Name:___________________________________________________________________Date:_____/_____/__________ 1. How many terms are in the following algebraic expression? _____ x – 8xyz + 6 + yz 2. Fill-in-the-chart: Algebraic Expression Coefficient(s) Variable(s) Constant(s) -3 + a – 9b 3. Evaluate when m = -8 and n = -5 : a) n² + (2n)² b) c) - 4² d) mn 11 – m 4. Matching (USE YOUR NOTES!): 5 A. 5 less than twice a number 2) _____ 2n – 5 B. 5 less the product of 2 and a number 3) _____ 5â2 + n C. the quotient of 5 and 2 times a number 4) _____ 5 – 2n D. 5 minus a number squared 5) _____ 5(2 + n) E. the product of 5 and 2, plus a number 6) _____ 5 - n² F. 5 times the sum of 2 and a number 1) _____ 2ð NAME:_______________________________________________________________________________ DATE: _____/_____/__________ Math-7 classwork PROPERTY PREVIEW Today We will: 1. Continue Properties Foldable 2. Practice the Following Properties: IDENTITY INVERSE COMMUTATIVE Associative REVIEW Identity Property: The answer STAYS the SAME! EXAMPLES Additive Identity 3+0=3 0+ 1 3 = 1 3 Multiplicative Identity 1 4 âŠ1= 1 4 1 ⊠-8 = -8 Just remember you can secure your identity if you: ZERO Add ______ OR Multiply by ONE _____ REVIEW Inverse Property: All about the OPPOSITE! EXAMPLES Additive Inverse 1 2 - + 1 2 =0 10 + (-10) = 0 This is like a zero pair! Multiplicative Inverse ðð ðð ðð ⊠ðð ð 3⊠ð = 500 500 3 3 =1 = =1 REVIEW Commutative Property: + = + EXAMPLES Commutative of Addition Commutative of Multiplication 2+9=9+2 2âŠ9 = 9âŠ2 (3âŠy)+7 = 7+(3âŠy) (3âŠy)+7 = (yâŠ3)+7 The order of the ADDITION changed The order of the MULTIPLICATION changed Associative Property: + + = + + EXAMPLES Associative of Addition Associative of Multiplication a+(b+c)=(a+b)+c a ⊠(b ⊠c) = (a ⊠b) ⊠c (3+4)+5=3+(4+5) (3 ⊠4) ⊠5 = 3 ⊠(4 ⊠5) Works for Addition and Multiplication Name:_________________________________________________________________Date:_____/_____/__________ FILL IN THE BLANK Identity Property âš The answer stays the ___________ same. Inverse Property âš All about the ___________________ opposite. Commutative Property âš _______________ changes ORDER Associative Property âš _______________ GROUPING changes You can use your foldable too! Identify the properties using the following answer bank: Associative of Addition; Associative of Multiplication Commutative of Addition; Commutative of Multiplication; Identity of Addition; Identity of Multiplication; Inverse of Addition; Inverse of Multiplication; 1. 31.7 + (-31.7) = 0 Inverse of A. ___________________________________ 5. (3+ 8)+ 2 = 3 + (8 + 2) ___________________________________ Associative of A. 2. abc = cba ___________________________________ Commutative of M. 6. 1 • -75 = -75 ___________________________________ Identity of M. 3. 0+¾=¾ ___________________________________ Identity of A. 7. 3/ 8 4. 5(4 • 6) = (5•4) •6 ___________________________________ Associative of M. 8. 7 + 5x = 5x + 7 ___________________________________ Commutative of A. • 8 3 =1 ___________________________________ Inverse of M. Today’s Lesson: What: sequences Why: To identify the common difference or ratio in a sequence and determine whether or not the sequence is arithmetic, geometric, or neither. vocabulary: • Arithmetic Sequence— goes from one term to the next term by always adding or _________________________ the same value. We subtracting difference call this the common __________________________. • Geometric Sequence— goes from one term to the next term by always multiplying or ______________________ by the same value. We dividing call this the common _________________. ratio Sequence Rule Common Difference OR Common Ratio 1) 2) 3) 27 -5, 3, 11, 19, ___ “plus eight” 80 5, 10, 20, 40, ___ “times two” -8 “minus 16, 10, 4, -2, ___ six” 4) 80, 20, 5, ð ð ___ Difference: 8 Arithmetic or Geometric ? Arithmetic Ratio: Geometric 2 16 1, 2, 4, 7, 11, ___ -6 “divide Ratio: ð by four” NA Expression n+8 2n Difference: Arithmetic n-6 Geometric ð ð Neither NA ð 5) Variable NA Sequence 6) ð ð , ð , ð 9 1, 3, ___ Rule Common Difference OR Ratio “times three” Arithmetic or Geometric ? Variable Expression Ratio: Geometric 3 3n 7) 4 1, 1, 2, 2, 3, 3, ___ NA NA Neither NA NA NA Neither NA 10) Bonus: 1,1, 2, 3, 5, 8, 13, 21 __ 1) A. 3, 9, 27 . . . Which of the following sequences is an arithmetic B. 1, 3, 6, 10, 15 . . . sequence? C. 52, 49, 46, 43 . . . 2) What would be the 5th term A. 125 of the following geometric B. 625 sequence? C. 30 1, 5, 25 . . . 3) Which of the following sequences is a geometric sequence? A. 27, CV 9, 3, 1 . . . B. 1, 2, 6, 24. . . C. 2, 4, 6, 8 . . . 4) What is the common difference in the following arithmetic sequence? 10, 6, 2, -2 . . . A. 4 B. -4 C. ¼ 5) What is the common ratio in the following geometric sequence? A. -2 B. 2 C. ½ 1, -2, 4, -8, 16 . . . 6) A. 4n Which variable expression describes the relationship B. -4n between any two consecutive C. ¼ n terms in the following sequence? -1, 4, -16, 64 . . . 7) Which variable expression describes the relationship between any two consecutive terms in the following sequence? A. n – 8 B. 8n C. n+8 -12, -4, 4, 12, 20 . . . 8) What is the common ratio in A. 2 the following geometric B. ½ sequence? 88, 44, 22, 11, 11/2 C. - ½ ... END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day. NAME: Math-7 NOTES DATE: ______/_______/_______ What: sequences Why: To identify the common difference or ratio in a sequence and determine whether or not the sequence is arithmetic, geometric, or neither. Arithmetic Sequence— goes from one term to the next term by always adding or _____________________ the same value. We call this the common __________________________. Geometric Sequence— goes from one term to the next term by always multiplying or __________________ by the same value. We call this the common _________________. Sequence (What comes next?) 1) -5, 3, 11, 19, ___ 2) 5, 10, 20, 40, ___ 3) 16, 10, 4, -2, ___ 4) 80, 20, 5, ___ 5) 1, 2, 4, 7, 11, ___ 6) 1 3 9 9 , , 1, 3, ___ 7) 1, 1, 2, 2, 3, 3, ___ BONUS: 1, 1, 2, 3, 5, 8, 13, ___ Rule Common + Difference OR x Ratio ÷ + Arithmetic or x Geometric ÷ Variable Expression Multiple Choice: 1) Which of the following sequences is an arithmetic sequence? A. B. C. 3, 9, 27 . . . 1, 3, 6, 10, 15 . . . 52, 49, 46, 43 . . . 2) What would be the 5th term of the following geometric sequence? 1, 5, 25 . . . A. B. C. 125 625 30 3) A. B. C. 27, 9, 3, 1 . . . 1, 2, 6, 24. . . 2, 4, 6, 8 . . . 4) What is the common difference in the following arithmetic sequence? 10, 6, 2, -2 . . . A. B. C. 4 -4 ¼ 5) What is the common ratio in the following geometric sequence? 1, -2, 4, -8, 16 . . . A. B. C. -2 2 ½ 6) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -1, 4, -16, 64 . . . A. B. C. 4n -4n ¼n 7) Which variable expression describes the relationship between any two consecutive terms in the following sequence? -12, -4, 4, 12, 20 . . . A. B. C. n–8 8n n+8 8) What is the common ratio in the following A. B. C. 2 ½ 22 Which of the following sequences is a geometric sequence? geometric sequence? 88, 44, 22, 11, 11/2 ... NAME:__________________________________________________________________________________DATE: _____/_____/__________ Math- 7 Homework For the following sequences, identify what comes next and write the variable expression: 1) 30 6, 12, 18, 24,… _____ Variable Expression: 4) n +6 62, 58, 54, 50…_____ 2) 1, 4, 16, 64, … _____ Variable Expression: ____________________ 5) 0.2, 0.4, 0.8, 1.6,…_____ Variable Expression: ____________________ Variable Expression: ____________________ 7) 0, 16, 32, 48, 64…._____ 8) 1.2, 2.3, 3.4, 4.5, ….____ Variable Expression: ____________________ Variable Expression: ____________________ 10) 128, 32, 8, 2, …._____ Variable Expression: ____________________ 11) 2 , -6, 18, -54,…_____ Variable Expression: ____________________ 3) 72, 36, 18, 9,…_____ Variable Expression: ____________________ 6) 1, 3, 9, 27,…_____ Variable Expression: ____________________ 9) 33, 37, 41, 45…._____ Variable Expression: ____________________ 12) 58, 50, 42, 34 …______ Variable Expression: ____________________ 13. What is the 8th term in the following sequence? 3, 9, 27, 81, 243, 729 . . . 14. What is the 6th term of the geometric sequence shown? 80, 40, 20 . . . 15. What is the common difference of the arithmetic sequence shown? -5, -1, 3, 7 . . . 16. What is the common ratio of the geometric sequence shown? 729, 243, 81, 27, 9 . . . 17. Write a variable expression that can be used represent the relationship between two consecutive terms of the following sequence: 8, 12, 16, 20 . . . 18. What is the missing tem in this sequence? 1, 5, 25, ____, 625, …. continued . . . Match each sequence with the variable expression that describes the relationship between the consecutive terms of the sequence. 1. ____ 2, 4, 6, 8, 10, … A. n + 10 2. ____ 1, 3, 9, 27, 71 B. 1/ 3. ____ 45, 41, 37, 32, 29, …. C. 0.2n 4. ____ 11, 21, 31, 41, 51, …. D. n + 5 5. ____ 10, 5, 2.5, 1.25, 0.625, …. E. n+2 6. ____ 11, 3, -5, -13, -21, …. F. 0.5n 7. ____ 100, 20, 4, 0.8, 0.16,….. G. n + (-2) 8. ____ 7, 10.5, 15.75, 23.625, 35.4375, ….. H . n + (-4) 9. ____ 36, 12, 4, 1.333, …. I. 1.5n 10. ____ -3, -6, -12, -24, -48, J. 3n 11. ____ -80, -75, -70, -65, -60, …. K. n + (-8) 12. ____ 1, -1, -3, -5, …. L. 2n 3 n 13. Which of the above problems are arithmetic sequences? _________________________ 14. Which of the above problems are geometric sequences? _________________________