Incoming 6th Grade Information Page

We are so proud of you for taking time to work on math over

the summer! Here are some helpful hints for success:

• You have learned many different strategies – use the one that works best for you!

• If you get stuck – each page has an example to help you. • It’s okay to ask parents and adults for help!

• The packet should be returned by the second week of school.

• Keep practicing your multiplication facts.

NAME:___________________

THINGS YOU SHOULD KNOW:

Order of Operations:

P: Parentheses

E: Exponents

MD: Multiplication OR Division

(from left to right)

AS: Addition OR Subtraction

(from left to right)

FORMULAS

Area: squares and rectangles

𝐴 = 𝑙𝑥𝑤

Volume: rectangular prism

𝑉 = 𝑙𝑥𝑤𝑥ℎ

Fractions/Mixed Numbers:

Adding and Subtracting: must have common denominators

Ø Find the least common multiple of the denominators in the problem

Multiplying: must make any mixed numbers into improper fractions

Multiply the numerators, then

multiply the denominators

Ø Simplify the final product by dividing the numerator and denominator by the same number

Decimals:

Adding and Subtracting: line up the decimals and bring it down into the sum or difference

Multiplying: count the decimal places in the factors…the total number of decimal places in the factors needs to be the same as the total number of decimal places in the product

SIMPLIFYING EXPRESSIONS >>>>>> Simplify each expression using the Order of Operations. <<<<<<

60 – (2 x 4) – 9

60 – 8 - 9

52 – 9 43

10 + (6 ÷ 2) – 4 6 x (2 + 3) – 3 x (8 – 2)

2 + 14 x 2 ÷ 4

2 + 3 x 5 - 9 81 ÷ 9 x 2 + 3

WRITING EXPRESSIONS Write an expression to represent each real-world situation.

Think: How would you solve it? DO NOT SOLVE!

You pay $1.25 per pound of apples. How much does it cost to

buy 3 pounds?

Answer: 3 x $1.25

Emma weighs 38 pounds. How much

does Gavin weigh if he weighs 10 pounds

less?

Four friends split a $32 bill. How much does

each friend pay?

Bill used a $10 bill to pay for a $4.65 cup of

coffee. How much change did he receive?

Nina left a $12 tip on a $42.50 lunch bill. How much money did Nina

leave?

A soccer team raised $4,250 for charity last year. How much did they earn this year if

they raised $575 more?

DESCRIBING PATTERNS >>>>>> Describe the pattern in each table.<<<<<<

Pounds Total Cost ($)

0 0 1 3 2 6 3 9

Answer: Each pound

costs $3.

Day Tickets Sold

1 30 2 60 3 90 4 120

Day Cookies Made

0 0 3 30 6 60 9 90

Bags Total Cost ($)

1 5 2 10 3 15 4 20

Kids Total Spent ($)

10 20 20 40 30 60 40 80

Day Raffles Sold

0 0 5 40

10 80 15 120

PLACE VALUE AND ROUNDING >>>>>> Find the value of the underlined digit.<<<<<<

What is the value of the underlined

digit?

899.354

Answer: 𝟓𝟏𝟎𝟎

What is the value of the underlined

digit?

32,962.8

What is the value of the underlined

digit?

5.9248

What is the value of the underlined

digit?

3,486.5

>>>>>>Round the number to the indicated place value. <<<<<<

Round to the nearest ten.

874.32

Answer: 874.32

870

Round to the nearest whole

number.

4.623

Round to the nearest tenth.

71.693

Round to the nearest

hundredth.

15.435

ADDING AND SUBTRACTING DECIMALS >>> Find the sum or difference. Remember to line up the decimals. <<<

13.2 + 6.84

Answer:

1 3.20 + 6.84 20.04

19.12 + 0.45 9.326 + 1.42 15.5 + 3.04

15.2 – 6.25

Answer:

1 5 . 2 0 - 6 . 2 5 8 . 9 5

9.35 – 0.6 10.362 – 1.2 30.5 – 3.23

MULTIPLYING AND DIVIDING DECIMALS >> Find each product (count the decimal places) or quotient (bring the decimal point up). <<

3.21 x 4.6

Answer:

3.21 X 4.6 1926 + 12840 14.766

8.9 x 4.1 6.12 x 4.3 9.86 x 0.2

13.2 ÷ 6

Answer:

2.2 6 13.2 -12 12 -12 0 2.2

9.4 ÷ 2 30.4 ÷ 8 29.2 ÷ 4

ADDING AND SUBTRACTING FRACTIONS/MIXED NUMBERS >>>MUST HAVE A COMMON DENOMINATOR<<<

12+ 6

23

Answer:

𝟏𝟐 =

𝟑𝟔

+𝟔 𝟐𝟑= 𝟔 𝟒

𝟔

𝟔 𝟕

𝟔= 𝟔 + 𝟏 𝟏

𝟔

𝟕𝟏𝟔

12+25

216+ 3

46

34+ 5

34

423− 1

25

Answer:

𝟒𝟐𝟑= 𝟒

𝟏𝟎𝟏𝟓

−𝟏𝟐𝟓= 𝟏

𝟔𝟏𝟓

𝟑𝟒𝟏𝟓

634− 2

14

45−12

812− 2

13

MULTI-DIGIT MULTIPLICATION AND DIVISION >>> Find each product or quotient. <<<

452 x 82

Answer:

452 X 82 904

+ 36160 37,064 37,064

5215 x 40 182 x 63 415 x 12

540 ÷ 20

Answer: 27

20 540 -40 140 -140 0 27

896 ÷ 14

156 ÷ 12 720 ÷ 48

AREA AND VOLUME

>>> Find the area of each quadrilateral.

Find the volume of each rectangular prism. <<<

Find the area:

4 in. 9 in.

Find the area:

8 cm

8 cm

Find the area: 2.9 m

7 m

Find the Volume:

Find the Volume:

Find the Volume:

SUMMER PACKET REFLECTION Name: ____________

After completing your Summer Math Packet, please answer the following questions:

1) List the Math skills and concepts that you are most confident with. In other words, which problems were the easiest for you to solve? (example… order of operations) ___________________________________________________ ___________________________________________________ ___________________________________________________ 2) List the Math skills and concepts that you found to be the most difficult. In other words, which problems were the hardest for you to solve? (example… dividing decimals) ____________________________________________________ ____________________________________________________ ____________________________________________________ 3) What are your expectations for Math class this year? What do you expect to learn? What do you expect Math class to be like? 4) Write two personal Math goals to strive towards this school year. For example… This year in Math class, I hope to memorize my Math facts. I also want to get better at solving word problems.

1. ________________________________________________

2. ________________________________________________