7th Grade Math Unit 1 Algebraic Reasoning

Transcription

1 7th Grade Math Unit 1 Algebraic Reasoning Name: Period: Common Core State Standards CC.7.NS.1 - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. CC.7.EE.1 - Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with rational coefficients. CC.7.EE.2 - Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Scope and Sequence Day 1 Lesson 1-1 Day 5 Lesson 1-4 Day 2 Lesson 1-2 Day 6 Lesson 1-5 Day 3 Quiz Day 7 Review Day 4 Lesson 1-3 Day 8 Test

2 IXL Modules SMART Score of 80 is required Due the day of the exam Lesson 1 4.G.4 Simplify expressions using order of operations and parentheses Lesson 2 7.S.1 Properties of addition and multiplication Lesson 3 6.X.3 Evaluate variable expressions with whole numbers 6.X.4 Evaluate multi-variable expressions 6.X.5 Evaluate variable expressions with decimals, fractions and mixed numbers Lesson 4 6.X.1 Write variable expressions 6.X.2 Write variable expressions: word problems Lesson 5 6.X.12 Add and subtract like terms

3 Lesson 1-1 Order of Operations Warm-Up Vocabulary A numerical expression is made up of and. When simplifying a numerical expression, must be followed so that everyone gets the answer. That is why mathematicians have agreed upon the order of operations. Order of Operations (Use the acronym PEMDAS or Please Excuse My Dear Aunt Sally) P Parenthesis Perform operations within grouping symbols E Exponents Evaluate Powers M D Multiply & Divide Do this IN ORDER from left to right (even if division comes first) A Add & Subtract Do this IN ORDER from left to right. S (even if subtraction comes first) Examples: Using the Order of Operations

4 Simplify the following expressions. Use order of operations to justify your answer: Examples: Using the Order of Operations with Grouping Symbols

5 Simplify the following expressions. Use order of operations to justify your answer: Helpful Hint: When an expression has a set of grouping symbols within a second set of grouping symbols, begin with the innermost set. 42 (3 4) 6 [(26 4 5) + 6] 2 24 (4 5) 4 [(32 4 4) + 2] 2 Examples: Application

6 Sandy runs 4 miles per day. She ran 5 days during the first week of the month. She ran only 3 days each week for the next 3 weeks. Simplify the expression ( ) 4 to find how many miles she ran last month. Jill is learning vocabulary words for a test. From the list, she already knew 30 words. She is learning 4 new words a day for 3 days each week. Evaluate the expression to find out how many words will she know at the end of seven weeks. Lesson 1-2

7 Properties of Numbers Warm-Up Vocabulary Commutative Property Associative Property Identity Property Distributive Property You can numbers in any order and numbers in any order. When you add or multiply, you can the numbers together in any. The of 0 and any number is the number. The of 1 and any number is the number. A property in which is applied to addition or subtraction of two or more numbers in which each term inside a set of parentheses can be multiplied by a outside the parentheses. Examples: Identify Properties of Addition and Multiplication

8 Tell which property is represented. (2 6) 1 = 2 (6 1) = = = = (5 1) 2 = 5 (1 2) Examples: Using Properties to Simplify Expressions Simplify each expression. Justify each step Examples: Using the Distributive Property to Multiply Mentally

9 Use the distributive property to solve the following: 6(54) 4(27) 8(19) 9(14) Lesson 1-3

10 Variables and Algebraic Expressions Warm-Up Vocabulary Variable A letter that represents a number that can. Constant Algebraic Expression A value that change. An expression that consists of one or more variables. It will also often contain constants and. Evaluate a number for the variable in an algebraic expression. Examples: Evaluating Algebraic Expressions

11 Evaluate k + 9 for each value of k. k = 5 k = 2 Evaluate a + 6 for each value of a. a = 3 a = 5 Multiplication and division of variables can be written in several ways Examples: Evaluating Algebraic Expressions Involving Order of Operations

12 Evaluate each expression for the given value of the variable (do not forget to use the order of operations). 4x - 3, for x = 2 s 3 + s, for s = 15 5x 2 + 3x, for x = 2 3x - 2, for x = 3 r 3 + r, for r = 12 4y 2 + 2y, for y = 3 Examples: Evaluating Algebraic Expressions with Two Variables

13 6 Evaluate a + 4b, for a = 3 and b = 2. 8 Evaluate w + 2x, for w = 4 and x = 2. Lesson 1-4

14 Translate Words into Math Warm-Up

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16 Examples: Evaluating Algebraic Expressions with Two Variables Write each phrase as an algebraic expression. the quotient of a number and 4 w increased by 5 the difference of 3 times a number and 7 the quotient of 4 and a number, increased by 10 a number decreased by 10 r plus 20 the product of a number and 5 4 times the difference of y and 8 When solving real-world problems, you may need to determine the to know which operation to use.

17 Examples: Translating Real-World Problems into Algebraic Expressions Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how are he can drive in h hours. On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly. Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours. At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour.

18 Lesson 1-5 Simplifying Algebraic Equations Warm-Up Vocabulary Term A number, a variable, or a product of and separated by + and -. Coefficient A number that is by a variable in an algebraic expression. A variable by itself has a coefficient of 1. Like Terms Terms with the same variables raised to the same. The coefficients have to be the same.

19 Examples: Identifying Like Terms Identify like terms in the list. 3t 5w 2 7t 9v 4w 2 8v 2x 4y 3 8x 5z 5y 3 8z Combining Like Terms Combining like terms is like similar objects. 4x + 5x = 9x To combine like terms that have variables, or the coefficients.

20 Examples: Simplifying Algebraic Expressions Simplify 6t - 4t 45x - 37y a 2 + 5b + 11b 2-4b + 2a 2-6 5y + 3y 2(x 2-13x) + 6 4x 2 + 4y + 3x 2-4y + 2x 2 + 5

21 Examples: Geometry Application Write an expression for the perimeter of the triangles. Then simplify the expression.