7th Grade - Summer Math Packet - gbtps

1 7th Grade - Summer math Packet 1 Unit: KNOWLEDGE of ALGEBRA, PATTERNS, and FUNCTIONS 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 5 and some number is written as: 5 + n because the operation that is associated with the word sum is addition.

2 The difference of a number and three tenths is written as: n - .3 because the operation that is associated with the word difference is subtraction. 1.) a number plus 21 2.) a number minus .7 3.) the difference of twenty-one hundredths and a number 4.) the sum of a number and forty-six 7th Grade - Summer math Packet 2 Unit: KNOWLEDGE of ALGEBRA, PATTERNS, and FUNCTIONS Objective: Evaluate an algebraic expression.

3 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 4n or 4 x 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. Examples: Evaluate 44 + n if n= 9 44 + n original expression 44 + 9 replace the variable with it s value 53 solution 1.

4 Evaluate 150 + n if n = 15 2.) Evaluate 12n if n = 9 3.) Evaluate 15n + 19 if n = 31 4.) Evaluate 30n if n = 5.) Evaluate 24n k if n = 6 and k = 8 6.) Evaluate nk 2b + 8 if b = , k = 8, and n = 7 7th Grade - Summer math Packet 3 Unit: KNOWLEDGE of ALGEBRA, PATTERNS, and FUNCTIONS Objective: Evaluate numeric expressions using order of operations. A numerical expression is a combination of numbers and operations.

5 The Order of Operations tells you which operation to perform first so that everyone gets the same final answer. The Order of Operations is: Parentheses, Exponents, Multiplication or Division (left to right), and Addition or Subtraction (left to right.) Examples: 48 (3 + 3) 22 original expression 48 6 - 22 simplify the expression inside the parentheses 48 6 4 calculate 22 8 4 divide 48 by 6 4 subtract 4 from 8 1.

6 (8 + 1) x 12 13 2.) 13 x 4 72 8 3.) 88 16 x 5 + 2 3 4.) 100 52 x 43 5.) 45 9 3 + 2 x 3 6.) (52 + 33) x (81 + 9) 10 7th Grade - Summer math Packet 4 Unit: KNOWLEDGE of ALGEBRA, PATTERNS, and FUNCTIONS Objective: Determine the unknown in a linear equation (addition & subtraction). Addition equations: Subtract the same number from each side of the equation so that the two sides remain equal.

7 Subtraction equations: Add the same number to each side of the equation so that the two sides remain equal. Examples: b + 3 = 6 original equation b 8 = 4 original equation - 3 - 3 subtract 3 from each side +8 +8 add 4 to each side b + 0 = 3 solution b + 0 = 12 solution b = 3 simplify b = 12 simplify 1.

8 G + 5 = 12 2.) s 12 = 29 3.) m + = 4.) k = 5.) w + = 22 6.) g = 7th Grade - Summer math Packet 5 Unit: KNOWLEDGE of ALGEBRA, PATTERNS, and FUNCTIONS Objective: Determine the unknown in a linear equation (multiplication & division). In a multiplication equation, the number by which a variable is multiplied is called the coefficient. In the multiplication equation 2x = 8, the coefficient is 2.

9 Multiplication equations: Divide both sides by the coefficient so that the two sides remain equal. In a division equation, the number by which the variable is divided is called the divisor. In the division equation 4x, 4 is the divisor. Division equations: Multiply both sides of the equation by the divisor so that the two sides remain equal. Examples: 4b = 16 original equation 6m = 11 original equation 4 4 divide both sides by 4 6 x 6m = 11 x 6 multiply each side by 6 1b = 4 solution 1m = 66 solution b = 4 simplify m = 66

10 Simplify 1.) 7x = 63 2.) 9k = 8 3.) 5b = 4.) 7n = 5.) 12m = 6.) 13p = 7th Grade - Summer math Packet 6 Unit: KNOWLEDGE of GEOMETRY Objective: Identify and describe diagonal line segments. A line segment connecting two vertices of a polygon is either a side or a diagonal. Examples: AE is a side of polygon ABCDE AD is a diagonal of polygon ABCDE 1.