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Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year in 5 th grade. The packet is due Thursday, September 6, 2018. The first Thursday of school. If you lose your packet, you can download a new copy from your school’s website If you are stuck on a problem try the list of websites as a resource. You can also use your Everyday math online resources that you used throughout the year. www.glencoe.com www.mathisfun.com www.coolmath.com www.aplusmath.com www.aaamath.com www.sheppardsoftware.com www.mathgoodies.com www.IXL.com This will be used as a review for your first quiz grade. Have a great Name: ________________________________________ School: ________________________________________

Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

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Page 1: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Summer Math Packet

Bridgewater/Raynham Regional School District

Grade 5 into 6

This packet is designed to help you retain the information you learned this year in 5th

grade.

The packet is due Thursday, September 6, 2018. The first Thursday of school.

If you lose your packet, you can download a new copy from your school’s website

If you are stuck on a problem try the list of websites as a resource. You can also use your

Everyday math online resources that you used throughout the year.

www.glencoe.com www.mathisfun.com

www.coolmath.com www.aplusmath.com

www.aaamath.com www.sheppardsoftware.com

www.mathgoodies.com www.IXL.com

This will be used as a review for your first quiz grade.

Have a great

Name: ________________________________________

School: ________________________________________

Page 2: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Dear Parents/ Guardians, As a sixth grade team, we would like to express to you the importance of avoiding

the “summer slide” and encouraging your child to review math concepts this

summer. Along with this review, we would ask that your child practice their

multiplication tables up to the 12s.

On the reverse side of this page, you will find a 100 question fact quiz. Any

problems that your child is unable to complete within 5 minutes are not

considered rote and should be studied & practiced. Below are some suggestions

of how your child may do this. Please check off what your child was able to use and

sign before your child returns to school in September.

Thank you for your support. We look forward to meeting you in the fall.

Sincerely,

The Sixth Grade Math teachers

-------------------------------------------------------------------------------------------------

Multiplication fact flash cards

Multiplication fact websites

o www.everydaymathonline.com (Fact Dash)

User name-

Password-

o www.xtramath.org

o www.aaamath.com

o www.multiplication.com

o www.funbrain.com (Math Baseball)

o www.sheppardsoftware.com

o another website:

Multiplication songs (Examples can be found on Itunes, Youtube, etc)

Other strategy (Please describe):

Page 3: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

1

Page 4: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Divide Multi-Digit Numbers 2

When one number is divided by another, the result is called a quotient. The dividend is the number that is divided and the divisor

is the number used to divide another number.

Find each quotient.

1. 595 ÷ 25 2. 874

38

3. 3,570 ÷ 85 4. 370

35

Example:

Find 592 ÷ 30.

19 R22 30) 592 Divide each place-value

–30 position from left to right.

292

–270

22 Since 292 – 270 = 22 and

22 < 30, 22 is the remainder.

The quotient is 19 R22.

Page 5: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Multiplying by Powers of 10 3 Find each product. Use mental math.

1. 10 x 0.06 = 100 x 0.06 = 1,000 x 0.06 = 10 x 0.6 =

2. 0.653 x 1,000 = 1.09 x 10 = 21.3 x 10 = 10 x 0.007 =

3. 1,000 x 0.046 = 0.46 x 1,000 = 0.46 x 100 = 0.46 x 10 =

4. 1.234 x 100 = 0.11 x 1,000 = 0.11 x 10,000 = 0.11 x 100,000 =

Page 6: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Visual Model Base 10 block model for 1.30

One Tenths

Place Value of Decimals 4

Write the decimal given by the model.

10. 11

Skill Examples

1. 156 = "One hundred fifty-six''

2. 1409 = 0ne thousand four hundred nine"

3. 14.009 = Fourteen and nine thousandths"

4. 2.07 = Two and seven hundredths"

Write the number in words.

6. 27.35 = ____________________

7. 1560 = ____________________

Write the decimal number for the words.

8. F i v e thousand seven hundred forty-nine and thirteen hundredths" = _______

9. N i n e hundred eighteen and fifty-seven thousandths" = _______

Page 7: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Comparing Decimals 5

Mark each decimal on the number line. Then write <, > or = to compare each value.

Write <, > or = to compare each set of decimals.

6 5.66 5.91

7. 1.36 1.9

8. 15.7 15.42

9. 0.8 0.49

1. 0.3 0.2

2. 1.7 1.8

3. 2.35 2.4

4. 3.7 3.55

Page 8: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Multiply Decimals by Decimals 6

When you multiply a decimal by a decimal, multiply the numbers as if you were multiplying all whole numbers. To decide where to place the decimal point, find the sum of the number of decimal places in each factor. The product has the same number of decimal places.

Multiply.

1. 7.2 × 2.1 2. 4.3 × 8.5

3. 2.64 × 1.4 4. 14.23 × 8.21

Example 1

Find 5.2 × 6.13.

5.2 one decimal place

× 6.13 two decimal places 156

52

+312

31.876 three decimal places The product is 31.876.

Example 2

Find 2.3 × 0.02.

2.3 one decimal place × 0.02 two decimal places 0.046 Add a zero to make three decimal

places.

The product is 0.046.

Page 9: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Place the decimal point.

Add a zero to continue dividing.

Divide Decimals by Whole Number 7

When you divide a decimal by a whole number place the decimal point in the quotient above the

decimal point in the dividend. Then divide as you do with whole numbers.

Example 1

Find 8.73 ÷ 9.

0.97 9) 8.73

–8 1

63

–63

0

8.73 ÷ 9 = 0.97 Compared with the estimate, the

quotient is reasonable.

Example 2

Find 8.58 ÷ 12.

0.715 12) 8.580

–84

18

–12

60

–60

0

8.58 ÷ 12 = 0.715 Compared with the estimate,

the quotient is reasonable.

Exercises

Divide.

1. 9.2 ÷ 4 2. 4.5 ÷ 5 3. 8.6 ÷ 2

4. 2.89 ÷ 4 5. 3.2 ÷ 4 6. 3.45 ÷ 15

Place the decimal point directly above the decimal point in the dividend.

Divide as with whole numbers.

Page 10: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Equivalent Fractions 8

Page 11: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Improper Fractions to Mixed Numbers 9

Page 12: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Simplifying Fractions 10

When a fraction i s in simplest form, 1 is the only common factor of its numerator and

Denominator.

Write in simplest form: _16

40

Step 1

Find the GCF of the numerator

and the denominator

Step 2

Divide the numerator and the

denominator by their GCF.

_16 = _16 ÷ 8

= _2

40 40 ÷ 8 5 Factors of 16: 1, 2, 4, 8, 16

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

GCF: 8

Check that _2

is in simplest form. 5

Factors of 2: 1, 2

Factors of 5: 1, 5

The only common factor of 2 and 5 is 1, so 2

5 is in simplest form.

Write each fraction in simplest form.

1. 6

10

Factors of 6: _______________________

Factors of 10:_______________________

Simplest form: _____________________

2. 12

30

Factors of 12: ______________________

Factors of 30:_______________________

Simplest form: _____________________

3. 9

36

Factors of 9: _______________________

Factors of 36:_______________________

Simplest form: _____________________

4. 20

25

Factors of 20: ______________________

Factors of 25:_______________________

Simplest form: _____________________

Write the following fractions in simplest form:

5. 6

18

6. 15

40

7. 8

30

8. 24

27

9. 20

24

10. 16

28

Page 13: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

Adding and Subtracting Fractions 11

Add or Subtract.

1. Find the lowest common

denominator (LCD)

2. Rewrite each fraction

using the LCD

3. Add or subtract

4.Simplify if possible.

Example 1

Example 2

Page 14: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

×4

×4

Comparing and Ordering Fractions 12

Example 1 Example 2

Compare each pair of fractions with <, >, or = .

1. 5

12

3

8 2.

6

8

3

4 3.

2

7

1

6

4. 4

5

8

11 5.

6

7

5

6 6.

4

9

9

20

To compare two fractions.

• Find the least common denominator (LCD) of the

fractions; that is, find the least common multiple of the

denominators.

• Write an equivalent fraction for each fraction using the

LCD.

• Compare the numerators.

Replace with <, >, or = to make 𝟏

𝟑

𝟓

𝟏𝟐 true.

The LCM of 3 and 12 is 12. So, the LCD is

12.

Rewrite each fraction with a denominator of 12.

1

3 =

12, so

1

3 =

4

12.

5

12 =

5

12

Now compare. Since 4 < 5,4

12 <

5

12 . So,

1

3 <

5

12 .

To compare two fractions.

• Cross multiply each fractions numerator and

denominator.

• Compare the product.

• The larger product shows the larger fraction.

Page 15: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

Multiply Fractions and Whole Numbers

You can multiply whole numbers and fractions by

writing the whole number as a fraction. Then multiply

the numerators and multiply the denominators.

Example 1

Find 𝟔 ×𝟑

𝟖.

6 ×3

8=

6

3

8 Write 6 as

6

1.

=6 ×3

1×8 Multiply.

=18

8=

9

4 or 2

1

4 Simplify.

13

Multiply Fractions and Fractions

Example 1

Find 𝟐

𝟓 ×

𝟑

𝟒.

2

5 ×

3

4 =

2 × 3

5 × 4 Multiply the numerators.

Multiply the denominators.

= 6

20 or

3

10 Simplify.

Multiply.

1. 1

2 ×

5

7 2.

3

4 ×

2

3 3.

5

6 × 8 4.

1

5 ×

1

2

5. 10 × 5

6 6.

3

7 ×

3

4 7.

1

5 × 4 8.

5

12 × 2

To multiply fractions, multiply the numerators and then

multiply the denominators.

2

3 ×

4

5 =

2 × 4

3 × 5 =

8

15

Page 16: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

14

Powers and Exponents

A product of like factors can be written using a base, the number used as a factor, and an exponent, which

tells how many times the base is used as a factor. Numbers expressed using exponents are called powers.

For example, 100 and 1,000 are powers of 10 because they can be written 102 as and 103.

Example 1

Write 4 × 4 × 4 × 4 × 4 using an exponent.

4 × 4 × 4 × 4 × 4 = 45 4 is used as a factor five times.

Example 2

Write 34 as a product of the same factor. Then find the value.

The base is 3. The exponent is 4. So, 3 is used as a factor four times.

34 = 3 × 3 × 3 × 3 Write 34 as a product.

= 81 Multiply.

Exercises

Write each product using an exponent.

1. 4 × 4 × 4 2. 7 × 7 × 7 × 7 × 7

3. 9 × 9 × 9 × 9 4. 8 × 8 × 8 × 8 × 8 × 8

Write each power as a product of the same factor. Then find the value.

5. 53 6. 62

7. 1.14 8. 0.73

Page 17: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

15 Numerical Expressions (Order of Operations)

Order of Operations

1. Simplify the expressions inside grouping symbols, like parentheses.

2. Find the value of all powers.

3. Multiply and divide in order from left to right.

4. Add and subtract in order from left to right.

Example 1 Find the value of 48 ÷ (3 + 3) – 2.

48 ÷ (3 + 3) – 22 = 48 6 – 2 Simplify the expression inside the parentheses.

= 486 – 2 Find 22.

= 8 – 2 Divide 48 by 6.

= 6 Subtract 4 from 8.

Find the value of each expression.

1. 7 + 2 × 3 2. 10 + 14 2 3. 16 – (4 + 5)

4. 8 × 8 4 5. 3 × 3 + 2 × 4 6. 25 5 + 6 × (12 – 4)

Page 18: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

16

Customary Units of Measure

Circle the greater length:

1. 10 in or 1 ft 2. 3 ft or 38 in 3. 1 ft. 7 in or 17 in

4. 4 ft 4 in or 56 in 5. 1 ft 9 in or 2 ft. 6. 7 ft or 2 yd

Write the equivalent measure:

7. 6 ft = _____________ in 8. 18 ft = _____________ yd 9. 1.5 ft = _____________ in

10. 4 yd = ___________ ft 11. 60 in = ___________ ft 12. 5,280 ft = ___________ mi

Page 19: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

17

Volume of Rectangular Prisms

Example

Find the volume of the rectangular prism.

Method 1 Use V = ℓwh.

V = ℓwh

V = 10 × 5 × 2

V = 100

The volume is 100 ft3.

Exercises

Find the volume of each prism.

1. 2.

3. 4.

The volume V of a rectangular prism is

the product of its length ℓ, width w, and

height h.

Symbols V = ℓwh

Model

The amount of space inside a three-dimensional

figure is the volume of the figure.

Volume is measured in cubic units. This tells

you the number of cubes of a given

size it will take to fill the prism.

Page 20: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

18

Identifying Polygons

Page 21: Summer Math Packet...Summer Math Packet Bridgewater/Raynham Regional School District Grade 5 into 6 This packet is designed to help you retain the information you learned this year

S K I L L

19

Graphing on the Coordinate Plane