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Summer Math Packet for Incoming Fifth Grade Students 1.) Identify the quantitative relationship between the underlined digit in number A and the underlined digit in number B. (4.NBT.1) Example: Student Name ______________________________________ Incoming Grade 5 Summer Math Packet 1 Number A 95 ,678 907 Number B 5 32 4,7 12 Quantitative Relationship: the digit in Number A is 10 times the value of the digit in Number B 1/100 times the value of the digit in Number B Number A 13 ,694 45 31 9 6 7,843 234 ,597 87,09 4 4,638 Number B 63 5 5 ,231 87,1 96 6 2 508,24 1 239 3,8 10 Quantitative Relationship: the digit in Number A is ___________ times the value of the digit in Number B ___________ times the value of the digit in Number B ___________ times the value of the digit in Number B ___________ times the value of the digit in Number B ___________ times the value of the digit in Number B ___________ times the value of the digit in Number B ___________ times the value of the digit in Number B
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Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

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Page 1: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

Summer Math Packet for Incoming Fifth Grade Students

1.) Identify the quantitative relationship between the underlined digit in number A and the underlined digit in number B. (4.NBT.1)

Example:

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

1

Number A

95,678

907

Number B

532

4,712

Quantitative Relationship: the digit in Number A is

10 times the value of the digit in Number B

1/100 times the value of the digit in Number B

Number A

13,694

45

319

67,843

234,597

87,094

4,638

Number B

635

5,231

87,196

62

508,241

239

3,810

Quantitative Relationship: the digit in Number A is

___________ times the value of the digit in Number B

___________ times the value of the digit in Number B

___________ times the value of the digit in Number B

___________ times the value of the digit in Number B

___________ times the value of the digit in Number B

___________ times the value of the digit in Number B

___________ times the value of the digit in Number B

Page 2: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

2.) Use < (less than), > (greater than), or = (equal to) to express the relationship between the two given multi-digit numbers. Remember, math statements are read from left to right. (4.NBT.2)

Example:

a.

b.

c.

d.

3.) Round the following numbers to the place indicated in parentheses. (4.NBT.3)

a. 43,592 (hundreds) ____________________________

b. 314,972 (ten thousands) _____________________________

c. 8,203 (thousands) __________________________

d. 67,843 (tens) ______________________________

e. 403,501 (thousands) ________________________

f. 59,692 (ten thousands) ________________________

g. 824,571 (hundred thousands) ____________________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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1,504 1,045>

thirty thousand four hundred fifty six 34,650

783 (7 x 100) + (8 x 1)

40,000 + 2,000 + 500 + 20 + 4 four hundred eighty seven thousand

600,000 + 7,000 + 100 + 40 + 9 700,000 + 30,000 + 6,000 + 100 + 30 + 8

Page 3: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

4.) Write the multiplication equation described below. (4.OA.1)

Example: 24 is 6 times as much as 4; 24 = 6 x 4

a. Seventy-two is eight times as much as nine; ____________________

b. 5 times as much as 6 is 30; ________________

c. Six times as much as three is eighteen; ___________________

d. Eight times as much as six is forty-eight; ___________________

e. Twelve times as much as seven is eighty-four; ___________________

5.) Write the following multiplication equations in words. (4.OA.1)

Example: 3 x 4 = 12; three times as much as 4 is twelve

a. 8 x 7 = 56; _____________________________________________________

b. 9 x 6 = 54; ____________________________________________________

c. 60 = 12 x 5; ___________________________________________________

d. 32 = 4 x 8; ____________________________________________________

e. 9 x 4 = 36; ____________________________________________________

6.) Solve the following problems. Show all work and write your answer in a complete sentence. (4.OA.2)

a. The Florham Park Soccer Club sold 86 bracelets as a fund raiser. The East Hanover Soccer Club sold 5 times as many. How many bracelets did the East Hanover Soccer Club sell?

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 4: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

6.) Solve the following problems. Show all work and write your answer in a complete sentence. (4.OA.2)

b. A giant sequoia tree at 280 feet tall is 7 times the height of an oak tree. How tall is the oak tree?

c. John and Mike each like to run every day. By the end of this past week, John ran 3 times as far as Mike did. If John ran 63 miles, how far did Mike run?

d. Bob the farmer planted ¼ the amount of corn that Tom the farmer did. If Bob plants 52 acres of corn, how much corn did Tom the farmer plant?

e. At the end of the season, the first place basketball team scored 6 times what the last place team scored. If the first-place team scored a total of 504 points, how many points did the last place team score?

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 5: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

7.) Write an equation that includes a variable to identify the arithmetic operation written in a word problem (without solving). (4.OA.2)

Example: It has been observed that twice the number of people order pancakes than order French Toast at the diner. If 54 people order pancakes, then how many people would order French Toast?

Let f = the number of people who would order French Toast; 2 x f = 54

a. There are 3 times as many cats as dogs at the local animal shelter. If there are 18 dogs at the shelter, then how many cats are at the shelter?

Let c = the number of cats at the shelter; ______________________________

b. Girl Scout troop 312 sold 25 more boxes of cookies than Troop 56. If Troop 312 sold 480 boxes, how many boxes did Troop 56 sell?

Let b = the number of boxes that Troop 56 sold; ______________________________

c. An auditorium has a total of 396 chairs in 18 rows. How many chairs are in each row?

Let c = the number of chairs in each row. ______________________________

d. Mrs. Pompeii’s class read 17 fewer books this year than Mrs. Brunello’s class. If Mrs. Brunello’s class read 52 books, how many books did Mrs. Pompeii’s class read?

Let b= the number of books read by Mrs. Pompeii’s class. _________________________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 6: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

8.) Add or subtract using the standard algorithm. Show your work and circle your answer. (4.NBT.4)

a.) 56,078 - 23,412 = b.) 5,602 + 14,587 = c.) 409,032 - 30,065 =

d.) 34,508 + 2,305 = e.) 908,005 - 97,843 = f.) 1,207 - 945 =

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 7: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

9.) Use strategies to multiply multi-digit numbers and explain the answer using equations, rectangular arrays, and area models (up to 4-digits by 1-digit or 2-digits by 2-digits). (4.NBT.5)

a. Write and evaluate the expression represented by the following array: _____________________

b. Use the rectangle below to create an area model to find the value of 24 x 56. Show your work by

marking the rectangle and finding the value. 24 x 56 = ____________________________

c. How many soda cans are there in an array of 8 rows containing 14 cans in each row? Draw the array

in the space below to find your answer. Write your answer here: ______________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 8: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

10.) Find each product using the standard algorithm. (4.NBT.5)

a.) 234 x 8 = b.) 5,683 x 6 = c.) 47 x 23 =

d.) 89 x 21 = e.) 84 x 75 = f.) 32 x 63 =

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 9: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

11.) Use strategies to divide multi-digit dividends by one-digit divisors and explain the answer using equations, rectangular arrays, and area models. (4.NBT.6)

a. There are 123 shoe boxes arranged in an array having 3 rows.

• How many columns are in this array? _____________________

• Show your work.

b. Solve the following using the rectangle below to create an area model. Use multiplication to check your answer.

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

9

Molly has 210 arcade tickets to give to 5 of her friends. She wants to give each friend the same amount. How many tickets will Molly give each friend?

Each friend will get ___________ tickets.

Page 10: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

c. Find each quotient. Use multiplication to check your answer.

i.) 345 ÷ 5 = ii.) 4,332 ÷ 4 =

iii.) 6,282 ÷ 9 = iv.) 8,430 ÷ 3 =

v.) 7,944 ÷ 6 = vi.) 182 ÷ 7 =

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 11: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

12.) Recognize and generate equivalent fractions and explain why they are equivalent using visual fraction models. (4.NF.1)

a. Use the rectangles below to create a model showing that is equivalent to .

• Label each rectangle with the fraction it represents.

b. Replace the question mark with the correct number to create equivalent fractions.

i.)

ii.)

iii.)

iv.)

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

11

23

46

23

= 8?

? = _______________

?3

= 1218

? = _______________

525

= ?75

? = _______________

38

= 21?

? = _______________

Page 12: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

13.) Compose equations from information supplied in word problems (with all 4 operations) using letters to represent unknowns. Solve the problems (4.OA.3)

a. Forty-five baseballs are divided among 15 boxes. How many baseballs are in each box? Write an equation using the variable b for the unknown quantity. Then solve the problem. Write your answer in a complete sentence.

b. Maria is 4 inches taller than Joseph. If Maria is 56 inches tall, how tall is Joseph? Write an equation using the variable h for the unknown quantity. Then solve the problem. Write your answer in a complete sentence.

c. Twelve pounds of jelly beans are being poured into 5 jars. When all the jars are filled, there are 2 pounds of jelly beans left over. Write an equation using j as a variable to represent how many pounds of jelly beans are in each jar. Then solve the problem. Write your answer in a complete sentence.

14.) Determine if a number between 1 and 100 is a prime or composite number. (4.OA.4)

a. Write a “P” on the line if the number is a prime number, and “C” if the number is composite

23 _______ 45 _______ 100 _______ 63 _______

17 _______ 81 _______ 39 _______ 11 _______

51 _______ 43 _______ 59 _______ 33 _______

b. List all the factor pairs for each number below.

64 _________________________________________________

27 _________________________________________________

18 _________________________________________________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 13: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

15.) Compare fractions using <, >, and = (4.NF.2).

a.

b.

c.

d.

16.) Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction. (4.NF.3)

a.) 5 ¾ + 4 ¼ = b.) 6 ⅝ - 2 ⅜ =

c.) 12 ⅗ + 2 ⅘ = d.) 7 ⅔ - 4 ⅓ =

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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38

? 716

? = _______________

49

? 36

? = _______________

69

? 13

? = _______________

14

? 312

? = _______________

Page 14: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

17.) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. (4.NF.3)

a. Sarah walked her dog ⅞ of a mile on Monday, ⅝ of a mile on Tuesday, and ⅜ of a mile on

Wednesday. How far did she walk her dog all together? ______________________

b. A gardener is planning his garden. Four-fifths of the garden will be used for flowers. Of the portion

devoted to flowers, ⅖ will be used for roses, ⅕ for tulips, and the rest for daisies. How much of the

garden will be used for daisies? ________________________

c. Boy Scout Troop 24 is selling popcorn to raise money for a local animal shelter. Mark sold ⅜ of a

case of popcorn, Tim sold ⅝ of another case, and Danny sold ⅞ of a third case of popcorn. How

many cases of popcorn were sold by the three boys? ______________________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 15: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

18.) Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. (4.MD.1)

a. Complete the table of equivalent measurements.

Unit A Unit B

3 feet _____ inches

________ grams 2 kilograms (kg)

2 hours ________ minutes

3 meters ________ centimeters (cm)

________ounces (oz) 2 pounds (lbs)

________ seconds 4 minutes

5 kilometers (km) ________ meters

19.) Solve 1-step word problems involving multiplication of a fraction by a whole number. Show your work. (4.NF.4)

a. One-fourth of the 24 boys on the swim team do the backstroke. How many boys do the backstroke on the team? ________________________

b. Five children each eat ¾ of a pizza. How many pizzas were eaten in all? _________________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 16: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

c. Two-thirds of the students in the fourth grade play a musical instrument. If there are 75 students in the 4th grade, then how many students play an instrument? ____________________

d. Each day for a week (7 days in a week), you walk your dog for ⅔ of a mile. How many miles have you walked after a week? ____________________

e. Three-eighths of the 64 cars at the dealership are silver. How many cars are silver? __________

20.) Add two fractions with respective denominators of 10 and 100 by writing each fraction as a fraction with denominator 100. Show your work. (4.NF.5)

a.) b.) c.)

d.) e.) f.)

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

16

2

100+

9

10

7

10+

16

100

5

10+

35

100

25

100+

4

10

2

10+

67

100

3

10+

25

100=

=

==

==

Page 17: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

21.) Use decimal notation for fractions with denominators 10 or 100. (4.NF.6) Write each decimal as a fraction and write each fraction as a decimal.

0.45 =_____________ 0.56 =_____________ 0.4 =_____________

72/100 =_____________ 6/10 =_____________ 18/100 =__________

22.) Solving word problems. (4.MD.2, 4.MD.3)

a. You are buying carpeting for your bedroom. You need to calculate the area of your room. Your room has a length of 15 feet and a width of 12 feet. How many square feet of carpeting will you need? Show your work. _________________ square feet.

b. Your parents want to put a fence up around your backyard. The backyard is a rectangle with a length of 120 feet and a width of 52 feet. How many feet of fence will your parents need? Show your work. _____________________ feet of fence.

c. Your birthday party began at 1:15 in the afternoon and ended at 3:45 P.M. How long did your party last? Show your work. ___________hours and _________ minutes.

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 18: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

d. You need 4 feet of ribbon for a Halloween costume. You have 37½ inches of ribbon. Do you have

enough? _____________ If not, how much more ribbon do you need to buy? _______________

Show your work.

e. You have 52 ounces of clay to distribute among boxes that hold one pound of clay each. Each box must be filled with one pound of clay, there cannot be partially filled boxes.

• How many boxes do you need?_________ • Will you have any clay left over? __________ • How much? ___________

f. The route for the bicycle tour was in the shape of a triangle, one part of the tour was 3.2 miles, another was 4.6 miles and third was 5.1 miles. How many miles was the tour all together?

Show your work. ______________________ miles

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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Page 19: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

g. Four friends go to lunch. The total cost of lunch was $25.32. One friend pays $8.56; another pays $7.23; the third friend pays $6.75. How much does the fourth friend pay? ____________________ Show your work.

h. Barnes and Noble book store is having a sale. You buy 3 books for $5.99 each. How much did you spend on the books? _________________ Show your work.

22.) Comparing decimals. Use <, >, and = to compare decimal numbers. Remember that math statements are read from left to right. (4.NF.7)

a. 0.43 ______ 0.4 b. 0.70 ________ 0.07 c. 1.2 _______1.02

d. 0.05 ________ 0.50 e. 3.4 ________ 3.43 f. 0.98 ____ 0.89

23.) Geometry (4.G.1)

a. Name one pair of parallel lines ________________________, and one pair of perpendicular lines

__________________ in rectangle ABCD below.

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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A

CD

B

Page 20: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

b. In trapezoid LMNO below name one acute angle ________________ and one obtuse angle

____________________. Which pair of lines are parallel? ___________________. Name a pair of

lines that are intersecting. _________________________.

c. Identify the following triangles as acute, obtuse, or right.

_______________________ ______________________ _____________________

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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L

O N

M

Page 21: Summer Math Packet for Incoming Fifth Grade Students 5 Summer Math.pdfSummer Math Packet for Incoming Fifth Grade Students 1.) ... There are 3 times as many cats as dogs ... Two-thirds

24.) Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems using a symbol for an unknown angle measure. (4.MD.7)

The sum of the interior angles of a triangle equal 180º. Find the value of the missing angle.

a. b. c. right triangle

n = ______________ n = ______________ n = ______________

25.) Symmetry. Draw all lines of symmetry in the shapes below. (4.G.3)

a. b.

c. d. e.

Student Name ______________________________________ Incoming Grade 5 Summer Math Packet

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60º

n 60º

30º

120ºn

45º

n