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SUBJECT Algebra I UNIT TITLE Number Properties and Operations BIG IDEA What symbols and terminology are used in Algebra? How are the four basic operations and properties of numbers used to simplify expressions? Topic: 1-1 Variables Objective: To simplify numerical expressions and evaluate algebraic expressions Core Content for Assessment: MA-11-1.3.1 Students will solve realistic problems to specified accuracy levels by simplifying expressions involving addition, subtraction, multiplication, and division. Essential Question: What is a variable and how are they used? Materials/Resources Textbook, pre-test, variable expression cards Procedures: 1. Warm up (10 question pretest) 2. Discuss having a job and rate of pay for the job. Complete the following chart assuming hourly rate is $6.00/hour: Hours Worked Total Pay Earned 1 2 3 4 3. What is the relationship between hours worked and total pay earned? Relate this to the equation Total Pay = $6.00 x Hours Worked or Total Pay = 6 x h where h can stand for the hours in the table or other values not in the table. h is a variable. 4. Go over vocabulary: Variable – symbol used to represent one or more numbers Values of the variable – numbers that can replace the variable Variable expression – expression that contains a variable Numerical expression (or numeral) – an expression that names a specific number 5. Have a table as follows on the front board: Variable Variable Expression Numerical Expression/Numeral Give each student a card and ask them to place it on the board in the appropriate column. Discuss why each card was placed in the column chosen. 6. Multiplication: discuss different ways to write multiplication and which one is preferred. 19 x n is the same as 19n or 19n Write each in a different way: 4xd mxn ½xx 7. Discuss: = is used to show two expressions are equal to each other (4 + 2 = 6) and ≠ is used to show when they are not (4 + 5 ≠ 8) 8. Substitution Principle- an expression can be replaced by another expression of the same value. Use to simplify the following expressions: a. 12 + (4 2) b. 12 (4 + 2) c. (3 + 2) (6 – 1) d. 12 x (12 – 2) Evaluate each expression when m = 1 and n = 2. e. 3(n + 4) f. (mn) + 4 g. m + 14n h. m 14 n 14 5 4 Evaluate the expression for the given values of the variable: i. bh when b = 22 and h = 6 j. 2l + 2w when l = 3 and w = 8 9. Class work: p.3 Oral Exercises 10. Homework: p.3-4 Problems as appropriate for level Lesson Assessments: Unit Pre-test Class work X 4t Y 3y b 12b d 6x + 2 m ½d–3 n 4(x – 2) t bh k (t - f) + 3 6 2+4 17 5 – 23 86 1/234 3.9 0.2 17 1/3 5 - .5 4 -6 2–½ 2½ 0+3 0 3+6-2 Topic: 1-2 Grouping Symbols Objective: To simplify expressions with and without grouping symbols Core Content for Assessment: MA-11-5.2.1 Students will apply order of operations to simplify algebraic expressions. Essential Question: What order should be followed when simplifying expressions? Materials/Resources Textbook, homework, warmup, krypto cards/flash app/graphing calc Procedures: 1. Warmup 2. Check homework 3. Grouping Symbol - device used to enclose an expression that should be simplified first. Parentheses 6(5 – 2) Bracket 3[9 + 2] 12 3 12 3 Fraction Bar means 45 4 5 (Make sure students know that multiplication symbols are left out of expressions using grouping symbols) 4. Order of Operations: discuss the order in which an expression is simplified. a. Start with innermost grouping symbol and work your way out. b. Do all multiplication and division from left to right. c. Do all addition and subtraction from left to right. P E M D A S Please Excuse My Dear Aunt Sally Parentheses Exponents Multiplication Division Addition Subtraction 5. Board Examples: Find the value of each expression. a. 5(8 + 3) b. 5(8) + 3 10 6 c. 10 2 d. 10 – [10 (8 – 3)] e. 3 + 8 2 4 f. Find the value of the expression when a = 4, b = 7, and c = 10 4a 2b ca 6. Play Krypto with cards/flash app/using random number feature of TI-84+. (Instructions to follow) 7. Homework: p.8 Written Exercises as appropriate Lesson Assessments: Homework check 1-2 Warm up Use only four 4’s to write a numerical expression that equals each of the following numbers. Remember to use parentheses when needed. Example for the number 1: 1. 2 = 4 4 4 4 2. 3 = 4 4 4 4 3. 5 = 4 4 4 4 4. 10 = 4 4 4 4 Warmup sample answers 1. 2. 3. 4. 2 = (4 4) + (4 4) 3 = (4 + 4 + 4) 4 5 = (4 4 + 4) 4 10 = (44 – 4) 4 (4 + 4) (4 + 4) = 1 Using the TI-84+ Random Number Feature to play Krypto Object of Krypto: Use the first five numbers and any of + - x () to write an expression equal to a sixth number. To use the calculator to play Krypto: 1. Generate the first five numbers by pressing m < 5 1, 26, 5)e . 2. Generate the sixth number by pressing m<1,26)e. 3. Use the first result to generate the second result.