Problems of the Week 10 - Apprendre… Autrement · 10. 9 Keeping Skills Sharp 1. 1800 2. 5 8 3. It...

Grade 6 • Page 28

10Problems of the Week

Visual

Multi-Step

Fraction Action

Problem-SolvingStrategies

Geometry/Measurement

What Do You Say?

Which line appearsto be headingtoward a value of250 at week 10?

John’s rubber ball bounces exactly halfthe height from which it is dropped. Hedrops the ball from a building that is64 feet tall. How highwill the ball bounce onits sixth bounce?

A package of ground beef weighs12 lb. A second package weighs

34 lb.

Together will there be enough to make6 quarter pound hamburgers? Explainhow you know.

If a square is cut along one of its diagonals,two polygons of equal area are formed. Willthis also be true of a regular pentagon? Drawand explain your answer.

From MathStars Vol. 6, No. 1

Everyone in a club ordered either a smallpizza for $3.50 or a sub for $4.50. There areten people in the club and the total bill was$38. How many ordered subs, and howmany ordered pizza?

# of Subs Cost # of Pizzas Cost Total

Write four pairs of equations that showmultiplication and division are inverseoperations.

500

400

300

200

100

05 100

A

B

C

Grade 6 • 9

MentalMath

10

Keeping Skills Sharp

1. Round to nearest 10: 836

2. What number is 3 tenths less than 1?

3. How much is 6 dimes, 3 nickels, and 1 quarter?

4. How many inches are in 4 feet?

5. How many cups are in a quart?

Translate into an equation and solve.

6. Nine less than what number is 6?

7. The sum of what number and 14 is equal to 21?

8. The product of 4 and 12 is divided by some number to get ananswer of 3. What is the number?

9. If 25 of a pizza costs $1.00, how much will the whole pizza

cost?

10. Eighteen is equal to twice what number?

1. Estimate the sum of 462 + 526 + 856

2. Which is greater? 58 or

716

3. Describe a 45° angle.

4. What is the product of the first five whole numbers?

5. How many yards are there in 2 miles?

6. What is the perimeter of a square with each side 12 meterslong?

7. What is the range of the following test scores?

69, 85, 72, 98, 85

8. 6 × 2 – 8 ÷ 4 =

9. If you have 5 blue marbles, 3 red marbles, 5 white marbles,and 7 yellow marbles, what is the probability of not getting ayellow if you draw one of them out of a sack?

10. Complete the pattern:1, 2, 4, 8, ___, ___, ___

*See answer key. The Mental Math section should not be duplicated for the students.

Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • 0

10Visual

Multi-Step

Fraction Action

Geometry/MeasurementNo. In a square, the diagonal is also a line of sym-metry. Regular pentagons have no lines of symme-try that pass through two vertices. Therefore, diago-nals will always form polygons of different sizes.

Bounce Height1st 32 ft2nd 16 ft3rd 8 ft4th 4 ft5th 2 ft6th 1 ft

The hamburger is only enough for 5 quarter-poundburgers.

Problem-Solving Strategies

What Do You Say?

Mental Math1. 840

2. 0,7

3. $1

4. 48 inches

5. 4

6. 15

7. 7

8. 16

9. $2.50

10. 9

Keeping Skills Sharp1. 1800

2.58

3. It is an acute angle with measure equal tohalf the measure of a right angle.

4. 120

5. 3520 yards

6. 48 meters

7. 29

8. 10

9.1320

10. 16, 32, 64

A is pointing to 250 at week 10.

Three ordered subs and seven ordered pizza.

Answers will 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 6 • Page 31


Visual

Multi-Step

Fraction ActionProblem-SolvingStrategies


What Do You Say?

Which drawing would give you a rectangular prism?

A B

Show how to divide half a cantaloupeinto 4 equal pieces. What fractionalpart of the whole cantaloupe does eachpiece represent?

(1) What happens to the area of a rectangle ifone side is doubled?

(2) What happens to the area of the rectangleif both the length and width are doubled?

Look for a PatternTen people are in a room. Each personshakes hands with all the other people inthe room. How many handshakes willthere be?

Explain how you know that 27 × 97 must beless than 3000 before you compute theanswer.

The judges at Marcy's skatingcompetition gave her scores of 9.6, 9.2,9.4, and 9.3. What score would the fifthjudge have to give Marcy to raise heraverage score to 9.4?

Grade 6 • Page 32

MentalMath

11


1. 4000 + 2000 + 50 + 40

2. 17000 – 5000

3. 3000 – 100

4. 5000 – 500

5. 2 × 7 × 5

6. Round to the nearest ten: 689.2

7. What is the smallest multiple of 8 and 10?

8. 0.033 ÷ 10

9. 64.2 × 100

10.14

+ 12

1. 100 + 20 + 5 =

2.12

14

14

+ + =

3. 0.2 + 0.3 + 0.5 =

4. 175 ÷ 25 =

5. 5 gallons = ___ quarts

6. Find the perimeter of a rectangle whose length is twice itswidth, if the width is 5 inches.

7. Find the median of the following temperature readings:

1˚, 10˚, 2˚, 9˚, 3˚, 8˚, 4˚, 7˚, 5˚, 6˚

8. 2 × 7 + 32 ÷ 9 =

9. If you spin the spinner 12 times,how many times would you expectit to land on B?

10. If the original figure continues to be rotated in a clockwisedirection, draw the next two figures.

_____ _____

R BY


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • Page 33

11VisualA

Multi-Step

Fraction Action


9.5


What Do You Say?

Mental Math1. 6090

2. 12,000

3. 2900

4. 4500

5. 70

6. 690

7. 40

8. 0.0033

9. 6420

10.34


2. 1

3. 1

4. 7

5. 20

6. 30 in

7. 5.5˚

8. 15

9. 4

10.

Diagrams may vary. Answer is 18 .

When one side is doubled, the area doubles. Whenboth dimensions are doubled, the area is multipliedby four.

First person must shake 9 hands. Second personmust shake 8 more. Third person must shake 7more etc. The last person (tenth) will already haveshaken hands with all the others.9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45

27 is less than 30. 97 is less than 100.So, 27 × 97 must be less than 30 × 100 or 3000.


Answer Key

Grade 6 • Page 34


Visual

Multi-Step

Fraction Action



What Do You Say?

Find the fourth cornerof the parallelogram.

Peter bought a used bicycle with someof his money. He made 3 payments of$29.75 each and spent $8.50 for 2 newtires. How much did he spend for thebicycle?

778,300,000 km is the average distancebetween Jupiter and the sun. Express this inmeters and centimeters.

Guess and TestA farmer has goats and ducks on his farm.If the animals have 60 eyes and 80 legs,how many ducks does he have?

Why would you write a number usingexponents instead of standard form?

A girl walks her dog to school everyday at 4 p.m. After she walks for

18 minutes, she still has 14 of the trip

to walk. How long will the rest of thetrip take?

0 5 10 15 20

5

10

Grade 6 • Page 35

MentalMath

12


1. Which is larger 78 or

79 ?

2. What is the approximate value of pi?

3. What is the formula for finding the areaof a rectangle?

4. How many ounces are in a pound?

5. Write 0.66 as a percent.

6. What is the sum of the first 3 prime numbers?

7.18

24

+ + 1

8. 1.14 ÷ 0.2

9. 8.3 – 4.5

10.5

12 2

6–

1. 140 – 70 =

2.12

14

– =

3. 0.5 + 0.25 + 0.25 =

4. 123 × 12 =

5. 2 miles = ____ feet

6. Find the area.

7. Find the median of thefollowing scores .

1 1 2 3 32 4 5 5 9 9 1 1 = 113 1 2 6 7

6 cm

12 cm

4 cm

8. 2 × 32 ÷ 9 + 7

9. On a multiple choice question with 4 answerchoices, what is the probability of choosing thecorrect answer if you guess?

10. Complete:

R, Y, R, Y, B, R, Y, R, Y, B, R, ___, ___, ___


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • Page 36

12Visual

Multi-Step

Fraction Action


$97.75

6 minutes


What Do You Say?

Mental Math

1.78

2. 3.14

3. Multiply the length times thewidth.

4. 16 oz

5. 66%

6. 10

7. 1 58

8. 5.7

9. 3.8

10.1

12


2.14

3. 1

4. 1476

5. 10,560

6. 48 cm2

7. 25

8. 9

9.14

10. Y, R, Y

10 goats and 20 ducks

778,300,000,000 meters77,830,000,000,000 centimeters

(12, 7)

Answers may vary. Good answers would includesaving space and to make easy comparisons.


Answer Key

Grade 6 • Page 37


Visual

Multi-Step

Fraction Action



What Do You Say?

A circle is drawn on a coordinate plane with the centerat (5, 8). The radius of the circle is 3.5. Give thecoordinates of four points which must lie on thecircumference of the circle?

Seven sisters wanted to plant gardens ofequal areas. Each garden had an area of48 yd2. If their gardens are arranged asseen below, what is the perimeter of theentire garden?

At the school picnic, the class spent12 hour eating,

34 hour playing

basketball, 23 hour playing soccer,

hour eating dessert, and hour

running to get out of the rain.(1) If the picnic started at 11:00 a.m.,when did it end?(2) How much more time was spentplaying than eating?

Sam spent half of his money on a shirt. Atanother store he spent half of the money hehad left. Then he bought a CD for $6.75.

He had $2.50 left over. Howmuch money did Sam havein the beginning?

Explain the multiplication property of one.Use the numbers 6 and 1 in yourexplanation.

y y y y

yy

x x

x x x

An airplane flying at an altitude of30,000 feet flies over a ship wreck which isknown to be 2 miles below sea level. Howfar apart are they?

120

1 5

Grade 6 • Page 38

MentalMath

13


1. Write in exponential notationsixteen to the seventh power.

2. Write 15 as a decimal.

3.5

12 of 24

4. How many ounces are in5 pounds?

5. 0.3 × 0.5

6. 600 – 51

7. Write the ratio of 6 blackbirdsto 8 bluebirds.

8. Estimate 11819

+ 2 112

9. 52 × 32 is the prime factor-ization for what number?

10. 5 + 114

1. 9 × 4 + 14 ÷ 7 =

2. 8 + (6 – 2) × 3 =

3. 5 + 1.25 =

4. 16 × 16 =

5. 14 ft = ___ yd ___ ft

6. Find the area of a rectangular garden whose length is 8 feet andwhose width is 72 inches.

7. Add one number to the following set of data (ages of children inyears) so that the mode does not change.

1, 1, 2, 2, 3, 3, 3, ___

8. 6 × 3 + 5 × 4 =

9. If the first letters of the months are written on cards (1 letter percard) and the cards are placed in a bag, what is the probabilityof picking a “J”?

10. Complete the pattern: A, C, E, G, I, ___, ___, ___


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • Page 39

13Visual

Multi-Step

Fraction Action


x = 8 and y = 6. The perimeter would be 76 units.

(1) The picnic ended at 1:10 p.m.(2) They spent 55 more minutes playing than

eating.


What Do You Say?

Mental Math1. 167

2. 0.2

3. 10

4. 80 oz.

5. 0.15

6. 549

7. 6 to 8 or 3:4

8. approximately 4

9. 225

10. 6 14


2. 20

3. 6.25

4. 256

5. 4 yd 2 ft

6. 48 ft2

7. Anything except 1 or 2.

8. 38

9.

10. K, M, O

Four other points are: (8.5, 8), 1.5, 8), (5, 11.5),(5, 4.5)

40,560 feet or about 7.7 miles

Use the strategy of working backwards.$2.50 + $6.75 is half of what he had in the secondstore. $9.25 = half of $18.50. $18.50 is half of whathe had in the first store. He must have started with$37.00.

Multiplying 1 by any number does not change it.Example: 6 × 1 = 6

312


Answer Key

Grade 6 • Page 40


Visual

Multi-Step

Fraction Action



What Do You Say?

Find the area andthe perimeter ofthe figure shown.The figure ismeasured incentimeters.

A candle was 45 centimeters long. Itwas lit and 20% burned off. Then thecandle went out. The next day the

candle was lit and 25% burnedoff. Then it went out. On the

third day the candle was lit, 13

burned off. How long was thecandle after the third day?

Lori and Randy had a new room to

paint. Lori spent about 29

20 hours

painting and Randy spent about 312

hours. About how much time didthey spend altogether on painting theroom?

A rectangle is drawn on a coordinate grid.One corner is at (7, 5) and another is a(19,5). The area of the rectangle is 48.Find the other two corners of therectangle.

Cindy wants to plant flowers around arectangular garden. The plants should be6 inches apart to allow for adequate growth.The perimeter of the garden is 30 feet. Thefirst plant is placed at a corner of therectangle. How many plants are needed?

Describe the following pattern:

1, 4, 9, 16, 25, 36,...

9

12

3

4

4

3

3

3

3

3

9

4

7

Grade 6 • Page 41

MentalMath


1. Write 3 to the 5th power in standard form.

2. One angle of a pair of supplementary angles has a measureof 42˚. What is the measure of the second angle?

3. Write 0.75 in fraction form.

4. How many pounds are in 3 tons?

5. How many minutes are in 12 hours?

6. 112

34

–

7. What is the probability of rolling a 6 on a fair die?

8.34

+ 12

9.12

12

÷

10. 3.2 – 1.4

1. 672 + 28 =

2. 7 × 4 – 2 ÷ 1 × 6 =

3. 6.72 – 2.8 =

4. 300 ÷ 25 =

5. Use <, >, or =.

72 inches ● 2 yards

6. Find the areas:

7. Add one number to the following set of scores so that the mediandoes not change:70, 60, 90, 80, 100.

8. 3 + 4 × 6 – 3 =

9. What is the probability of the spinner

landing on Y?

14

10. Complete:

1, 2, 2, 4, 8, 32, 256, ___

10 7

7

10 7

7

7

Y 4G Y


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • Page 42

14Visual

Multi-Step

Fraction Action


18 cm


What Do You Say?The numbers in the pattern are squares. Also thedifferences between the numbers is a sequence ofodd numbers.

Mental Math1. 35 = 243

2. 135˚

3.34

4. 6,000 pounds

5. 720 minutes

6.34

7.16

8. 114

9. 1

10. 1.8Keeping Skills Sharp1. 700

2. 16

3. 3.92

4. 12

5. 72 inches 2 yards

6. Area #1 is 94.5 square units.Area #2 is 119 square units.

7. 80

8. 24

9.

10. 8,192

228 square centimeters is the area. The perimeter is80 centimeters.

About 6 hours

A diagram is useful. The answer is 60 plants.

The other two corners could be at (7, 1) and (19, 1)or at (7, 9) and (19, 9).

2 4


=

Answer Key

Grade 6 • Page 43


Visual

Multi-Step

Fraction Action



What Do You Say?

Which square does not have one-half shaded?

Misty spent 12 of her allowance buying

four comic books. She spent 14 of her

allowance buying 7 pens that cost 50cents each. How much did each comicbook cost?

Draw a figure with 5 faces, 8 edges and5 vertices.

Little Red Riding Hood was taking a basketof walnuts to her granny. Along came thewolf and demanded half of the nuts. Butluckily Red found another nut along theroad. Then the wolf returned and tookhalf the nuts she had. A kindlysquirrel gave her two more. Whenthe wolf returned the last time,he settled for only one-fourthof her nuts. Red made it toGranny's with 15 nuts. Howmany did she start with?

Explain how to locate points on a grid. Use(2, 3) as your example.

A B C

D E F

Shade the circle to show 13

of 14

.

What fractional part of the circle is13

of 14 ?

Grade 6 • Page 44

MentalMath

15


1. Write 0.25 as a percent.

2. Four quarts = ____ cups

3. Six meters = ___ centimeters

4.14

34

+

5. Two minutes = ____ seconds6. Compare and order from least to greatest:

12

, , 1, 14

34

7. What are the factors of 12?

8. 0.36 + 5

9.23

45

×

10. 425 + 175

1. 139 + 267 + 982 =

2. When graphing on the coordinate plane, the vertical axis iscalled the _______________.

3. 0.425 + 0.175 =

4. 67 × 34 =

5. Are vertical angles congruent or supplementary?

6. Find area and perimeter:

7. Find the mean of the following ages: 3, 10, 4, 3, 7, 3

8. Simplify: 6 + 7 × 2

9. If the letters in the word “math” are written on cards, what is theprobability of picking one card at random and it being from thefirst half of the alphabet?

10. Complete the pattern: 3, 8, 13, 18, 23, ___, ___, ___

6 in

6 in


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • Page 45

15Visual

Multi-Step

Fraction Action


$1.75

13

of 14

= 112


What Do You Say?

Mental Math1. 25%

2. 16

3. 600

4. 1

5. 120 seconds

6. 14

, , , 112

34

7. 1, 2, 3, 4, 6, 12

8. 5.36

9.8

15

10. 600

Keeping Skills Sharp1. 1,388

2. y-axis

3. 0.6

4. 2278

5. congruent

6. A = 36 in2 P = 24 in

7. 5

8. 20

9.14

10. 28, 33, 38

F

Work backwards. The answer is 70 walnuts.

Start at the origin. Move 2 units to the right, thenmove 3 units up.

3 4


Answer Key

Grade 6 • Page 46


Visual

Multi-Step

Fraction Action


What Do You Say?

Four men are on one side of a bridge.They must get to the other side in 17minutes. Only 2 men can cross thebridge at a time and one of them musthave the flashlight. When two mencross, they must walk at the pace of theslower man. They must carry theflashlight back across (no throwing it).

Man A walks the bridge in 1 minute.Man B walks the bridge in 2 minutes.Man C walks the bridge in 5 minutes.Man D walks the bridge in 7 minutes.

How can they get across the bridge intime?

The Titanic is 225 miles below the

surface of the Atlantic Ocean. If you

dive at the rate of 34 miles per hour,

how long would it take you to get tothe ship?

Using 12 square tables, combine them tocreate rectangular banquet tables.Complete the chart below. What are thedimensions of the table that will seat themost people? the least people?

Mrs. Jones has been cutting ribbons to use for

awards. She has 12 yard left. When two

students give their ribbons to Mrs. Jones, she

has a total of 34 yard. What length of ribbon

would be needed to make 7 student prizes?


Explain why order of operations is soimportant. Give examples to illustrate yourexplanation.

x x x xxxx

xxx

x x x x

Number of small tables Length Width Seating

12 4 3 14

In a frog race, frog A can move 5 feet in 5seconds. Frog B moves 600 inches in aminute and frog C moves 2 yards in 8seconds. Which frog is fastest?

Grade 6 • Page 47

MentalMath

16


1. Round 8.475 to the nearest tenth.

2. Estimate: 78 + 31

3. 10 + 10 + 10 + 20 + 20

4. Add:

5. Find one-half of 998.

6. Add: 347 + 653

7. What is 13 of 27?

8. Find the area of a square with sides of 5 meters.

9. Subtract: 1000 – 457

10. Multiply: 43 × 11

1. Add: 3 + 4 + 7 + 6 + 5 + 5

2. 212 – 1

12 =

3. 6.3 + 0.63 + 63 =

4. 91 ÷ 30 =

5. 18 inches = ____ feet

6. Find the perimeter of a rectangular garden whose length is 8 feetand whose width is 72 inches.

7. The following high temperatures were recorded for the first sixdays of the month. What would the high temperature need to beon the seventh day so that the mean for the seven days would beexactly the same as the mean for the first six days?

34˚, 41˚, 39˚, 43˚, 45˚, 50˚

8. Simplify: 6 + 3 + 4 ÷ 2 × 3

9. If the first letters of the days of the week are put on cards (1 letterper card), and the cards are put in a bag, what is the probability ofdrawing an “S” when drawing a card from the bag?

10. Complete: 1, 6, 2, 6, 6, 3, 6, 6, 6, ___, ___, ___, ___, ___


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

1 4

1 2

1 8+ +

Grade 6 • Page 48

16Visual

Multi-Step

Fraction Action


D + A (7 minutes), A back (1 minute),B + C (5 minutes), B back (2 minutes),A + B (2 minutes), total of 17 minutes

165 or 3.2 hours


What Do You Say?

Mental Math1. 8.5

2. 110

3. 70

4.

5. 499

6. 1000

7. 9

8. 25 m2

9. 543

10. 473


2. 1

3. 69.93

4. 3 r. 1

5. 1.5

6. 28 feet or 336 inches

7. 42˚

8. 15

9.27

10. 4, 6, 6, 6, 6

Length 4, width 3, seating 14 — leastLength 12, width 1, seating 26 — most

78 yard

Frog A is the winner at 12 in./sec.Frog B travels at 10 in./sec.Frog C travels at 9 in./sec.

Answers will vary.


78

Answer Key

Grade 6 • Page 49


Visual

Multi-Step

Fraction ActionProblem-SolvingStrategies


What Do You Say?

Who is the shortest adult?

7654321

Heig

ht

10 20 30 40 50 60 70

Laurin

Jamie

Cheryl

MabelTomeka

Tyrone

Thomas

Age

Five students each bring 16 yards ofribbon to school for a project. Howcan the ribbon be divided so that Anngets exactly twice as much as Susan?

Two sixth graders volunteered to helpclear a nature trail behind their school.

Marc worked 216 hours and Kim worked

323 hours. How many hours did they

work altogether?

Lazy River flows 450 meters in 15 minutes.Boze Creek flows 1 km in 30 minutes andTodd's Branch flows 5 km in 2 hours. Whichis fastest?

Find x.

Beginwith x

Divide by 6 Add 12

Subtract526

Describe how you would find the measuresof each angle in a triangle.

Grade 6 • Page 50

MentalMath

17


1. of 5

2. How many centimeters are in 3 meters?

3. Is 38 closer to

12 or 1?

4. 3 hours 15 minutes = ___ minutes

5. Write the ratio of 6 green balls to 10 red balls infraction form.

6. Add: 11.3 + 12.81

7. What is 25 ÷ 4?

8. Subtract: 16 – 1.84

9. 25 × 8

10. Add: 14

+ 24

+ 5

1. 16 + 23 + 4 + 17 =

2. What is the sum of two complementary angles?

3. 1.6 + 2.3 + 4 + 1.7 =

4. Multiply: 4.6 × 18.3

5. How many sides are there in a trapezoid?

6. Find the area:

7. Find the mean of the following measurements:

10 m, 10m, 12m, 12m, 14m, 14m, 5m

8. Simplify: 32 ÷ 9 + 2 × 7

9. If 2 fair coins are tossed, what is the probability that both willland on heads?

10. Complete the pattern: S, M, T, W, ___, ___, ___

4 cm

2 cm

10 cm

2 cm


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

12

Grade 6 • Page 51

Essentials

WE

E

K BY W

EE

K17Visual

Multi-Step

Fraction Action


Ann gets 513 , Susan gets 2

23 .

Answer: 5 56


What Do You Say?Answers will vary.

Mental Math

1. 2 12 or 2.5

2. 300 centimeters

3.12

4. 195

5.35 or

6. 24.11

7.1

10

8. 14.16

9. 200

10. 5 34


2. 90°

3. 9.6

4. 200

5. 73.2

6. 28 cm2

7. 11 m

8. 15

9.14

10. T, F, S(Days of the week)

Mabel

Answer: 114

Lazy River flows at 1.8 km/hr.Boze Creek flows at 2.0 km/hr.Todd’s Branch flows at 2.5 km/hr.


610

Answer Key

Grade 6 • Page 52


Visual

Multi-Step

Fraction Action



What Do You Say?

A rectangular field is divided into 4 rectangularsections. The area of rectangle x is 72 square feet.The area of rectangle y is 30 square feet. The area ofrectangle z is 60 square feet. Find the perimeter of thefield.

April is 1 year older than Amanda.Wendy is 2 years older than April.Joe is 3 years older than Wendy.Carol is 4 years older than Joe. Theaverage age of the children is 6.How old is Amanda?

The three circles in the figure arecongruent. Point M is the midpoint of AOand AM = 3 cm. Find the area of therectangle.

At a class picnic there are 7more students than adults. Ifthere are 39 people in all,how many students arethere?

Explain how you would determine how toplace the following fractions in order fromsmallest to largest.

12

, , , , 18

13

14

16

Paul works for 3 hours. Sally works

212 times as long as Paul. Rasheed

works 34 hour less than Paul. Toshi

works 113 times as long as Rasheed.

How long does each person work?

AO

M

w x

y z

Grade 6 • Page 53

MentalMath

18


1. How many days are in two years?

2. Estimate: 4.6 + 6.2 + 7.84

3. How many centimeters are in one kilometer?

4. Write in fraction form: 0.05

5. 250 + 10 + 100

6.58

– 48

7. 0.64 ÷ 0.2

8. 2 ÷ 12

9. 1.3 + 4.2

10. 312 – 1

12

1. 2 3 ■

1 ■ 9

+ ■ 1 46 1 8

2. Shade in 23 of the squares.

■ ■ ■ ■ ■ ■

3. 2 ■ . 4– 2 . 8 9

2 3 . 5 ■

4. If 4 cats each catch 8 miceevery day, how many mice willthey catch during the month ofJanuary?

5. If you run 1,760 feet in a race,what part of a mile is this?

6. How many feet of fencing do Ineed if 2 sides of my backyardare each 6 yards, 1 side is15 yards and the house will beused as the fourth side?

7. Find the median weight for thefollowing measurements:

85 lbs, 68 lbs, 42 lbs, 44 lbs,

31 lbs, 32 lbs, 48 lbs, 65 lbs,

35 lbs, 28 lbs

8. Simplify: 6 × 2 + 4 – 8 ÷ 2

9. If the probability of John makinga 100 on his test was 80%, whatis the probability of John notmaking a 100?

10. Complete the pattern:

6, 8, 7, 9, 8, 10, 9, ___, ___, ___


Write answers here:

1. ___________

2. ___________

3. ___________

4. ___________

5. ___________

6. ___________

7. ___________

8. ___________

9. ___________

10. __________

Grade 6 • Page 54

18Visual

Multi-Step

Fraction Action


Amanda is 2 years old.

Paul works 3 hours.Sally works 7.5 hours.Rasheed works 2.25 hours.Toshi works 3 hours.

Problem-Solving StrategiesThere are 23 students and 16 adults.

What Do You Say?

Mental Math1. 730 days

2. 19

3. 100,000

4.5

100 = 1

20

5. 360

6.18

7. 3.2

8. 4

9. 5.5

10. 2

Keeping Skills Sharp1. 2 3 5

1 6 9+ 2 1 4

6 1 8

2. ■ ■ ■ ■ ■ ■

3. 26.4– 2.89

23.51

4. 992

5.13

6. 81 feet

7. 43 lbs

8. 12

9. 20%

10. 11, 10, 12

Rectangle x has dimensions 6 × 12.Rectangle z has dimensions 12 × 5.Rectangle y has dimensions 5 × 6.Rectangle w has dimensions 6 x 6.The perimeter is 58 feet.

The rectangle is 30 × 12, area is 360 cm2.

Since all numerators are equal to 1, the largestdenominator will represent the smallest fraction.Put them in order with largest denominator first,smallest denominator last.


Answer Key

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