Summer Math Packet for Sixth Grade Students: Activities and Review, Summaries of Reasoning

Download Summer Math Packet for Sixth Grade Students: Activities and Review and more Summaries Reasoning in PDF only on Docsity!

Name

Students Entering

Sixth Grade

Summer Math Packet

---

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

I

I

I I ·

I

I

iName --------------------------------------- (^) Review

2 Adding and Subtracting Decimals

Find 1.7 + 2.45.

Line up the decimal points. t

1. 7

1

1. 7 0 -+ Write zeros to

• 2. 4 5 show place value.

t Place decimal point in answer.

Find each sum or difference.

t

+13.

t

9."15.4 ~ 8 = __

11. 1.34 + 4.1 = __ _

13. 448 + 1.75 + 80.3 = __ _

Find 36.57 - 4.6.

Line up the decimal points. t 5 15 3 6. 5 7 3 ¢. ~ 7 Write zeros to

• 4. 6 - 4. 6 0 -+ show place value. 31 D 9 7

t Place decimal point

in answer.

10. "3 -2.54 = __ _

12. 133.01 - 5.6 = __ _
13. 12.3 + 0.61 + 100 = ~__
14. 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?

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?

co. I

. a> Vi ~ c

(^0) CI) '6 \J « c 1\1 E II) e u.^0 t:: 0 (J')^0 0

t.) (^) ) !

:Name __________________ _

Find 4.3 x 2.7.

Multiply as you would with whole numbers.

Co.unt the number of decimal places in both factors. The total is the number of decimal places in the product.

2

x 2.

x 2.7 -+-

1 decimal placE?

• 1 decimal place 301 860 1 1 61

Find e.ach product.

X 8.

x. 8.

x.

X 0.1 2

x 3.

x 4.

9. 23 X 0.47 = --- 10.^ 0.9^ X^5 ~^ __^ _

.loll') 8~" ("\Qvf\11-VoV /'-. V.I 1- __ _

15. A roll of paper towels contained 250 sheets.

2 decimal places

x 0.

8 .. (^1). X 1 3

11 .. 168 X 2.25 = ___

Each sheet was 8.75 inches long .. How long was the roll?

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

,

1

co if) Ii) ~ c· (^0) U) :a" ~ C ro E U) ~ 0 LL t:l g- .U (f) @

. I il

II i

Ii

I

. iI

;I

·1! ·Name

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.

Use the graphs to answer each question.

1 a How fllany archers scored 4 buli's eyes?

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

Number of Houses Sold

ffi ::. ~-:::--[·~I.:··;r=I=·:I~~l~:::f:]

i ~: ,:~:l!=~:;:~:I~::~F~jbi Jan Feb Mar Apr May Jun Jul Aug. Month

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

6a The school's goal was to raise $1 ,500.

About how much did they raise in all?

500r..·· ................·....·^ lengths....·..······....·..·.._..^ ·........of·^ ..the··.. ·· .. ^ ..Great ··.................^ - lakes............................................ , ~ 4001-·....·..·..·..·..·......···· ..·:······..····.. ·· ....··.. ·.. ·..··........................................................................... ,

g 300

.c

g> Q) 200

..J 100

o

Superior Michigan Erie Huron Ontario Lake

Archery Results x xx x x x xx x x x x x^ x^ x x ( I (^) .1 I I I» 0 1 ·2 3 4 5 6 Number of Bull's-eyes Scored

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?

500.·....·..^ School··.. ··_·--·..^ ·Book.... ....· ........Fund _ ..·....^ ··Drive..···.... ·........ , 400 r--..·...... __ ·..···.. - .. · .. · {Ii -- ~ 300 ~ '0 200 o 100

o

1 st 2nd 3rd' 4th 5th Grade

CD ~ ~c .£2^ o ' ~ ~ E (/)

. ~ 0 . u.t::' .0^ o C/) @

r'

w .5^ d c:o 1ao. :J ~ Co

, Name ----------------------~----------------------------------

Geometric Ideas

• A line is a straight path of points that goes on forever in~~ two directions. Examples: AS"GK.
• A ray is a part of a line with one endpoint, extending forever in only one direction.~~ Examples: FD, FB.
• 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.

A

B

• 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 1& [ row is PT met 1 "yas!^ no Use the diagram. at the right. Name t.he following~

1. three line segments
2. two parallel lines

~

3. two lines that intersect DT

4. two congruent line segments·

.~ ~

~ 5. two lines perpendicular to BR

@

-.:-., ' ..

6. two midpoints of line segments

I

:'".': II . I '

j'^ I

JII

Name __~______________________________ __

Review

10 Adding and SubtractingF:ra.ctions

F' d 2 In 3 + 1 6'

al@ 9 12 15 Multiples of 3

I(a) 12 18 24 30 Multiples of 6

The least common denominator is 6.

F· In^ d 14" - s'^1

. 4. 8,1216@ Multiples of 4 5.10' 15@ 25 Multiples of 5

The least common denominator is 20.

Write equivalent fractions. (^) ~ = ~ Write equivalent fractions.

4" = 20

Add.

• '6 = '6 Subtract. 5 6

Find each sum or difference. 1 ')

11 k

2. 12 - ~ = ---

I: II II

I II I I

1 20

5. 12 - 12 = -- 6. :2 + 3' = --

9. '5 + 10' = -- 10. :2 + '5 = --

12. Meg practiced the- piano' .f.or 1~ hr. She did ho~ework

for' ~ hr. How much longer dId she do 'homework than

she practiced the piano?

E^0 C 0 :g () -0^ ::J W C 0 ~ <1l a..^ Q) ©

To add mixed numbers, you can add the fractional parts to the whole number parts, and then simplify.

F In d 24" 2 + 3 1

The fractions have a common denominator. Add the fractions. Then add the whole numbers.

+3~

Find 3% + 4t· Write equivalent fractions with the LCD.

3

+4 1 -^4 1

Add the Iwhole numbers. Add the fractions. Simplify if possible.

+ "79^111

7 L

Find each sum. Simplify your answer.

c. ..,;I. (^) a.1V 4 -LI -11118- 3 -

Find 4 + 3~.

Add the whole numbers; then add the fraction.

+3~

2. 4i + 1 i =
3. 8~ + 1 152 =.-----'------
4. 7 + Si =

7. In 2001, the men's indoor pole vault record was 20i ft..

The women's record for the indoor pole vault was 15 1b 2 ft. What is the combined height of the two records?

8. Writing^ in^ Math^ How high^ is^ a stack of library books if one^ book

is .it in. high, the second book is 1 ~ in. high, and the third is 2 ~ in. high? Explain how you soived this problem.

. 3 2 Fmd (^) Lf x J"

OneWay Draw a picture. Simplify if possible.

'-----y--" 3 4 6 of the 28 squares have overlapping shading. 3 2 6 So, "4x7"=28'

Simplify 2

6 8 to 1~'

Another Way Multiply the numerators and denominators. Simplify if possible. ~x.£ 4 7 3 x 2 6 4 x 7 28 -~ - 14

Write an equation for each picture ..

. 1'.

Find each product. Simplify if possible.

3. '§'x1.- 8 3-

Simplify Find the GCF of any numerator and any denominator.

The GCF of 2 and 4 is 2. Divide 2 and 4 by the GCF. 1 3 Z· 3 .% x 7" = 14 2

6. ~ x ~ =

7. Number Sense Can you simplify before multiplying 14 x ~~? Explain.

.! ;

,!

I

. (^) "'.! ,.

.

Name

--------~---------------------------------------------------

Multiplying Mixed Numbers

How to find the product of two mixed numbers:

Find 3~ x 4~.

Step 1 Estimate by rounding.

3~ x 4.

3 2 1 1

4 x 5 = 20

Then write each mixed number as an improper fraction.

3~ x 4.

3 2 1 1

11 x ~

3 2

Step 2 Look for common factors and simplify.

Find each product. Simplify if possible.

2. 2t x 2i =
3. 6 x 3t = (^) 4. 1 i x 3t =
4. 4t x 16 = (^) 6. 1 t x 2~ =

Step 3 Multiply. Write the product as a mixed number.

1 16"2 is close to 20, so the answer.is reasonable.

7 = Number Sense Is 2 x 17% greater than or less than 36? Explain.

'/

I )

:.

! !. I I; H Ii i!ii )! i'; it

l![f

t~if Ii: II [)

jI

I'

II

t ,

r

'II,

!t

l

I

! I

:f [ 1

f'

Name

---

Customary Measurement

R 10 .. 1

Units of length Units^ of^ Capacity

foot (ft) 1 ft = 12 in. cup^ (c)^ 1 c^ =^ 8 fluid^ ounces^ (oz)

yard (yd)

mile (mi)

1 yd = 3 ft

1 yd = 36 in.

1.mi = 5,280 ft

1 mi = 1,760 yd

pint (pt) 1 pt = 2 c

quart (qt) 1 qt = 2 pt

gallon (gal) 1 gal = 4 qt

How to change from one unit of measurement to another: To change from larger units to smaller units in the customary system, you have to multiply.

To change from smaller units to larger ones, you have to divide.

120 yd = ft

1 yd = 3 ft

120 X 3 ft = 360 ft

120 yd = 360 ft

Complete.

1. 36.in. =

3. Sib =
4. 1.5 mi =

7. 2T^ =

9. 640z =

11. 4 gal =

.. I ",v. ,...0.0^ r^ ILID =

15. 4.5 qt =

2560z = c 1 c = 80z 256 -;- 8 = 32

ft 2.^4 qt=

oz 4. 39 ft =

ft 6. 3.5 gal^ =

Ib 8.^16 pt^ =

Ib 10.^ 3yd =

pt 12. 55yd^ =

OZ 14.^20 pt^ =

c 16. 205 yd =

17. Reasoning A vendor at a festival sells soup for $1.25 per cup or $3.75 per quart. Which is the better buy?

c

yd

qt

qt

in.

ft

gal

ft

< .s^0 c 0 ~ 0 "0^ :::J W C (^0) ~ «J Ql a.. @

(.

· i

Changing one metric unit another:

To change from a larger unit to a smaller unit, multiply by a power of ten.

To change from a smaller unit to a larger unit, divide by a power of ten. 3.B L = mL

A liter is a larger unit than a milliliter. To

change from liters to milliliters, multiply. 1 L = 1,000 mL

3.B x 1,000 = 3,BOO

3.B L = 3,800 mL

100 m = km

The meter is a smaller unit than the kilometer. To change from meters to kilometers, divide.

1,000 m = 1 km

100 m.= 0.1 km

Name the most appropriate metric unit for each measurement.

1 D mass of a cow 2. length of a carrot 3. capacity of a thimble

Complete.

4~ 45 g = mg 5. 3450 mL =

60 4.5m = mm 7. 1.68 L =

Be 28cm = mm 9.^ 7,658 9 =

10. 600 cm = m 11. 5,000 mg =
11. 5.1 km = m 13. 1.7BO L =
12. 0.780 L = mL 15. 4,300 m =
13. 9,000 cm = m 17.^ B,OOO^ mg =

18. Reasoning It is recommended that people have 1 9 of

calcium each day. How many milligrams of calcium is that?

L-

mL

kg

mL

km

~ .E^ c.:i .0^ C ~ U U^ :J ill c o ~ m 0..(J) @

I

You can use formulas to find the area of a square or rectangle. Find the area of a square that is 7.2 m on Find the area of -a rectangle with a length

each side. (~ of 4 em and a width (w) of 12 em.

Use the formula A = 8 2. Use the formula A = I X w.

A = (7.2)

A=S1.

The area is 51.84 m^2.

Find the area of each figure.

1BO

.. B.3cm

4.2km

6.3 km

A = 4 X 12

A = 48

The area is 48 cm^2.

10.4 ft

u

3.1 ft

8.8 ft

5. Reasoning What is the iength of a rectangle that has an area of 120 ft2 and a width of 8 ft?
6. Number Sense What is the area of a square that is 12.4 em on each side?

I-

Name ____________________________________ __

Review

Ratio and Proportion

You can use ratios to compare two quantities.

2 balloons to' 3 'sticks You can write ratios as;

words 2 to 3 with a colon 2: 2 as a fraction 3

18

A statement that two ratios are equal is called a proportion.

1 balloon 2 balloons 2 sticks = 4 sticks

1 1 x 2 2 :2=2x2=

21 = 2. 4 IS^ a propo,rt' Ion.

Write each ratio. Use words, a colon, or a fraction.

1. Write the fatio of squares to circles.

DODD 000

2. The Computer Club has 20 girls and 15 boys. Write the ratio of girls to boys in the club.

Tell if the ratios form a proportion. Write yes or no.

3. 4" 12 -;.---

4. 39 --

5'"6 10 ---

6."6 18 --

Complete ea~h table so that all ratios are equal. '

8. I ; I I I I

17 121 1421631

9./ 4 1 120 I I

I 5 1 1 0 I 150 I

10. The ratio of ~he width to the length of a painting is 3 to 7. If the painting is 42 in. long, how wide is it?

,11.. The ratio of the number o~ moons the planet Neptune has tq

the number that Saturn has is 4 to 9. Saturn has 18 moons.

, How many moons does Neptune have?