Sixth Grade Summer Math Packet

Name

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Dear Parents, The attached packet provides a range of activities that review and e:xp-a-nd on the math concepts yourchi·ld has learned in school this past year. It is designed to be worked on for 15 to 30 minutes a day throughout the summer, rather than completed in just a few days at the beginning or end of summer. The goal is to keep skills sharp to be ready to move _forward into the n.e?d school year.. 'lYe .have provi~~d answers . for grades 3=6 and ask you to please review the work with your child as it is completed. Students will be asked to hand in their completed work the first week of school. Have a great summerl

The SeacrestStaff

Table of Contents 41)

Adding and Subtracting Decimals

41)

Multiplying with Decimals

41)

Dividing with Decimals

41)

Interpreting Data

41)

Geometric Ideas

41)

Measuring and Drawing Angles

41)

Adding and Subtracting Fractions

41)

Adding Mixed Numbers

41)

Subtracting Mixed Numbers

41)

Multiplying Fractions

41)

Multiplying Mixed Numbers

41)

Problem Solving Strategies

41)

Measurement- Customary & Metric

e

Perimeter

41)

Area

41)

Ratio and Proportion

41)

Fractions, Decimals, and Percents

41)

Probability

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Review

2 Adding and Subtracting Decimals Find 1.7 + 2.45.

Find 36.57 - 4.6. Line up the decimal points.

Line up the decimal points.

t

t

1

1.7 + 2.45

1.70 + 2. 4 5

-+

Write zeros to show place value.

4.15

t

5 15

36.57 3 ¢.~ 7 - 4. 6 - 4. 6 0 31 9 7

-+

Write zeros to show place value.

D

t

Place decimal point in answer.

Place decimal point in answer.

Find each sum or difference.

t 1.

2.65 +13.30

2.

8 .97

6.

5.

+ 66

9."15.4

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1 00 0.22

8 = __

11. 1.34 + 4.1

13. 448

t 1 4.1 0 - 3.05

= _ __

+ 1.75 + 80.3 = _ __

3.

+

7.

6.8 +237.29

12. 133.01 - 5.6

" 8.

0.5 - 0.23

= _ __

14. 12.3 + 0.61 + 100

= ~_ _ co

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>. a>

Vi

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9 - 0.6

10. "3 -2.54 = _ __

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4.

744 36.2

c

15. On the 3-days of their vacation, the Davis family travel~d 417 mi, 45.3 mi, a'nd 366.9 mi. How far' did they travel. all together?

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16.. Etta bought a calculat.or for $15. Glenn .found th'E} . s~me model for $9.79. How much more did Etta. pay than Glenn did?

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Find 4.3 x 2.7. Co.unt the number of decimal places in both factors. The total is the number of decimal places in the product.

Multiply as you would with whole numbers. 2

4.3 2.7 11 . 61

4.3

x

x 2.7 301

-+-+-

+

~

1 decimal placE? 1 decimal place 2 decimal places

860 1 1 61 Find e.ach product.

14

1.

2.

8.8 112 1120 X

5.

9. 23 X 0.47

x

.9

X

3.3 0.1 2

6.

2.1 5 x. 8.3

=

---

3.

1.6

10. 0.9 X 5

7~

~

0.4 x 3.2

4.

0 .51 x 4.2

8 ..

_ __

0 .05

x 0.3

1 .35 X

13

11 . 168 X 2.25 = _ __ 1

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15. A roll of paper towels contained 250 sheets. Each sheet was 8.75 inches long .. How long was the roll?

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Tania bought 3 new sweaters, Each sold for $-19.99. How much did she spend?

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Review

6 ,Dividing with Decimals

1-"'\

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Find 36.8

-7-

16.

t

2.3 1 6)3 6 . 8 -32 4 8

Place the decimal point.

2.

2

1 6)3·6 . 8

-+

Think: 20)40

Multiply 2 x 16. Subtract. Bring down 8. Multiply 3 x 16. Subtract.

-~

Try 2 in the quotient.

o Find each quotient.

2. 3. 9)1 4 1 . 3

2. 6)1 3 1 .4

1. 6)1 3.8

4. 5)388 . 5

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TID -DO 0 )))) 5. 7)6.6 9 .-2

9. 269.12

-7-

7.41)274.7

6.2 8)2 6 3 . 2

10. 311.56

8 = __

-7-

8. 7)34.2.3

4 = _ __

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11.2,229.62 -;- 46

= '_ __

12. 1,449.09

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81 =:= _ __

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'1;3. A photographer bought 36 rolls What was the price of one roll?

of film for $136.44. '

14. Four students each ran' 100 m in a AOO-m relay race. The' t~am's total time was 49.44 sec. Find the average time of each runner.'

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The bar 'graph shows the lengths in miles of the Great Lakes. Lengths of 'bars represent lengths of lakes. Which 'is the shortest Great Lake? The shortest lake is Lake Ontario.

lengths of the Great lakes 500r..·· ................·....·....·..······....·..·.._..·........·..··..·· .._.. ··.................-............................................, ~

4001-·....·..·..·..·. ·......···· ..·:······..····.. ·· ....·_·.. ·..·..··...........................................................................,

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300

g>

200

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100

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Superior Michigan

Erie Lake

Huron

Ontario

Use the graphs to answer each question. 1 How fllany archers scored 4 buli's eyes?

Archery Results

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x

x x (I

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Jan Feb Mar Apr May Jun Jul Aug. Month

II

x x x x x

x x

x

x

I» I I 3 0 1 ·2 4 5 6 Number of Bull's-eyes Scored

2. What was the most common number of bull's-eyes scored?

Number of Houses Sold

x x x x .1

3. In which month were the most houses sold?

4. In which. month were about the sam.e number soid as were said in August? r'

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5a Which grades raised about the same' amount for the school book drive?

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School Book Fund Drive

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500.·....·_..··..·_·_·--·..·__...._...._·........ _ ..·....·_·..··_·....·........_,

.£2

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400 r--..·......__ ·..·_··..- .._·_ .. ·

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-- 300

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The school's goal was to raise $1 ,500. About how much did they raise in all?

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100

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1st

2nd

3rd' 4th Grade

5th

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Geometric Ideas • A line is a straight path of points that goes on forever in two directions. Examples: AS"GK. ~~

A

• A ray is a part of a line with one endpoint, extending forever in only one direction. Examples: FD, FB.

B

~~

• A· line seg~ent is part of a line with two endpoints. Examples: CF, MQ. • A midpoint is the point halfway between the endpoints of a line segment. Example: Point L is halfway between points J and M on JM. • Congruent line segments are ·Iine segments that have the same length. Example: OR is congruent to.ST. • Parallelli~s are in the sa(m~ plane but do not intersect. Example: AS is parallel to 8'T. mw

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Use the diagram. at the right. Name t.he following~ 1. three line segments

2. two parallel lines

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3. two lines that intersect DT w d

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4. two congruent line segments·

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5. two lines perpendicular to BR

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6. two midpoints of line segments

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How to measure

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an angle:

angle:

Step 1 Place the protractor's center on the angle's vertex.

Draw an angle of 52°. Step 1 Draw a ray.

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s.tep 2 Place the 0° mark on one side of the angle.

Step 2 Place the protractor's center on the endpoint. Line up the ray with the 0° mark. Step 3 Using the scale with the 0° mark, place a ' point at 52°. Step 4 Draw the other ray.

N

LMN = 60° Step 3 Use the scale beginning with ttie 0° mark to read the measurement where the other side of the angle crosses the protractor.

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LABe = 52°

Classify each 'angl'e as acute, right, obtuse, or straight. Then measure the angle.

1.

/ L

2.

Draw an angle with each measure. co

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7. 0.04

8. 0.35

9. Number Sense Sheila got 87% of the problem correct. Patrick got '190~ correct. Who scored higher?

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Review

20

Probability What is the probability of spinning an A?

What is the probability of spinning a B?

number of As 4 -+ total.possible outcomes

1 4

The probability is ~

The probability is

2

-+

or~.

-+ -+.

number of Bs total possible outcomes

1.

Complete.

1. What is the probability of spinning a 1?

D D

-+

number of 1s

-+

total poss1ble outcomes

2. What is the probabHity of spinning a 3?

D D

The probability is _ __

-+

number of. 3s

-+

total possible outcomes

The probability is _ __

Give the probability of each .outcome. 3. spinning an N _ __

4. spinning an S _ __

5. spinning an S or G _ __

6= spinning an S, G, or N _ __

A number cube has 6 sides numbered 1, 2, 3, 4, 5, and 6. Find each probability. 7. rolling a 3 _ __

8. roliing an even number _ __ 1,000 in = 1 km

polntatS2·•.

100 + 1000 ='0.1

stop 4 Draw !he other ruy.

100m= 0.1 km Name the most appropriate metrlc unit for each measurement. 1. mass of a cow

2. length of a carrot

.kg

3. capacity of a thimble

em

inL ------------

!he anglo

Complete.

4.459

45~OOO

6. 4.5 m -

4 f 500

280 10. 600 co, 6 12. 5.1 km - 5,100 14. 0.760 L 780 16. 9,OOOcm 90 a.

LMN= 50' step 3 Use !he sc.al. beginning with !he 0' mllrl< toroad!he~wIle!o!heolh«sldGof

28cm=

mg

5. 3450mL

mm mm m

mL m

3.45

1 ,680 9. 7,658g- ~.658 11. 5,000 mg 5 13. 1.780L- 1,780 15. 4.300 m - 4.3 17. 8.001 mg - 8 7. 1.68 L -

CfO$SS$

the protroctor.

.

c LABC=S2'

L· mL kg

mL

Acute; 50°

km

Draw an angle with each measure.

18. Reasoning It is recommended that people have 1 g of calcium each day. How many milligrams of calcium Is that?

1,000 mg

U,.wilhLessontG-2.

117

Straight; 1800

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~ultiplying Fractions

R 5-2

An?txt· One Way . Orawapictufe.SinplifyH

Ih

posWIe.

Simplify FIr$!

AnotherWttt Mufl%>lYihelltMlll>llltors and denomloators. stmpflfy ff possllie.

txt =g~ =!a

Ffnd the GCFflfWi

hurnerator and Wi denomlnato,.

The GCF of2 and 4 Is 2. DIvIde 2 and 4 by !he GCF.

_2

-14

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3

"4 6 of the 28 squares have overlapping shading.

So,txf=fs. Simplify !a to f.4. Write an equation for each picture.

1.~.

~m

1 X 1 _

'6

Find each prod'ft. Simplify ff possible.

3·i Xt=

t

.

5.i x f=

~1~Q________

1

3-18

7 4.

t x -ft "'" ...1r.=2'---_ ___ 2'

6.t Xi= ~9~'_______

7. Number Sense Can you simplify before multiplying 14

x ~? Explain.

No, because there is no common factor to divide by Use with Lesson &-2.

55