 x 109

8.

9. 12

10. 512

Answer: 14 m2

Answer: 24 green marbles added 2736

= 34

(15 • 25) + (2 + 4 + 6…+ 28) 585 seatsOr make a table

Row Seats1 252 273 29

A With a small range, you would expect the median and mean to be close together.B Median; median 75, mean 71.4

The dimensions of the rectangles are:6 cm × 10 cm, 7 cm × 9 cm, 3 cm × 8 cm,4 cm × 5cm, and 1 cm × 2 cm.The dimensions of the square will be13 cm × 13 cm.

811


Answer Key

Grade 8 • Page 61



Visual

Multi-Step

Data/Investigations


What Do You Say?

The nine volumes of amathematics encyclopedia areon the right. They are in thisstrange order because theirowner, a lover of fractions,has noticed that the volumenumbers can be read as afraction which equivalent toone-half. Can you show how thevolumes can be arranged so that theymake the fraction equivalent toone-fourth?

6 7 2 9

1 3 4 5 8

Tina and Tess go shopping together andbuy identical items. Each girl buys 4pairs of shorts, 5 shirts, and 2 pairs ofshoes that can all be mixed andmatched to wear. If each girl wearsnew clothes to school tomorrow, what isthe probability that Tess shows up inexactly the same oufit as Tina?

The polygon shown is a quilt pattern.The pattern measures 2 inches from A toB. The actual quilt block will be 8inches from A to B. What will its areabe?

Describe thepattern in thethird diagonalrow.

20

32

1

6

1

10

35

1

10

35

131

4151

6171

11

1415

1617

15 1521 21

Make an Organized ListMegan, Lindsay and Allison work out at theFitness Center after school. Megan goes every3 days, Lindsay every 4 days and Allison playssoccer, so she can only go every 8 days. Onwhat days in the next 6 weeks will Lindsay andMegan be at the Fitness Center on the sameday? On what days will Lindsay and Allisonbe at the Fitness Center the same day?

Adapted from The Problem Solver 8, 1988 CreativePublications

A B

A drawer contains 5 black socks, 3 brown socks,and 1 blue sock. Jess is going to pull 3 socks outof the drawer without replacing them. What isthe probability that he gets a black sock first, ablack sock second, and a blue sock third?

Grade 8 • Page 62

MentalMath

21


1. Estimate: 218 + 3

67

2. –3 • (–9)

3. Which of the following is the largest: 0.438, 0.5,0.004, 0.43?

4. Find the reciprocal of 216 .

5. 2 ÷ 19

6. Solve for b: b – (–2) = 7

7. 30 inches = ____ feet

8.35

• 12

9. –5 + –4

10. Round 4.018 to the nearest hundredth.

1. Solve for k: –51 = k

–13

2. Solve for r: –126 = 21r

3. Solve for b: 252

7– = b

4. Arrange these numbers in order from least to greatest:

2, 4, –1,35 , –7,

12 , –

15

5. Simplify this expression: 4(m+ 5) + 7(2m + 6).

6. Evaluate 4 2

2( )b c

c+

if a = 3, b = 5, and c = 4.

7. Write as an inequality: y is less than 10.

8. Graph the set of numbers on a number line: {–3, 0, 2}

9. I = VR If I = 44 and R = 5, find V.

10. Write an inequality for the following: the amount, s, that

Mrs. Phillips will spend is not more than $56.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 63

21Visual

Multi-Step

Data/Investigations



What Do You Say?Starting with the first number, 1, you add 2 to get thesecond number, 3; then add 3 to get the third num-ber, 6; then add 4 to get the fourth number, 10; thenadd 5 to get the fifth number, 15; and then add 6 toget the sixth number, 21. Each time you add 1 morethan you did the previous time.

Mental Math1. 6

2. 27

3. 0.5

4.6

13

5. 18

6. 5

7. 2 12

feet

8.3

10

9. –1

10. 4.02

Keeping Skills Sharp1. 663

2. –6

3. –36

4. –7, –1, –15 ,

12 ,

35 , 2, 4

5. 4m + 20 + 14m + 42 = 18m + 62

6. 7

7. y < 10

8.

9. V = 220

10. S ≤ 56

439217568

= 14

They have 4 × 5 × 2 of 40 outfit possibilities.Probability is 1/40.

Lindsay and Megan — days 12, 24, 36Lindsay and Allison — days 8, 16, 24, 32, 40

–3 –2 –1 0 1 2 3

Answer: 144 square inches

Answer: 59

48

17

5126

× × =


Answer Key

Grade 8 • Page 64



Visual



What Do You Say?

Draw 3 different arrangements of 16 cubes.

In the final four digits of a license plate,the sum of the first two equals the sum ofthe last two. Also, the sum of the firstand last is twice the sum of the middletwo, and the first two form a two digitnumber that is twice that formed by thelast two. The number does not containany 0’s. What are the final four digits inorder?

From Mathematics Teacher February 1997

Collect a week's worth of newspapers.Stack, measure and find the volume of thenewspapers.What would be the volume of a year’sworth of newspaper? Mark off an areaequivalent in volume in your classroom.Make a function table showing theaccumulation of newspapers from 1 to 20years. Write an equation with twovariables representing the function.Graph the function. Makeyour data count!Write an article toencourage recyclingof newspapers.Support yourposition.

Explain how you would find the mean, medianand mode of the following test scores:

100, 95, 95, 80, 92, 75, 99, 75, 76, 89

Use a Formula: C = n (1 + r)t

A movie ticket costs $7 today. Inflation isexpected to grow by 4 percent a year for thenext several years. If n represents the currentcost of the ticket, predict the cost (C) of theticket if this inflation rate continues (a) for 5 years (b) for 30 years.

Look through the almanac for data over time.See if you can find some data that fall along astraight line when graphed. Use the line tomake predictions about the variables involvedin the future.

Grade 8 • Page 65

MentalMath

22


1. Write the ratio 12:4 in 2 other ways.

2. Write as an improper fraction: 378

3. Write 297 as a mixed number.

4. 8 cm = ____ m

5. Write 3 lb. 1 oz. in ounces.

6. Write 20% as a fraction.

7. Write as a decimal: 2%

8. 43 • 42

9. Solve for t: –13t = 52.

10. What percent of 18 is 6?

x

45°

1. Write three fractions equivalent to 35 .

2. Find x:

3.54

45

58

× × =

4. Write 33% as a ratio.

5.12

+ 38 =

6. 17% of 5.66 =

7. An angle greater than 90° is called _______.

8.

9. 212 ÷

27 =

10. 5 – 6 – (–9) =

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Find the median and mode: 1, 2, 5, 3, 9, 7, 2


Grade 8 • Page 66

22Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 12 to 4,

2.318

3. 4

4. .08 m

5. 49 ounces

6.15

7. .02

8. 45

9. –4

10. 33 %


1.6

109

153050

, ,

2. 45°

3.58

4. 33:100

5.78

6. 0.9622

7. obtuse

8. median = 3, mode = 2

9. 834

10. 8

Answer: 5427

(a) $8.52 ($7.00 × 1.045 )(b) $22.70 ($7.00 × 1.0430 )

Answers will vary.It might be helpful to provide the students withisometric dot paper.

Answers will vary.

Answers will vary.

12 4

Arrange the scores in ascending order.Average the middle two scores to determine themedian.Divide the sum of the ten scores by ten to determinethe mean.The mode is the most common score.

1 7

13


Answer Key

Grade 8 • Page 67



Visual

Multi-Step

Data/Investigations


What Do You Say?

Jack weighs 45 of his weight plus 40

pounds. What is Jack’s weight?

On a map, three towns lie in a straightline. Abbeyville is 35 miles fromBeantown. On the map this distance is2 cm. The distance from Abbeyville toClarkton is 13 cm on the map. IfBeantown is between Abbeyville andClarkton, how far is it from Beantownto Clarkton in miles?

Explain how to change .1 to a fraction.

The number of chirps made by a cricket in oneminute is a function of the temperature. The

formula is t = 14 n + 40, where t is the

temperature in degrees Fahrenheit and n is thenumber of chirps in one minute.A What is the temperature if a cricket makes

150 chirps per minute?B At 60°F, how many chirps a minute does a

cricket make?C At what temperature does the cricket stop

chirping?

Use two different colored number cubes. Identify oneof the cubes as “x”-values and the other as the“y”-values. Roll the number cubes and create anordered pair. Graph the point. Roll the cubes again andgraph the point.What is the slope of the line determined by the two points?

What is the probability that when fivepeople meet that at least two of them areborn in the same month? How can you setup a simulation to discover this answer?Can you set it up with regular numbercubes? A dodecahedron? A spinner?Marbles of different colors?

Grade 8 • Page 68

MentalMath

23


1. 2.36 x 200

2. Simplify 23

3.4?

= 2035

4. 12 10–

5. Find the perimeter of a garden that measures 12 feet by4 feet.

6. How many minutes are in a day?

7. 25 = ____

8. Which is greater: 52 or 25?

9. 1 – 56

10. Write as a fraction: 8.5

1. What is the theoretical probability of choosing a vowel from theword MATHEMATICS?

2. Cali bought a sweater priced at $60. If the sales tax is 9%, what isthe total purchase price of the jacket?

3. Two angles whose measures have a sum of 180° are called_______.

4.34

6 12

× =

5. Find the amount you save when you buy a $210 bicycle on sale for15% off.

6. Find the interest to the nearest cent: $5000, 8.5%, 1 year.

7. Write 525 % as a fraction.

8. Express as a unit rate 5 million people in 400 square miles.

9. Solve the proportion: 34

= 9N

10. On a scale drawing 1 centimeter represents 2 meters. What lengthon the drawing should be used to represent 3.2 meters?

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 69

23Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 472

2. 8

3. 7

4. 2

5. 32 feet

6. 1,440 minutes

7. 5

8. 25

9.16

10.


1.4

11

2. $65.40

3. supplementary

4. 478

5. $31.50

6. $425.00

7.27

5008. 12,500 people in one square mile

9. N = 12

10. 1.6 centimeters

Answer: 200 pounds

Anwer: 192.5 miles

A 77.5°FB 80 chirpsC 40°F

Answers may vary. The experiment would be hardto perform with number cubes, but students may finda way. With a dodecahedron, a spinner with 12sections, or with marbles of 12 colors in a box, thestudents can assign a number or color to each of the12 months. Then, the dice, docecahedron, ormarbles will be used five times to select a month.When five have been selected, that represents agroup of five people. If the experiment is donemany times, the experimental probability can becalculated.

Answers will vary.

17 2

Let n = .1

10n = 1.1 ( n = .1 )

9n = 1n = 1

9


Answer Key

Grade 8 • Page 70



Visual

Multi-Step

Data/Investigations


What Do You Say?

Jenna has $65.00 to spend. She found apurse for $15.95, a shirt for $18.00 and apair of shoes for $28.50. She must pay6% sales tax on her purchases. Whichitems should she buy if she wants tospend as much of the $65.00 as possible?(She might buy more than one of anyitem, if advantageous.) Explain youranswer.

1. Have students attend or watch a basketball game andcollect data on the number of shots attempted and thenumber of shots made (exclude foul shots).

2. Have students put data into a table.3. Make a scatter plot using the data.4. Does there appear to be a relationship between the

number of shots attempted and the number of shotsmade?

Pam and Ellen are selling lemonade for a projectat the local recreation center. They havecalculated the cost of a cup of lemonade to be22¢. They plan to make 150 cups of lemonade.If they sell each cup for 30¢, how much profitwill they make? How many cups do they needto sell to make $25.00 profit? Explain how yougot your answer.

On graph paper, draw one of yourinitials using block letters as shown.Now create a dilation of this letter usinga scale factor of 2. How does the area ofthe dilation compare to the area of theoriginalletter?

Place the first six counting numbers inthe circles so that the sum on each side ofthe triangle is nine. Is is possible to usethe numbers four to nine to make the sumof each side the same?

Each of five friends has 20 baseball cards andthey decide to trade cards as follows: Mollygives Jim one card, Kyle gives Bob one card,Molly gives Kyle two cards, Lisa gives Mollythree cards, Lisa gives Bob five cards, Kylegives Lisa one card, Molly gives Bob twocards, Bob gives Kyle one card, and Jim givesBob three cards. Who has the greatest amountof cards? Who has the smallest amount ofcards?

Grade 8 • Page 71

MentalMath

24


1. 15 cups = _____ pints

2. 36 = ____

3. Write 230,000 in scientific notation.

4. Write 1.07 × 104 in standard form.

5. If 27 = –3x, then x = ____

6. The point located at (–3, 7) is in which quadrant?

7. Find a solution for y = x – 2.

8. Solve: What number increased by eight is 35?

9. Write as a mixed number: 294

10. 100 = ____

1. (32 + 11) – 4 + 25 ÷ 5 =

2. Find the perimeter of a regular octagon with sides 2.3 meters.

3. Find the circumference of a circle with diameter of 16.5 cm.

4. If a= 12 and x = 4, then (2a – x)(2x – 6) =

5. Simplify: –15 + – 27

3

6. Simplify: f + 35

= 34

7. Solve for q: q – (–83) = 121.

8. Find the surface area of a cube with edges of 5 cm.

9. 112 ounces = _____pounds

10. An angle less than 90° is called ________.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 72

24Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 7.5 pints

2. 6

3. 2.3 x 105

4. 10,700

5. –9

6. II

7. Some possible answers:

(4, 2)(2, 0)(3, 1)

8. 27

9. 714

10. 1

Keeping Skills Sharp1. 21

2. 18.4 meters

3. 51.81 cm

4. –6

5. –14

6. f = 3

20

7. q = 38

8. 150 cm2

9. 7 pounds

10. acute

Answer: Two purses and a pair of shoes; $64.02

The area of the dilation is four times the area of theoriginal letter.

$45.00Actual cost $33.00Profit $12.00They must sell 313 cups to make $25 profit.

Bob has the most (30 cards) and Lisa has the least (13cards).

Answers will vary.

1

23 4

5 6

4

56 7

8 9 This section provides anoral drill for sharpeningone's mentalcomputation. Beforeeach session give thesedirections, "Numberyour paper from 1 to 10.Write your answer asthe questions are calledout. Each question willbe repeated one timeonly."

Answer Key

Grade 8 • Page 73



Visual

Multi-Step

Data/Investigations


What Do You Say?

Eric drew two squares side by side. The perimeter ofthe resulting rectangle is 90 meters. What is the area ofthe rectangle?

When the line 3x + 4y = 48 crosses thefirst quadrant, a triangle is formed. Findthe area of this triangle.

Draw this design after it has been rotatedclockwise around the origin 90°.

1. Students collect data from classmates onheight in inches and foot length.

2. Make a scatter plot using the information.3. Students determine relationship of data.

Drawing a Picture or Making a ModelA nonagon is a polygon with 9 sides. Howmany different diagonals can be drawn in anonagon?

Describe two ways an equation andinequality are different.

Grade 8 • Page 74

MentalMath

25


1. Write as a decimal: three hundred-fifty two andthirty-six thousandths.

2. Evaluate 2m3 if m = 5.

3. 1100 =

4. Write 1123 as an improper fraction.

5. Express as a unit rate: 20 miles in 4 hours

6. Write the ratio as a percent: 33:100

7. Simplify: 6x + 3x + 2y

8. Name the first five whole numbers.

9. True or false: 0.6 = 35

10. Give the coordinate of the point that is 6 units to the rightof the y-axis and 4 units below the x-axis.

1. Find the area of a rectangle whose length is 15 yards and whosewidth is 9 yards.

2. Solve for r: 21r ≤ –378.

3. Find the median: 6 12 8 36 10

4. Write the expression and evaluate: seven cubed divided by sevensquared.

5. Find the GCF for 16y and 40y2.

6. 42 – 3.9

7. Give four positive multiples of 30.

8. Write the fraction in simplest form: 18

126

9. Which is greater: 14

or 311

?

10. Factor 124.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 75

25Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 352.036

2. 250

3. 1

4.353

5. 5 miles/hour

6. 33%

7. 9x + 2y

8. 0, 1, 2, 3, 4

9. True

10. (6, –4)

Keeping Skills Sharp1. 135 square yards

2. r ≤ –18

3. 10

4.73

72 = 7

5. 8y

6. 38.1

7. 30, 60, 90, 120

8. 17

9.3

11

10. 22 • 31

Answer: 450 m2

Answer: 27

1) An equation has one answer and an inequalityhas more than one.

2) The signs used in writing an equation and aninequality are different.

The triangle has vertices at (0,0), (0,12) and (16,0).The area is 96 square units.

Answers will vary.


Answer Key

Grade 8 • Page 76



Visual

Multi-Step

Data/Investigations


What Do You Say?

Distinct numbers areassigned to regions A, B,and C in the given rectangle.The numbers shown in thecircles represent the sums ofthe numbers assigned to theregions that border eachcircle. What number is assigned toregion B?

A B

C22

2935

The sum of the ages of the Smith’s fourchildren is 25. Maria’s oldest brother issix times as old as she is. Her next-to-the-oldest brother is 5 years older than she is,and the youngest of her brothers is twiceMaria’s age. How old is each of theSmith’s children?

You have a circular swimming pool witha radius 6 meters and volume of about533.8 cubic meters. Your neighbor has acircular pool with a diameter that is thesame as the radius of your pool. Thedepth of the pools are the same. Explainhow to find the volume of your neigh-bor’s pool. Find the volume. Comparethe volumes. You and your neighbordecide to drain the pools and paint theinside surfaces. If your neighbor needsthree cans of paint for his pool, howmany cans of paint will you need to paintyour pool? Explain your solution.

Ages of 24 Night Class Students

2 3 5 5 83 0 1 2 2 4 4 4 4 5 6 6 7 8 8 94 0 1 3 3 8

A Find mean, median and mode of the data set.B Which of the measures from part A best

represents the data set? Explain your thinking.C Construct a box-and-whiskers plot for the data.D Give the range, lower extreme, upper extreme,

lower quartile and upper quartile.E What percent of the data is represented by the box

in the box-and-whiskers plot?

A cylinder has a radius of 12 inch. How tall

must it be if the volume should be at least15 cubic inches?

Explain why this statement can bemisleading:A negative and a negative is a positive.

Grade 8 • Page 77

MentalMath

26


1. Simplify (x2)3

2. Solve for x: x – 7

10 = –9

10

3. Do the following ratios form a proportion? 47

2035

,

4. Simplify: (2x2)(3x3)

5. State the quadrant in which the x-coordinate is negative andthe y-coordinate is positive.

6. How many hours are in a week?

7. Is the ordered pair (5, 0) a solution to 6x + y = 30?

8. 9.32 – 5.1

9. Identify the variable in the expression: 2x2 – 4.

10. 6 lb 12 oz

+ 4 lb 8 oz

1.

2. Round to the nearest tenth: 5.182, 1.93, 34.694, 62.96

3.

4. Write the next 3 terms: 12, 19, 26, 33…

5. Is the bottom figure a rotation, translation,or reflection of the top figure?

6. Solve for b : b – 2 38

= 112

7. Express –256 as a fraction.

8. 2 14

–43

9. Solve for m: 56

2 • 2 = m

10. Evaluate (x + y)2 if x and y = –0.2.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

What is the top number of a fraction called?

What is the measure of a right angle?


Grade 8 • Page 78

26Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 6x5

2.–15

3. yes

4. numerator

5. Quadrant II

6. 168 hours

7. yes

8. 4.22

9. x

10. 11 lb 4oz

Keeping Skills Sharp1. numerator

2. 5.2, 1.9, 34.7, 63.0

3. 90°

4. 40, 47, 54

5. translation

6. 378

7. –176

8. –3

9.2518

= 1 718

10. 0.16

Answer: B = 8

Answer: 2, 4, 7, 12

Answer: at least 19.1 inches

It needs to say the product of two negative numbersis a negative number.

You can find the height of your pool by usingV = πr2h. 533.8 = π(62)h; h is approximately 4.7meters. The neighbor's pool would have volume:π(32)(4.7) = about 133 cubic meters. (You could

also reason that the neighbor's pool has to have 14

the volume of yours.) The surface that the neighborpaints is π(9) + π(6)(4.7) = 116.9 square meters.The surface area you will paint is π(36) + π(12)(4.7)= 290.3 square meters. Now set up a ratio:

3116 9 290 3. .

=x

x = about 7.5 so 8 cans should be bought.

A Mean 34.83, median 34.5, mode 34

B No, statistically there is not enough difference.

C

D range = 25, lower extreme = 23,

upper extreme = 48, lower quartile = 31.5,upper quartile = 38.5

E 50%

20 30 40 50


Answer Key

Grade 8 • Page 79



Visual



What Do You Say?

The diagram consists of four congruentsquares made with twelve 2-inchtoothpicks. By moving exactly threetoothpicks, form three congruentsquares so that each toothpick forms aside of a square. What is the percent ofincrease in the perimeter of the figure?

One zip weighs as much as four zaps.Six zaps weigh as much as threezowwies. Five zowwies weigh as muchas two swooshes. If one swoosh weighsone hundred pounds, how many poundsdoes one zip weigh?

At one point early thisseason Chipper Joneswas batting .500. Aftergetting 3 hits in 10 at-bats in his next 2 games,his average dropped to.333. How many hitsand at-bats must he havealtogether?

Mr. Money has nickels, dimes, andquarters. In how many ways can he makechange for 50¢?

When you change from a smaller unit ofmeasure to a larger unit of measure, youget a smaller number for an answer.Explain why?

The Big Brown Teddy Bear Factoryuses two geometrically similiarpatterns to produce 10"-tall bears and30"-tall bears. If one bag of stuffingis needed to fill the entire volume of a10"-tall bear, how many bags ofstuffing will be needed to fill thevolume of a similar 30"-tall bear?

From 1997-98 Mathcounts School Handbook

Grade 8 • Page 80

MentalMath

27


1. The sum of the measures of two angles of a triangle

is 85°. What is the measure of the third angle?

2. If one acute angle of a right triangle measures 52˚, what is

the measure of the other acute angle?

3. True or False: 0.2 + 0.4 = 0.06

4. 3:8 = 6:____

5. -28 + 13

6. Simplify: 3x2 + 2x2 + 3x + 4x

7. -32 • -6

8. 45 5– ÷ 2 • 4 =

9. If a = 20, find the value of 4a + 5.

10. Write as a simplified algebraic expression: the product of 2xand 10r.

1. –3 • –8

2. Find the volume of a cylinder with a radius of 3 feet anda height of 7 feet.

3. What are the prime factors of 72?

4. 324 9÷ =

5. Solve for k: k

15 = – 5

6. 10% of what number = 15

7. 629 ÷ 2

13

8. Write the reciprocal of 423 .

9. Simplify:

3 gal 2 qt+ 1 gal 6 qt

10. Write as a word phrase: 19n

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 81

27Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 95°

2. 38°

3. False

4. 16

5. -15

6. 5x2 + 7x

7. ray

8. 80

9. 85

10. 20rx

Keeping Skills Sharp1. –24

2. 197.82 ft3

3. 2, 2, 2, 3, 3

4. 6

5. k = –75

6. 150

7. 223

8. 314

9. 4 gal 8 qt or 6 gal

10. the product of 19 and a number n

perimeter = 8 units perimeter = 12 units50% increase

Answer: 80 pounds

4 hits at - bats12 = .333

Make a systematic list..25 .10 .0521 2 11 1 3

54 23 42 61 8

10 The chart shows 9 ways.

When measuring an object, it takes fewer of a largerunit of measure than it takes of a smaller unit ofmeasure. Examples: 36 inches = 3 feet, 4 quarts = 1gallon, 3 feet = 1 yard, 100 cm = 1 m, 1000m = 1km

Answer: 27 bags


Answer Key

Documents

Problems of the Week 19 - NCWiseOwlmath.ncwiseowl.org/UserFiles/Servers/Server_4507209... · Problems of the Week Visual Multi-Step Data/Investigations Problem-Solving Strategies