Gulf Shores Middle School 7 th Grade Summer Math Packet Advanced Pre- - - AP Math Reetz

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1 Gulf Shores Middle School 7 th Grade Summer Math Packet Advanced Pre- - - AP Math Reetz Instructions: The students should complete all sections of the math summer packet by studying the provided notes, working the practice problems, and taking the performance assessment. Due Date/Submission: A hard copy of these packets must be turned into Mr. Reetz at the start of the school year no later than Thursday, August 20. Grading: The packet grade will be included as part of the student s first quarter grades. It is categorized as three Homework grades. Homework assignments are averaged as 20% of quarter grades. Holt McDougal Geometry

2 7 th $Grade$ $Summer$Math$Packet$ Domain: EXPRESSIONS & EQUATIONS CCRS Standards: 13 Write, read, and evaluate expressions in which letters stand for numbers. 13c Evaluate expressions at specific values of their variables. Objective: Evaluate an algebraic expression. A variable is a symbol, usually a letter, used to represent a number. Algebraic expressions are combinations of variables, numbers, and at least one operation. Multiplication in algebra can be shown as 8n or 8 n The variables in an algebraic expression can be replaced with any number. Once the variables have been replaced, you can evaluate, or find the value of, the algebraic expression. Example 1: Evaluate 25 + n if n = 7 Example 2: Evaluate 12x if x = n = Replace n with 7. 12x = 12(6) Replace x with 6. = 32 Add 25 and 7. = 72 Multiply 12 and 6. Example 3: Evaluate 5x 20 if x = 10 5x 20 = 5(10) 20 Replace x with 10. = Use order of operations. = 30 Subtract 20 from ) Evaluate n if n = 35 2.) Evaluate 16n if n = 3 3.) Evaluate 14n + 19 if n = 4.) Evaluate 30n if n = ) 6.)

3 7 th $Grade$ $Summer$Math$Packet$ Domain: EXPRESSIONS & EQUATIONS CCRS Standards: 13 Write, read, and evaluate expressions in which letters stand for numbers. 13a Write expressions that record operations with numbers and with letters standing for numbers. Objective: Write an algebraic expression to represent unknown quantities. A variable is a symbol, usually a letter, used to represent a number. Algebraic expressions are combinations of variables, numbers, and at least one operation. Examples: The sum of 3 and a number is written as 3 + n addition. because the operation that is associated with the word sum is The difference of a number and seven tenths is written as n 0.7 word difference is subtraction. because the operation that is associated with the 1.) 2.) a number plus 0.2 a number minus 3.) 4.) the sum of a number and 51 the difference of seventy-three hundredths and a number.

4 7 th $Grade$ $Summer$Math$Packet$ Domain: EXPRESSIONS & EQUATIONS CCRS Standards: 12 Write and evaluate numerical expressions involving whole-number exponents. Objective: Read, write, and represent whole numbers using exponential notation. Exponent Base 3 4 = = 81 Common Factors 1.) Write 10 4 as a product of the same factor. 2.) Write 2 6 as a product of the same factor. 3.) Evaluate ) Evaluate ) Write in exponential form. 6.) Write in exponential form.

5 7 th $Grade$ $Summer$Math$Packet$ Domain: EXPRESSIONS & EQUATIONS CCRS Standards: 12 Write and evaluate numerical expressions involving whole-number exponents. 13c Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Objective: Evaluate numeric expressions using order of operations. Examples: original expression calculate 4 2 and calculate 16 3, 3 8, and divide 18 by add 48 and subtract 3 from 72 1.) ) ) ) ) )

6 Integers and Rational Numbers SECTION A Family Letter: Integers Dear Family, The student will be learning about integers and how these numbers relate to the coordinate plane. The set of integers includes the set of whole numbers (0, 1, 2, 3,...) and their opposites ( 1, 2, 3,...). Number lines will be used to introduce the concept of opposite numbers. The opposite of a number is the same distance from 0 on a number line as the given number. In mathematics, this is called absolute value. Absolute value is designated by the symbol. Absolute value is always positive because it denotes distance from zero, and distance cannot be negative. 7 = 7 7 = 7 The student will learn how to add, subtract, multiply, and divide integers by following a few very important, yet simple, guidelines. Vocabulary These are the math words we are learning: absolute value the distance a number is from zero on a number line integers the set of whole numbers and their opposites opposites (additive inverse) numbers that are the same distance from zero on a number line Guidelines for Adding Integers If the signs are the same, find the sum of the absolute values of the integers and give that sum the same sign of the integers in the problem. Find the sum Think: Find the sum of 5 and 7. The signs are the same so give the sum the sign of the integers = 12 If the signs are different, find the difference of the absolute values. Use the sign of the integer with the greater absolute value. Find the sum Think: Find the difference between 1 and 8. Because 8 > 1, use the sign of = 7 To subtract integers, change the subtraction sign to an addition sign and then add the opposite of what is shown. Then use the guidelines for adding integers. Subtract. A ( 3) = 5 Add the opposite of 3. Since 8 > 3, use the sign of 8. B ( 4) = 9 Add the opposite of 4. The signs are the same, so use the sign of the integers.

7 Name Date Class Integers and Rational Numbers SECTION A At-Home Practice: Integers Graph each integer and its opposite on a number line Find each sum ( 14) ( 63) ( 47) Find each difference (13) 9. 8 ( 7) Find each product ( 3) Find each quotient ( 9) ( 6) Solve. Check your answer. 17. m + 8 = j = = c d = 24 6 Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry

8 Name Date Class Integers and Rational Numbers Performance Assessment Suppose you are in charge of setting up tables and ordering appetizers and cookies for an awards dinner. The principal expects 168 seventh-graders and 112 eighth-graders to attend the dinner. Each grade will have dinner in a separate room. 1. Decide how many tables and how many chairs per table you will need, based on the following criteria: No more than 15 tables in each room, and no more than 15 chairs per table. All tables in both rooms must have the same number of chairs. Only 280 chairs can be ordered. 2. Decide how many appetizers to order and how many each student will get, based on the following criteria: Each student in the seventh grade gets an equal number of appetizers. Each student in the eighth grade gets an equal number of appetizers. You cannot order more than 700 appetizers. You want to order as close to 700 appetizers as possible. 3. What fraction of students who are expected to attend are seventhgraders? Write the fraction in simplest form. 4. If only 155 seventh-graders and 95 eighth-graders attend the dinner, write an equation where x is the number of students who do not attend and solve for x. How many students do not attend? 5. Which fraction is greater: the fraction of students expected to attend that are seventh-graders or the fraction of students who did attend that are seventh-graders? Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry

9 Name Date Class Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry

Integers and Rational Numbers

Integers and Rational Numbers A A Family Letter: Integers Dear Family, The student will be learning about integers and how these numbers relate to the coordinate plane. The set of integers includes the set of whole numbers (0, 1,,,...)