Problems of the Week 1 - SharpSchoolmathlearnnc.sharpschool.com/UserFiles/Servers/Server_4507209/File... · with gum balls of 6 different colors. ... Grade 8 Answer: 374.4 pounds

Grade 8 • Page 1

Geometry/Measurement

1Problems of the Week

Visual

Multi-Step

Data/Investigations

Problem-SolvingStrategies

What Do You Say?

Draw a picture to answer the following question based onthe information given:Margaret walked 8 blocks south and 3 blocks east fromher home to school. After school she walked 2 blocksnorth and 1 block east to the park. From the park shetraveled 1 block north and 2 blocks westto visit her friend. How far doesMargaret have to walk to return home?

An aquarium is 36 inches long, 24inches wide and 16 inches tall. Theaquarium is filled with distilledwater to a level of 12 inches. If acubic foot of distilled water weighs62.4 pounds, how many pounds ofwater are in the aquarium? Expressyour answer as a decimal correct tothe nearest tenth.From 1996-97 Mathcounts School Handbook

The Gum MachineKaren and Diane are having an argument.They both know that the machine is loadedwith gum balls of 6 different colors. Karenfeels lucky. She thinks she can get each colorby using only 6 pennies. Diane feels it willtake at least 15. Let’s assume that the machineis loaded with an equal number of each color.How many pennies do you think are needed toget one of each color? Do you agree witheither Karen or Diane? Use a fair number cubeto experiment and find your answer.

Four students are called to sit in four chairs ona stage. The students are Bob, Brenda, Carol,and Don. Bob and Brenda are cousins. If thestudents are called up in random order and takeseats in the order in which they are called,what is the probability that Bob and Brendawill sit next to each other?

Jack Bean-Stalk has a school teacherwho knows a few magic tricks of herown. She is watching her magic beansgrow according to this pattern.Day 1 2 3 4 5 6 7…# of beans 1 1 2 3 5 8 13…On which day will she have enoughmagic beans to give at least 5 to each ofher 20 students?

Johnny has trouble finding the LCD whensubtracting fractions. You want to help him.Write the steps Johnny needs to follow inorder to find the LCD.

Grade 8 • Page 2

MentalMath

1

Keeping Skills Sharp

Grade 8

1. (5 + 3)5

2. (2)(5)(0)(7)(8)

3. Write .03 as a fraction.


5. Solve for y: 13

y = 3

6. True or False: 522 ÷ 18 = 18 ÷ 522

7. 5 – 17

8. Write 25,000 in scientific notation.

9. 28 • 22

10. Simplify: 2x + 5y – 7x + 2xy

1. 3 + 8 • 2 – 5 =

2. 10% of 100 =

3. 9 • 7 • 5 =

4. 12 ÷ 4 + 5 • 2 – 24 ÷ 6 =

5. 2[(4 + 11) ÷ (12 – 7)] =

6.42 317 8

+– =

7. .97(10) =

8. 313 + 2

17 =

9. .343 ÷ 10 =

10. 36 ÷ .6 =

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 3

1Visual

Multi-Step

Data/Investigations


Problem-Solving Strategies

What Do You Say? Answers will vary;however, students could mention using the primefactorization of each denominator to determine theLCD.

Mental Math1. 40

2. 0

3.3

100

4.13

5. 9

6. False

7. 12

8. 2.5 × 104

9. 210

10. –5x + 2xy + 5y

Keeping Skills Sharp1. 14

2. 10

3. 315

4. 9

5. 6

6. 5

7. 9.7

8. 51021

9. .0343

10. 60

Grade 8

Answer: 374.4 pounds

Answers will vary depending upon experiments.

Strategy: make an organized list or use a formula.B BR C D B BR D C B C BR DB C D BR B D BR C B D C BRBR B C D BR B D C BR C B DBR C D B BR D B C BR D C BC BR B D C BR D B C B BR DC B D BR C D BR B C D B BRD BR C B D BR B C D C BR BD C B BR D B BR C D B C BR

24 possible…12 they sit together…Answer 12/24 = 1/2

N

S

EW

Home

8 bl

ocks

3 blocks

2 blocks1 block1 block

2 blocksPark

School

Boyfriend

2 blocks west5 blocks north

Answer: Day 12

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

F

Grade 8 • Page 4



Visual

Multi-StepData/Investigations


What Do You Say?

Nine one inch cubes are puttogether to make a “T.” Ifthe complete figure is paintedred, how many cubes haveexactly 4 red faces?

A square is folded in half to form arectangle. If the resulting rectanglehas a perimeter of 15 inches, what isthe area of the original square?

Imagine a new type of lottery. To make thefour-digit number, digits are randomly chosenfrom 1, 2, 3 and 4, and no digit is repeated.The order of the digits is important. If yourlottery number is 1234, what is the probabilitythat you will win?

NCTM Math Journal Sept/Oct 1996

Will these two expressions always be equal?Explain.

x y x y – –

An estate valued at $62,000 is left by awill as follows: to each of twograndchildren a certain sum, to the sontwice as much as to the twograndchildren together, and to thewidow $2,000 more than to the son andgrandchildren together. How muchgoes to each?

Working BackwardsFind the starting number on this flow chart:

??÷ 3

– 3 7

Grade 8 • Page 5

MentalMath

2


1. In what quadrant would you find the ordered pair(–2, –3)?

2. Identify the mode of the data:{5, 7, 13, 7, 1, 5, 6, 7}

3. 8 – 3 + 2 – 7 + 12

4. 60 falls between what two consecutiveintegers?

5. 5 • 8 • 5

6. 7 – 134

7. Write the next number in this pattern:3, 9, 27, 81, ___

8.1215

= ?5

9. True or false: 2 • 3 • 7 = 3 • 7 • 2

10. 7 13

÷

1. 5 + 3 • 2 + 12

2. 22 + 4 – 23 ÷ 4

3. Order these numbers from least to greatest: – 12 , 0, –3, 1, –1

4. 8 = ■ 3

5. Compare: 13

? 14

6. Compare: 1528

? 1942

7. List all the factors of 36.

8. Explain why 1 is a prime number.

9. 30 = ____

10. Half of a dozen

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 6

2Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. III

2. 7

3. 12

4. 7 and 8

5. 200

6. 514

7. 243

8. 4

9. True

10. 21


2. 6

3. –3, –1, – 12

, 0, 1

4. 2

5. >

6. –3, –1, –12 , 0, 1

7. (1, 2, 3, 4, 6, 9, 12, 18, 36)

8. It has only 1 factor.

9. 1

10. 6

Answer: 5

Answer: 25 inches2

Answer: 4 • 3 • 2 • 1 = 24 1

24

Answer: The grandchildren each get $5,000; the songets $20,000; and the widow gets $32,000.

Answer: 156

The two expressions are not always the same. Forexample, if x = 3 and y = –5 3 – (–5) = 8 while 3 – – 5 = – 2


Answer Key

Grade 8 • Page 7



Visual



What Do You Say?

Consider the shape shown.Can you keep the perimeterthe same and make the areasmaller? Larger? If so, drawthe picture.

NCTM Magazine

During Bully's first week working in achina shop he breaks a vase that costs$45.89, two glasses that cost $16.25each, and a platter that costs $135.49. Ifhe makes $5.25 an hour, how manyhours will he have to work to pay for thethings he broke?

Tom has some cubes that are 2inches on each side. How many ofthem will fit into a box that is a cubewith each side 4 inches long?

For the set (3, 4, 5, 8, x) the mean, median,and mode all have the same value. What isthe value of x?

Make a DiagramMartinez’s A-1 Cars and Trucks is having asuper sale. José and Alex are setting up the lot.Mr. Martinez gives them a diagram of the lotand these directions. “Put the 4-door car infront of the van. Put the jeep between the truckand the van. Put the sports car to the left of the2-door and 4-dor cars.” How did Mike andDon set up the lot?

Will the expression 5x always be smaller

than 5? Explain.

Grade 8 • Page 8

1. .765 + 3.876 + 5

2. Convert .5 to a fraction.

3. Find the area:

4. Find the area:

5.37 14

=x

Solve for x.

6. Three loaves of bread cost $3.87. How much do two loaves cost?

7. Find 55% of 480.

8. 6 out of 40 is equivalent to ___ out of ___.

9. 4 + 3 • 6 ÷ 9 – 8

10. 15 + 0.5

MentalMath

3


1. What is 25% of 20?

2. (2 × 103) • (3 × 104)

3. Solve for x: 12x = 36

4.12

13

–

5. Multiply three tenths by two tenths.

6. Compare 12 and .50.

7. 3x2 + 3y + 7x2

8. Solve for x: x2 = 25

9. Express .08 as a fraction in simplest form.

10. If you simplified(–3) (4)(–7)(–8)(2)(–15), would your answer be positive or nega-tive?

5

2

3

2

2

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

mm

mm

cm


Grade 8 • Page 9

3Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 5

2. 6 × 107

3. 3

4.16

5. .06

6.12 = .50

7. 10x2 + 3y

8. –5, 5

9.8

100225

=

10. positive

Keeping Skills Sharp1. 9.641

2.12

3. 6 square meters

4. 3.14 square centimeters

5. 6

6. $2.58

7. 264

8. Answers will vary: 3 out of 20, 12 out of 80etc.

9. -2

10. 15.5

Answer: 41

Answer: 8

Answer: 5

T J VSC 2D 4D

SC 2D 4DT J V

or

No. If x is less than one, x will divide into 5 more

than 5 times. Also, if x is negative, 5x will be

negative and therefore less than 5.


Answer Key

Grade 8 • Page 10



Visual

Multi-Step

Data/Investigations


What Do You Say?

Mr. Ellen had the following exercise on the overheadprojector for his class to do when they came in Mondaymorning. What was his message to the class? Look ator draw this number line and fill in the letters given inthe instructions. The first one is done for you.

M to I is +4 O2 to O3 is +4I to O1 is –8 O3 to G1 is –6O1 to N1 is +7 G1 to D is +3N1 to N2 is +2 D to G2 is +8N2 to O2 is –8 G2 to R is –4

M I

A prism with a square base has aheight of 45 centimeters; the volume is7,200,000 cm3. Find the area of thebase.

Martinez’s A-1 Cars and Trucks is having asuper sale. What would be the total price of allthe vehicles if the least expensive is $10,000less than the most expensive, the van costs$5,500 more than the jeep which costs thesame as the 4-door, the truck costs $25,000, thesports car costs $30,000, and the 2-door is theleast expensive and costs $2,000 less than the4-door?

2.5 × 102 = ______ × 103

Explain how you know your answer iscorrect.

Jamal was hired to do somelawn work for $40 a day, buton the condition that forevery day he was idle, heshould forfeit $15.50. At theend of 20 days he had$467.00. How many dayshad Jamal been idle?

A television station plays 3 songs and 4 com-mercials every 20 minutes. For one 20 minutesegment the director chooses three differentsongs to be played and the producer choosesfour different commercials. The producer thendecides that the order will be song, commercial,two songs, three commercials. How manypossible arrangements are there for this 20minute segment?

I

Grade 8 • Page 11

MentalMath

4


1. .7 + .02 + 4

2. What is the LCM of 8 and 12?

3. What is the GCF of 8 and 12?

4. What is the complement of a 30° angle?

5. (0.03)2

6. Write 1.7 × 105 in standard form.

7. Multiply: x2(2x + 3)

8. 7 • 2 + 6 ÷ 3

9. Solve for k:

23

= 8k


5

4

3

4

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

m

m

m

m


1. 3 + 2 – 1 × 4 =

2. Find the perimeter:

3. Find the measure of angle A.

4. 5% of 34 =

5. 0.3 • 0.4 =

6. Express 7.4% as a fraction and a decimal.

7. Solve for n: 12n = 84

8. 25 + [48 ÷ (12 + 4)] – 16 =

9. Solve for x: x + 2 = 6

10. Multiply 2.96 • 5.67; round the answer to thenearest hundredth.

A60°

Grade 8 • Page 12

4Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 4.72

2. 24

3. 4

4. 60°

5. 0.0009

6. 170,000

7. 2x3 + 3x2

8. 16

9. 12

10.34


2. 18 meters

3. 60°

4. 1.7

5. .12

6.37

500 and 0.074

7. 7

8. 12

9. 4

10. 16.7832, 16.78

Answer: “GOOD MORNING”

Answer: 160,000 cm2

Answer: $146,500

Answer: 6 days idle 14 • $40 = 5606 • 15.5 = 93

$467

2.5 × 102 = 0.25 × 103

The two numbers are equivalent, so if we multiplyone of them by ten by increasing the exponent, thenwe must also divide it by ten by shifting the decimalpoint in 2.5 one place to the left.

144 possible arrangements3 x 4 x 2 x 1 x 3 x 2 x 1 = 144


Answer Key

Grade 8 • Page 13



Visual



What Do You Say?

Show how to slice thiscube so that the crosssection is a trapezoid.

At a local store, the price of all televisionswas reduced 25%. Store employees are

given an additional 20% discounton sale prices. What would be

the cost a store employee would payfor a television originally

priced at $360?

1997-98 Mathcounts Handbook

A cube has a surface area of 294 cm2.What is its volume?

A math class earned the following set ofscores on a test:

43560 4 571 2 3 384 993Create a box plot from these scores.

Logical ReasoningSuppose two identical tanks are to be filledwith water. The first tank begins filling 5minutes before the second tank beginsfilling. The first tank can be filled in 30minutes. The second tank can be filled in 20minutes. How much time will pass beforeboth tanks hold the same amount of water?

A poll asks students 3 questions: Do you playtennis? Do you swim? Do you ride a bike? Theresults are tallied, and the percentage of studentswho participate in each sport is found. Whyshould these data not be presented in a circlegraph?

Grade 8 • Page 14

MentalMath

5


1. Simplify: 98 • 3 + 2 • 3

2. Write 1.31 as a percent.

3. Find the volume of a cube with sides measuring2 centimeters.

4. Find the surface area of a cube with sides measuring2 centimeters.

5. Which distance is greater: 5.1 km or 5001 m?

6. Round 25.9878 to the nearest hundredth.

7. Solve for x: 2x + 3 = 7

8. What is the mean for the following set of numbers{7, 4, 7}?

9. What is 80% of 50?

10. Simplify: x – 7y + 4x – 2y

1. How many inches are in 19 yards?

2. 12 – 3.987 =

3. Four pencils and one pen cost $1.25. Two pencilsand three pens cost $2.25. What is the cost of onepen?

4.34

512

– =

5. Write the next two numbers in this pattern:3, 4, 7, 11, ____, ____

6. Using the distributive property, write an

expression equivalent to 4(x + 3).

7. Express 100,000 in scientific notation.

8. Find the area of a rectangle 6" by 4" .

9. Write in simplest form: 1016

10. Which is greater: 12

or 13

?

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


Grade 8 • Page 15

5Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 300

2. 131%

3. 8 cm3

4. 24 cm2

5. 5.1 km

6. 25.99

7. x = 2

8. 6

9. 40

10. 5x – 9y

Keeping Skills Sharp1. 684 inches

2. 8.013

3. $.65

4.4

12 = 1

3

5. 18, 29

6. (4 • x) + (4 • 3)

7. 1 × 105

8. 24 sq. in

9.58

10.12

Answer: $216

Answer: 343 cm3

Answer: Both tanks will be half full fifteen minutesafter the first tank starts to fill or ten minutes afterthe second tank starts to fill.

Each student may participate in more than one or innone of the sports. The percentages might not addup to be exactly 100%.

30 40 50 60 70 80 90 100


Answer Key

Grade 8 • Page 16



Visual



What Do You Say?

How many cubes are in thefigure? Be sure to countthe hidden cubes.

In a triangle, the largest angle is 29degrees more than the smallest. Theother angle is 13 degrees larger thanthe smallest. What is the smallestangle in the triangle?

In Pollville, records are kept on the previousmayors. Here are the ages of the last sixmayors when they were voted into office:

45 88 37 42 41 44

Compare the mean and median. Which is amore representative measure of the averageage? Why?

Draw a DiagramThere are 16 tennis players in a singleelimination tournament. How many tennismatches will be played during thetournament?

A student’s scores on 4 math tests were 89,92, 95, and 85. What will he need to makeon the 5th test to have an average of 93? Isthis possible?

Margie had an average of 87 onher first five test scores. On thenext two tests she did better. Shemade 1 point higher on theseventh test than she did on thesixth. Her average on all seventests was now 90. What were hertwo new test scores?

Grade 8 • Page 17

MentalMath

6


1. Evaluate if x = 3: 3x2 + 2

2. Solve for z: z3

= 721

3. (23)2

4. Simplify: 2x(x – 3y)

5. What percent of a day is18 hours?

6. Find the area of the shaded portion

of the rectangle:

7. True or false: –7 < – 49

8. –3 – (–8)

9. Convert 14 milligrams to grams.

10. 12 • 13 – 12 • 3

Input3407

Output791

1. Write all prime numbers between 15 and 25.

2. 3 is to 15 as 4 is to ____.

3. Express 13 as a decimal.

4. 313 • 4

18

5. 40,320 ÷ 1.5

6. Evaluate 2a + 7b if a = 5 and b = 3.

7. 16 + 23

8. Find the prime factorization of 120.

9. Find the perimeter of a rectangle 2.5 cm by 1.5 cm.

10. Complete the table:

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

10

10

5 5

m

m

m

m


Grade 8 • Page 18

6Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 29

2. 1

3. 26 or 64

4. 2x2 – 6xy

5. 75%

6. 25 square meters

7. False, the two are equal.

8. true

9. 0.014 g

10. 120

Keeping Skills Sharp1. 17, 19, 23

2. 20

3. .333…

4.554

or 13 34

5. 26,880

6. 31

7. 12

8. 23 • 3 • 5

9. 8 cm

10. 15

Answer: 97 and 98

Answer: 46 degrees

Answer: 15

Answer: 104. This is possible if there is a bonusproblem on the test.

Answer: 35

Answer: The median is less sensitive to theoutlier, 88.


Answer Key

Grade 8 • Page 19



Visual



What Do You Say?

Add a square to the figure so that the area is 6 squareunits and the perimeter does not change.

Pebble Pebble!A pebble is thrown into a cylindricalwater pool 3 feet in diameter causingthe water to rise 0.0015 inches. Whatis the volume of the pebble in cubicinches?

The surface area of a cube is486 square inches. What is thenumber of inches in the length ofone of the edges?

From 1997-98Mathcounts School Handbook

Guess and then CheckJack has a total of 10 nickels and quarters. Ifthe value of the coins is $1.70, how manyquarters does he have?

You are given a scatter plot and told toestimate and draw a line of best fit.Explain how you do this.

Give an example of data that would show a(1) positive relationship, (2) negativerelationship, (3) or no relationship whendisplayed on a scatter plot.

Grade 8 • Page 20

MentalMath

7


1. Solve for x: 13 x + 7 = 1

2. Write 3313% as a decimal.

3. How many quarters equal $20.75?

4. A six-pack of soda sells for $2.28. What is the cost per can?

5. Write 54 as a percent.

6. Convert 1.23 × 103 to standard form.

7. Simplify: 130

8. Solve for x: 14 x – 8 = 12

9. 18 is between what two consecutive integers?

10. True or False: (0.2)(0.8) = 0.16

1. What is the mode for the following set of scores:

{75, 62, 71, 88, 73, 88, 72, 77}?

2. 3 • 7 – 4 • (8 + 2) =

3. Give the 6th term in the sequence 1, 4, 9, 16…

4. 6 is 15% of what number?

5. Simplify: (2x2)3

6. 75% of 19.00 =

7. Add four to the multiplicative inverse of 23 and simplify.

8. Draw an obtuse angle and estimate its measure.

9. For the given parallelogram determine the measure of

angle x.

10. What percent of 4 is 7?

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


60° 120°

xx

Grade 8 • Page 21

7Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. x = –18

2. .3

3. 88

4. $ .38

5. 120°

6. 1,230

7. 1

8. 80

9. 4 and 5

10. True


2. –19

3. 36

4. 40

5. 8x6

6. 14.25

7. 512

8. Answers will vary

( 90°< measure of angle <180°)

9. 125%

10. 175%

Answer:

Answer: π (18)2 × 0.0015 1.53 cubic inches

Answer: 9 inches

Answer: 6 quarters

Answer: The line should follow the general path ofthe points. The line should have an equal number ofpoints above and below it and should pass throughas many of the points as possible.

Answers will vary.1. Positive: amount of money earned and spent2. Negative: age of car and the car's value (The car

is not a classic.)3. No: Your height and month of birth


Answer Key

~~

Grade 8 • Page 22



Visual



What Do You Say?

The dot patterns show the first three square numbers.

Show the next two square numbers. Use exponentsto write each number.

Simplify the following expression:

x + 4(y + 8x)

Write the property that allows you tocomplete each step (out to the side).

On five tests (on which scores could rangeanywhere from 0 to 100, inclusive) Johnnyhad an average of exactly 88. Find the lowestscore Johnny could have received on one test.

Make a TableThe sum of two brothers’ ages is 38. Onebrother is ten years older than the other.How old is each brother?

Estimate the measure of the indicated anglein degrees. Explain or show how you gotyour estimate.

x

In the diagram, lines m and n areparallel. The measure of angle 1 is 44˚more than the measure of angle 2. Findthe smaller of the two angles.

1 2 n

m

Grade 8 • Page 23

8


1. 25 + –5

2. True or False: 160

= 0

3. Solve for x: x4 – 6 = –16

4. Express 2.3 × 104 in standard form.

5. In which quadrant does the ordered pair (–3, 4) lie?

6. Convert 5,000,000 millimeters to kilometers.

7. Write 489,000 in scientific notation.

8. 19 – 23

9. 0 – 612 + –3

10. –11 – 7

1. Find the mean of 4, 6, 3, 12, 5.

2. Find the median of the numbers in Problem #1.

3. What are the next 2 numbers in the pattern?

–1, 2, –4, 8 –16, ___, ___

4. Order from least to greatest:

.5, .05, .5001, .49

5. Find the measure of angle x:

6. Simplify:2x2y + 7x + 2x2y – xy2

7. An elevator started at the first floor and went up 18 floors. Itthen came down 11 floors and went back up 16. At whatfloor was it stopped?

8. (3x2y)3

9. Find the area of a circle with radius of 8 cm.

10. What does area mean?

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

MentalMath

80°x


x

Grade 8 • Page 24

8Visual

Multi-Step

Data/Investigations


Problem-Solving StrategiesAnswer: 14 years, 24 years

What Do You Say?135˚

Sample explanation: 90˚ + .5 ( 90˚) = 135˚

Mental Math1. 20

2. False

3. –40

4. 23,000

5. II

6. 5 km

7. 4.89 × 105

8. –4

9. –912

10. –18


2. 5

3. 32, –64

4. 0.05, 0.49, 0.5, 0.5001

5. 100°

6. 4x2y + 7x – xy2

7. 24

8. 27x6y3

9. 201 cm2

10. Number of square units needed to cover asurface

42 52

x + 4(y + 8x) = x + 4y + 4 • 8x Distributive Property = x + 4y + 32x Substitution = x + 32 x + 4y Commutative Prop. of Add. = 1x + 32x + 4y Multiplicative Identity = (1 + 32)x + 4y Distributive Property = 33x + 4y Substitution

100 88 • 5 = 440 440100 – 400100 40100 ■400

Answer: The smaller angle is 68 degrees.


Answer Key

Grade 8 • Page 25



Visual

Multi-Step

Data/Investigations


What Do You Say?

You have to wrap gift boxes for yourclub project. Each box is 4.5 incheswide, 7 inches long, and 4 inches tall.What size rectangle do you need to cutto cover the box?Gift wrap paper comes in sheets whichare 30 inches wide and 36 inches long.How should you cut your rectangles tomake the best use of the paper?

If each circle has a diameter of 50 feet,find the distance around the racetrack?

The data values below are the speeds (inkilometers per hour) of ten trucks travelingon Interstate 95.

80, 65, 70, 60, 60, 70, 73, 70, 59, 46

Interpret and construct a box plot. Analyzethe data. Compute the mean. How does themean compare with the median?

Guess and CheckUsing the digits0, 1, 2, 3, 4, 5, to fill in theboxes. Make asubtraction problem withthe smallest possibleanswer.

Explain in words how you would solve:n – 8 = 12

Using Color Cubes…1. Make a rectangle that is

14 red,

14 blue,

18 yellow

and the rest green.

2. Make a rectangle that is 15 yellow,

12 blue

and 3

10 red.

3. Make a rectangle that is 13 blue,

14 red,

16 yellow and the rest green.

How many cubes of each color are in the aboverectangles?Is there more than one possible solution?

Grade 8 • Page 26

MentalMath

9


1. ( – – – )3 4

2. Simplify: 4(2x – 4)

3. If a $36 shirt is on sale for 25% off, what is the sale price?

4.

5. –8 + 15.32

6. If 7 out of 10 students like pizza, how many students shouldlike pizza in a class of 30?

7. Solve for x: x2 = 121

8. -250 ÷10 x 3 + 7

9. –3.5 + 8

10.34

3

1. Compare perimeter and circumference.

2. ____ ÷ 4 + 6 = 16

3. Determine the measure of angle x.

4. Simplify:(2 × 103)(4 × 108)

5. – –310

12

6. How much less is the square root of 64 than 62 • 4?

7.56

14

÷

8. –16 + (20 • 6) ÷ (6 + 2) + 31

9. Find the mean, median, and mode for the following set of data:{ 0.2, 0.4, 0.1, 0.6, 1.2, 1.1 }

10. What is the sum of the first 5 square numbers?

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________


016

x

60°

x

Grade 8 • Page 27

9Visual

Multi-Step

Data/Investigations



What Do You Say?

Mental Math1. 1

2. 8x – 16

3. $27

4. 0

5. 7.32

6. 21

7. –11, 11

8. 68

9. 4.5

10.2764

Keeping Skills Sharp1. Distance around a polygon vs. the distance

around a circle.

2. 40

3. 30°

4. 8 × 1011

5. – 810

= – 45

6. 136

7.206

= 3 26

= 313

8. 30

9. mean: 0.6, median: 0.5, mode: none

10. 55

There is more than one solution possible dependingon the total number of cubes used to make eachrectangle. A possible solution for each follows: 1. 2 red, 2 blue, 1 yellow, 3 green 2. 2 yellow, 5 blue, 3 red 3. 4 blue, 3 red, 2 yellow, 3 green

Answer: 200 + 50 × 3.14 is about 357 feet…about120 yards.

LE: 46UE: 80LQ: 60UQ: 70

Median: 67.5Mean: 65.3 They are very close.

Answer: 301– 254

47

The smallest sheet of paper that will work is 11.5 in.× 17 in. If you cut the large sheet of paper into foursheets, each 18 × 15, the least paper will be wasted.

Add eight to both sides of the equation.n = 20

40 50 60 70 80


Answer Key

Documents

Problems of the Week 1 - SharpSchoolmathlearnnc.sharpschool.com/UserFiles/Servers/Server_4507209/File... · with gum balls of 6 different colors. ... Grade 8 Answer: 374.4 pounds