Week 9/12 – 9/16 Monday – Pretest Tuesday – Translate notes and practice

1. Week 9/12 – 9/16 Monday – Pretest Tuesday – Translate notes and practice Wed- Translate classwork, remediation Thurs – Distributive notes and practice Friday – Quiz Translate and distributive

2. Homework Wk of 9/12 – 9/16 Homework Wk of 9/12 – 9/16 Copy or Print out. Show all work. Fold paper in half, questions on left and answers on right. Write a math expression for each sentence. • Bacteria culture, b, doubled • Triple John’s age y • A number, n, plus 4 • Quantity, t, less 6 • 18 divided by a number, x • n feet lower than 10 • 3 more than p • The product of 4 and m • A number, y, decreased by 20 • 5 times as much as x Simplify using distributive property. 11. 6 (w + z) 12. A(8 + b) 13. 2(4 + 5) 14. 6 (x – 9) 15. y(6 – m) Review 16. What are the 5 parts of a box and whisker plot. Vocabulary – Define each word 17. Coordinate Graph 18.Coordinate Pair 19. Dependent Variable 20. Independent Variable

3. Monday Pretest

4. WednesdayWarm – Up: Copy and answer. • What is the sum of 6 and 8? • What is the difference between 8 and 6? • What is the product of 8 and 6? • What is the quotient of 8 and 4?

5. Examples Understanding Algebra Word Problems Words Indicating Addition • And • Increased • More • More than • Plus • Sum • Total • 6 and 8 • The original price of $15 increased by $5. • 3 coins and 8 more • Josh has 10 points. Will has 5 more than Josh. • 8 baseballs plus 4 baseballs • The sum of 3 and 5 • The total of 10, 14, and 15

6. Examples Understanding Algebra Word Problems Words Indicating Subtraction • Decreased • Difference • Less • Less than • Left • Lower than • Minus • $16 decreased by $5 • The difference between 18 and 6. • 14 days less 5 • Jose completed 2 laps less than Mike’s 9 • Ray sold 15 out of 35 tickets. How many did he have left? • This month’s rainfall is 2 inches lower than last month’s rainfall of 8 inches. • 15 minus 6

7. Examples Understanding Algebra Word Problems Words Indicating Multiplication • Double • Half • Product • Times • Triple • Twice • Her $1000 profit doubled in a month. • Half of the $600 collected went to charity. • The product of 4 and 8 • Li scored 3 times as many points as ted who only scored 4. • The bacteria tripled its original colony of 10,000 in just one day. • Ron has 6 CD’s. Tom has twice as many.

8. Examples Understanding Algebra Word Problems Words Indicating Division • Divide into, by, or among • quotient • The group of 70 divided into 10 teams • The quotient of 30 and 6

10. Class work: Copy Question and Practice writing parts of algebraic expressions from the following word problems 3 less than x y divided among 10 The sum of t and 5 n minus 14 5 times k The total of z and 12 Double the number b x increased by 1 The quotient t and 4 Half of a number y

11. Ticket out the door: (copy all)Match the phrase with the correct algebraic expression. y – 2 2y y + 2 y/2 2 - y 2 more than y 2 divided into y 2 less than y Twice y The quotient of y and 2 y increased by 2 2 less y The product of 2 and y y decreased by 2 y doubled 2 minus y The total of 2 and y

12. Wednesday Warm-Up 1. Write 3 sentences to represent this math expression: x + 5 2. Find the range of this set of data: 2, 4, 5, 2, 9

13. Translating Phrases into Math Expressions: Copy and Answer • 1. The sum of a number and ten. • 2. Eighteen more than a number. • 3. Five less than a number. • 4. The product of a number and three. • 5. The difference of a number and seven. • 6. The difference of seven and a number. • 7. Two more than a number. • 8. Sixteen less than twice a number. • 9. Five times the sum of a number and four. • 10. Three times the difference of a number and one. • 11. The quotient of a number and six. • 12. Two-thirds of a number. • 13. Eight more than a twice a number. • 14. The difference of a number and eight, divided by ten. • 15. Three more than the sum of a number and four. • 16. Double the difference of a number and seven. • 17. Nine less than the product of a number and two. • 18. The quotient of two and three more than a number. • 19. The product of triple a number and five. • 20. Sixteen less than the sum of three and a number.

14. Translating Phrases into Math Expressions • 1. The sum of a number and ten. X + 10 • 2. Eighteen more than a number. x + 18 • 3. Five less than a number. X - 5 • 4. The product of a number and three. 3x • 5. The difference of a number and seven. x - 7 • 6. The difference of seven and a number. 7 - x • 7. Two more than a number. x + 2 • 8. Sixteen less than twice a number. 2x - 16 • 9. Five times the sum of a number and four. 5 (x+4) • 10. Three times the difference of a number and one. 3(x-1) • 11. The quotient of a number and six. X / 6 • 12. Two-thirds of a number. 2/3 x • 13. Eight more than a twice a number. 2x + 8 • 14. The difference of a number and eight, divided by ten. (x -8)/10 • 15. Three more than the sum of a number and four. (x+4) + 3 • 16. Double the difference of a number and seven. 2(x – 7) • 17. Nine less than the product of a number and two. 2x - 9 • 18. The quotient of two and three more than a number. 2/(x +3) • 19. The product of triple a number and five. 3x (5) • 20. Sixteen less than the sum of three and a number. (3 +x) - 16

15. Thursday Warm-Up Translate into a math phrase The sum of triple a number and 5 A number divided by 6 is 5

16. Distributive Property examples • http://teachers.henrico.k12.va.us/math/ms/c20708/01NumberSense/1-5DistributiveProp.html

18. Write a math expression to match each statement. 1. The product of a number and 5 increased by 2 2. The quotient of 6 and a number Simplify using the distributive property 3. 5( apples + 2 bananas) 4. 4(5 + a) Friday Warm-Up

19. Quiz

20. 1.   add 43 to a number n2.   a number x divided into 253.   7 times a number e4.   take away a number c from 165.   difference of a number q and 246.   product of a number r and 417.   13 more than a number j8.   a number a less 499.   a number v decreased by 2810.   a number b multiplied by 4611.   30 minus a number h12.   a number u divided by 3613.   quotient of 23 and a number e14.   8 less than a number y15.   subtract a number m from 19 16.  sum of a number z and 3417. the product of 6 and a number j18.   3 increased by a number p19.   33 increased by a number u20.   add 6 to a number k21.   take away a number f from 20 22. The quotient of a number j and 623.   sum of a number b and 3524.   a number x times 4425.   a number w decreased by 1226.   a number j minus 1027.   32 less a number t28.   48 multiplied by a number q29.   4 divided by a number s30.   difference of a number c and 2 Writing EquationsCopy the question on the left , answer on the right.

21. This week Mon – Evaluate Tues – Simplify Wed – Review Thurs – Solving one step Fri - Quiz

22. HW this Wk 9/19 – 9/23 Homework Wk of 9/12 – 9/16 Copy or Print out. Show all work. Questions on left. Answers on Right. Evaluate each expression. • xy, for x = 3 and y = 5 • 24 – p * 5, for p=4 • 5a + b, for a = 6 and b = 3 • 6x, for x = 3 • 63 ÷ p, for p = 7 Simplify each expression. • 2m – 1y + 3y + 2m • 6 + 4y – 2 • 5t – t + 8k – 6k • 4ab +5 + 3ab + 20 • 3w + 5f – f + 7 • Use distributive to simplify 6( x + 4) • Write a math expression for the quotient of a number and 6 increased by 2 • Review - Find the lower quartile of 6, 5, 2, 5, 7, 8, 9. Define each vocabulary word. 14. Equation 15. Pattern 16. Relationship 17. Rule 18. Scale 19. Table 20. Variable

23. Monday Warm-Up Simplify using distributive property • 6(a + 5b) • 6x(y – 3) Write this math expression in 3 ways: (9 ÷ x) – 4 Find the mean of 5, 6, 2

24. Steps to Evaluate Expressions 1. Replace each letter in the expression with the assigned value. 2. Perform the operations in the expression using the correct order of operations. Example: 2x + 4 , when x = 3

25. Solve the following problems using the number given for the variable. Work out each problem on the left and answer column on the right. x= 2 w = 1, y = 3, z = 5 3x + 4 = (x + 8) ÷ 2 5x + 4 = 6x ÷ 4 12 – 3x = 9 – x = x– 5 2x + 2 5w – y = 3z + 5 ÷ w= 2y + 3 = wyz + 2 = z – 2w = 25 – 2y = 7y – 3z = 4yw – x=

26. Tuesday Warm-Up Evaluate each expression. • 18a – 9b, for a = 1 and b = 2 • m + n ÷ 6, for m = 12 and n = 18 • 3ab – c, for a = 4, b=2, and c = 5

27. SIMPLIFYING ALGEBRAIC EXPRESSIONS Combining Like Terms

28. In algebraic expressions, like terms are terms that contain the same variables, such as 2n and 5n. Variables are the letters that follow a coefficient, like x or y or even m or b. Think of it this way: 2n and 5n are like brother and sister – they have the same last name, n. Only the numerical coefficients are different.

29. Are these like terms? 5x and 5y No, they are not, because they contain different variables. What about these? 5x and 6x? Yes, because they contain the same variables.

30. Coefficients are the constants that come before a variable. In our example 2n and 5n, the coefficients are 2 and 5. Now that you know what these things mean, let’s try an example and combine like terms.

31. This expression has 2 terms. 2 and 5 are the coefficients, and the n’s are the variables. 2n + 5n means that you have 2 n’s and are adding 5 n’s to them. So isn’t 2n + 5n the same as saying nn + nnnnn? It is! How many n’s do you have? 2n + 5n = 7n

32. Let’s do some more. 7p + 3p = That means ppppppp + ppp How many do you have all together? You have 10 p’s, so 7p + 3p = 10p

33. You try some. 4x + 12x = 5b + 14b = 15c – 9c = 10f – 2f =

34. How did you do? 4x + 12x = 16x 5b + 14b = 19b 15c – 9c = 6c 10f – 2f = 8f Getting it? Great!

35. Now, what if you were asked to simplify an expression like this: 2a + 3a + 4a? Everyone here has the same last names, so you can just combine them. aa + aaa + aaaa = aaaaaaaaa So, 2a + 3a + 4a = 9a

36. You doing great, so let’s try some more. How in the world would you simplify an expression like this? 2a + 3a + 4d? What’s up with that different last name? It’s no big deal – watch. You can’t combine terms with different last names, so this is what you do.

37. 2a + 3a +4d just means you have 2 a’s plus 3a’s plus 4d’s. aa + aaa + dddd SO, Combine like terms and you will get 5a + 4d. That’s it!!!!! That’s how you simplify that!

38. This is fun. Let’s do some more. 3a + 4a + 5x = 5a + 2a + 7g = 6b + 2a + 2b = 10x + 3y + 4x = How did you do? Did you remember to just combine the like terms?

39. 3a + 4a + 5x = 7a + 5x 5a + 2a + 7g = 7a + 7g 6b + 2a + 2b = 8b + 2a 10x + 3y + 4x = 14x + 3y If you got them all, you’re sharp! Did you notice we mixed up the numbers? It doesn’t matter in what order they appear – just put the same last name together!

40. If you are having trouble with this, we’re going to take a moment to get you on track. If a’s are apples and p’s are peaches, and we tell you Jane brought in 3 apples, Mike brought in 3 peaches and Susan brought in 3 apples, what would you have? You’d have 3a + 3p + 3a, right?

41. If you combine your like terms, you would have 3 apples plus 3 peaches plus 3 apples. 3a + 3p + 3a which would equal aaa + ppp + aaa SO, aaa + ppp + aaa = 6a + 3p Isn’t that easy? Better than writing all those a’s and p’s!

42. Okay, you combining like terms masters, let’s really rock. Try these. They are longer and more involved, but you can do them. Just put the same last names together, but don’t try to combine different last names.. 3v + 6p + 4p + 2v 4b + 7b + 9r + 2b + 2r 12c – 4c + 3d + 4d

43. 3v + 6p + 4p + 2v = 5v + 8p 4b + 7b + 9r + 2b + 2r = 13b + 11r 12c – 4c + 3d + 4d = 8c + 7d That last one was a little tricky, wasn’t it? Just remember that the sign ( + or - ) right in front of a number belongs to that number. We want to show you something else.

44. What if we gave you this expression? 12c – 4c + 3d + 4d – 3d – 2c Wow. We can do this. Let’s start with the c’s. 12c – 4c – 2c leaves you with 6c. Now deal with the d’s. 3d + 4d – 3d leaves you with 4d. It’s not a negative 4, it’s positive, so it’s +4d. The solution is 6c + 4d. Remember that the sign in front of a number belongs to that number. We want to show you one more.

45. What do you make of this? 5w + w = ? That w all by itself is the same as 1w. We just don’t write the one, because in the mathematical world, it is understood that it is just one. Don’t make the mistake of forgetting to include all the terms. If you need to write the 1 in front of a variable to help you remember, go ahead. It’s okay with us. So 5w + w is the same as 5w + 1w which equals 6w.

46. COPY ALL

47. Copy, work out and Answer Practice problems Challenge problems 1.) 3 + 3(x+ 2) 2.) 1 − 5n − 7n 3.) 38 +7(7n+ 4) 4.) 4x + 5(3x+ 3) 5.) 5 +2(8x+ 4) • 2k + 10k • 3m + 9m – 6m • 2a + 3b + 4 • 5mj – 4mj + 6mj • 12x + 9a + 5 – 3x • 7t + k + 3t + 9k • 5ab + 7t – ab + 6t • 7y + 9h + 2 – 6h – y • 10q + 3q + 5z +8z – 9 • 25r + 67j +6 +10r

48. Wednesday Warm-Up • Simplify each expression. • 1.) 1 + 8x +5x • 2.) 7 + 6x+ 9x+ 9 • 3.) 3 + 8 x+ 2 • 4.) 5 + 8n+ 4n • 5.) 9 + 3x+ 1 +2x

49. Group assignment • You will be assigned a group. • You will be given a sheet of chart paper. • 3. In the center of your group will be a set of numbered problems. • 4. You will be given 10 minutes to work out each of the problems neatly in your section of the chart paper. • 5. No talking is allowed. Any groups caught talking or sharing answers will loose points • 6. Once you are finished working out all of the questions in your section, wait for further directions.

50. #1 The difference between a number tripled and six. #2 Evaluate 2xyz – 3abc – 4dog, if a = 2, b=3, c= 1, d=2, o=4, g=1,x=5, y= 6, z=2 #3. Simplify 2m + 3t – t + 7m - 8 #4. What is the interquartile range of 6, 2, 3, 4, 5, 7 #5. If Tim has the following grades 50, 90, 78 so far. If he needs to have an 70 average. What is the lowest grade he can get for his final grade?