DRSS Class of 2021

Summer Math Review Packet

Parents:

Our sixth graders had a busy year learning new math skills. Mastery of these skills is extremely important in

order to develop a solid math foundation. Each year builds upon the previous year’s skills in math. Any

content that was missed in sixth grade will affect math performance in seventh grade, and so on. Any time

spent learning or reinforcing these concepts will be very beneficial for your child.

Please complete 4-5 worksheets per week. Each page is used to practice a specific skill. After your child has

completed the math problems, if you feel your child is still struggling on a certain concept and needs further

practice, you can visit some of the web sites listed on this page. You can also visit

http://drss6thgrade.weebly.com/ and search under the math tab for helpful hints. If you are still confused,

please email Mrs. Shores with any questions or concerns.

Please have your child return this completed packet during the first week of school to Mrs. Shores. If you

misplace this packet, it will always be available at http://drss6thgrade.weebly.com/summer.html.

Also included is an answer key on different color paper for use in assisting your child.

Reminder - Practicing multiplication and division facts are VERY important!

Please do not let your child use a calculator!

Enjoy your summer!

Excellent websites for fun learning and reinforcement of math skills:

www.sumdog.com: all 6th graders will still have free accounts over the summer.

www.ixl.com: this site will limit the number of problems per day, or you can pay for full access.

www.catchupmath.com: if you use the code “goodmath15” it is only $10 for 3 month access.

www.aplusmath.com: this is a good website for quick fluency practice.

www.mathisfun.com: this is a good site for explanations and videos.

www.funbrain.com: lots of fun games to choose from.

www.coolmath-games.com: even more games.

www.youtube.com: if all else fails, search youtube for great instructional videos!

Grade 6 Content Overview

Ratios and Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.

The Number System

Apply and extend previous understandings of multiplication and division to add, subtract, multiply, and

divide fractions.

Multiply and divide multi-digit numbers and find common factors and multiples.

Apply and extend previous understandings of numbers to the system of rational numbers.

Expressions and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

Reason about and solve one-variable equations and inequalities.

Represent and analyze quantitative relationships between dependent and independent variables.

Geometry

Solve real-world and mathematical problems involving area, surface area, and volume.

Statistics and Probability

Develop understanding of statistical variability.

Summarize and describe distributions.

Mathematical Practices

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Important Vocabulary

even number A number that has 2 as a factor.

odd number A number that does not have 2 as a factor.

factor One of two or more whole numbers that are multiplied to get a product. For example, 13

and 4 are both factors of 52 because 13×4=52.

prime number A number with exactly two factors, 1 and the number itself.

Ex: 11, 17, 53, 101.

composite number

A whole number with factors other than itself and 1 (that is, a whole number that is not

prime).

Ex: 6, 15, 20, 1,001.

multiple The product of a given whole number and another whole number.

Ex: Some multiples of 3 are 3, 6, 9, and 12.

greatest common factor

(GCF)

The greatest factor that two or more numbers share.

Ex: 1, 2, 3, and 6 are common factors of 12 and 30,

but 6 is the greatest common factor.

least common multiple

(LCM)

The least multiple that two or more numbers share.

Ex: Common multiples of 6 and 8 include 24, 48, and 72,

but 24 is the least common multiple.

square number

A number that is a result of the product of another number multiplied by itself.

Ex: 9 is a square number because 3x3=9.

64 is a square numbers because 8x8=64.

A square number can also be represented by tiled arranged to form a square.

factorization

Two or more factors multiplied together in order to get a specific number. Another name

is “factor string.”

Ex: 2 x 50 = 2 x 2 x 25 = 4 x 5 x 5 = 100

prime factorization A factor string that includes only prime numbers.

Ex: 2 x 2 x 3 x 5 = 60

factor tree

A strategy used to find prime factorization.

Ex:

exponent

The small raised number that tells how many times a factor is used.

Ex: 53 means that 5 is multiplied by itself 3 times: 5×5×5.

74 means that 7 is multiplied by itself 4 times: 7x7x7x7.

expression A combination of numbers (and/or variables) and operations (addition/subtraction/etc.).

Ex: 3+7 2x5 (13-3)+0 x+3-6

equivalent expressions Expressions that represent the same quantity.

Ex: 3+7 = 2x5 = (13-3)+0 = x+3-6

distributive property

A property used to rewrite expressions that involve addition and multiplication. It states

that for any three numbers A, B, and C: A(B+C) = A(B) + A(C)

Ex: 5(8+2) = 5(8) + 5(2)

5(8+2) = 5(10) = 50

5(8) + 5(2) = 40 + 10 = 50

ratio

A comparison of two quantities. These are often expressed with a phrase such as “the

ratio of 3 to 5” which means “3 for every 5.” Such ratio comparisons are often written as

common fractions (3/5) or in the special notation “3 : 5.”

unit rate

A unit rate is a rate in which the second number (usually written as the denominator) is

1, or 1 of a quantity. For example, 1.9 children per family, 32 miles per gallon, and 3

flavors of ice cream1 banana split are unit rates. Unit rates are often found by scaling

other rates.

percent

“Per-cent” means “per-100” or “out of 100.” A percent is a special decimal or fraction in

which the denominator is 100.

Ex: When we write 68%, we mean 68 out of 100, 68/100, or 0.68.

improper fraction

A fraction in which the absolute value of the numerator is greater than the absolute

value of the denominator.

Ex: The fraction 5/2 is an improper fraction.

The fraction 5/2 means 5 halves and is equivalent to 2 1/2.

mixed number A number that is written with both a whole number and a fraction.

Ex: The number 2 ½ represents 2 wholes and a half of a whole.

rational number

A number that can be written as a fraction, where the denominator is not 0. This does

not mean that it always appears as a fraction.

Ex: 12, 899, 7/15, 0.2, and 0.33333...

reciprocal

A factor by which you multiply a given number so that their product is 1.

Ex: For example, 3/5 is the reciprocal of 5/3,

and 5/3 is the reciprocal of 3/5 because 3/5 × 5/3 = 1.

area

The measure of the amount of surface enclosed by the boundary of a figure. To find the

area of a figure, you can count how many unit squares it takes to cover the figure. You

can find the area of a rectangle by multiplying the length by the width. This is a shortcut

method for finding the number of unit squares it takes to cover the rectangle. If a figure

has curved or irregular sides, you can estimate the area. Cover the surface with a grid

and count whole grid squares and parts of grid squares. When you find the area of a

shape, write the units, such as square centimeters (cm2), to indicate the unit square that

was used to find the area.

perimeter

The measure of the distance around a two-dimensional figure. To find the perimeter of a

figure, you count the number of unit lengths it takes to surround the figure. When you

find the perimeter of a shape, write the units (such as centimeters, feet, or yards) to

indicate the unit that was used to find the perimeter. The perimeter of the square below

is 12 units, because 12 units of length surround the figure. The perimeter of the

rectangle is 18 units. Notice that the rectangle has a greater perimeter, but a lesser area,

than the square.

vertex

A corner of a polygon. For example, G, H, I, J, and K are all vertices in the pentagon

below. All angles have vertices: For example, in the hexagon below, angle AFE has a

vertex at F.

volume

The amount of space occupied by or the capacity of a three-dimensional shape. The

volume is the number of unit cubes that will fit into a three-dimensional shape. You can

find volume of a rectangular prism by following this equation: V = L x W x H

surface area The area required to cover a three-dimensional shape. The area of all the surfaces of a 3-

D shape combined.

net

A two-dimensional pattern that can be folded into a three-dimensional figure.

prism

A three-dimensional shape with a two bases (top and bottom) that are congruent

polygons and lateral faces that are parallelograms.

pyramid

A three-dimensional shape with one polygonal base, and lateral faces that are all

triangles that meet at a vertex opposite the base.

variable A quantity that can change. Letters are often used as symbols to represent variables in

rules or equations that describe patterns.

independent variable

One of the two variables in a relationship. Its value determines the value of the other

variable called the dependent variable.

Ex: If you organize a bike tour, the number of people who register to

go (independent variable) determines the cost for renting

bikes (dependent variable).

dependent variable

One of the two variables in a relationship. Its value depends upon or is determined by

the other variable called the independent variable.

Ex: The distance you travel on a car trip (dependent variable)

depends on how long you drive (independent variable).

Prime Factorization

Hint: Draw factor trees on separate paper if needed.