6th grade algebra

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complete explanations for 6th grade algebra problems. …

complete explanations for 6th grade algebra problems.
Consistent with common core standards.

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  • 1. th 6 Grade Math - Algebra By Jessica Corriere and Robert Richards Check out www.greenazibo.com for more math help
  • 2. http://www.greenazibo.com/ Problem 1.What value of x makes the equation below true? 7 + x = 84 A. B. C. D. 12 77 83 91
  • 3. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. 7 + x = 84 Subtract 7 from both sides to isolate x 7 + x – 7 = 84 – 7 x = 77 The correct answer is B, 77
  • 4. http://www.greenazibo.com/ Solve simple proportions within context Problem 2. Guafi selects 15 pieces of fruit. If 3 out of 5 of these fruit are bananas, b, how many bananas does Guafi select? A. 3 B. 9 C. 13 D. 25
  • 5. http://www.greenazibo.com/ How To Solve Facts provided; There are 15 total pieces of fruit There are 3 bananas for every 5 pieces of fruit Write a formula that expresses those two statements; 15 pieces of fruit (3 out of every 5 pieces of fruit) is a banana. G-Zibo Tip – In a word problem, the word “is” means equals in the formula 15 (3/5) = b There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever you do to one side of the problem you must do to the other side of the problem. 15 (3/5) = b Simplify the left side Multiply 15 times 3/5 Then you have 9=b B is the correct answer
  • 6. http://www.greenazibo.com/ Translate two-step verbal sentences into algebraic equations Problem 3.What algebraic equation represents “three times the difference of a number, x, and nine equals fifteen”? A. B. C. D. 9x -3 = 15 3(9) – x = 15 9 – 3x = 15 3(x – 9) = 15
  • 7. http://www.greenazibo.com/ How To Solve The statement gives 3 times the difference of x and 9 3(x – 9) equals 15 The word equals determines where the equal sign goes, 15 on one side, Everything else on the other 3(x -9) = 15 Choice D is the correct answer
  • 8. http://www.greenazibo.com/ Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc. Problem 4. A circle has a radius of 18 inches. What is the circumference of the circle in terms of π? G-Zibo Tip- C = 2πr C = circumference r = radius π = pi = 3.14 A. B. C. D. 36π 20π 18π 9π
  • 9. http://www.greenazibo.com/ How To Solve The problem states “in terms of π”, that means that π must be part of the answer. Substitute 18 for the radius (r) in the formula provided in the tip C = 2 x π x 18 C (circumference) = 36π The correct answer is A
  • 10. http://www.greenazibo.com/ Translate two-step verbal sentences into algebraic equations Problem 5.The number of solar panels, s, installed along Oak Street is 3 less than 4 times the number of solar panels, installed along Poplar Street. Which expression can be used to determine the number of solar panels on Oak Street? A. B. C. D. = 7s = 12s = 3-4s = 4s-3
  • 11. http://www.greenazibo.com/ How To Solve Analyzing the statement it shows Oak Street is (equals) 3 less (negative) than 4 times (multiply) Poplar street solar panels, s, In this case, 3 is a negative number because of the statement, "3 less than". 4 is a positive number and then it is multiplied by the variable s because of the statement, "4 times Poplar street solar panels, s". = -3 + 4s Now rearrange the formula to look like one of the answers above; Choice D is the correct answer. G-Zibo Tip: Many times word problems such as these can be very frustrating and confusing. It is important that if you are feeling frustrated by this type of problem try again after when you are feeling refreshed and have a clear mind. As the concept sinks in by repeating the problem (practice, practice, practice) try substituting the solar panels for another object and the street names for another location. Make up your own word problem and solve (practice, practice, practice).
  • 12. http://www.greenazibo.com/ Solve and explain simple one step equations using inverse operations involving whole numbers Problem 6.What is the value of n in the equation below? 66 + n = 226 Show your work Answer_________________
  • 13. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever you do to one side of the problem you must do to the other side of the problem. 66 + n = 226 Subtract 66 from each side 66 + n - 66 = 226 – 66 n = 160
  • 14. http://www.greenazibo.com/ Solve and explain simple one step equations using inverse operations involving whole numbers Problem 7. At a recycling center there are 16 pallets of used car batteries to recycle. The manager places 8 batteries per pallet for shipping to the factory. He uses the equation below to calculate the total number of batteries, b, to recycle. b/8 = 16 What is the total number of batteries to ship to the factory? Show your work Answer_________________
  • 15. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. b/8 = 16 Multiply both sides by 8 to cancel out the 8 in b/8 b/8 x 8 = 16 x 8 b = 128
  • 16. http://www.greenazibo.com/ Solve and explain simple one-step equations using inverse operations involving whole numbers Problem 8. The tide on the island of Tonga changes from 4.7 feet at high tide to 1.3 feet at low tide. Write an equation that shows the change in tide when x represents the number of feet the tide increased. Equation_________________ How many feet did the tide increase? Show your work Answer_________________
  • 17. http://www.greenazibo.com/ How To Solve Set up a formula that will look for the difference between the high tide and low tide. High tide equaled 4.7 feet Low tide equaled 1.3 feet The equation would be 4.7 feet – 1.3 feet = x 3.4 feet = x The tide increased by 3.4 feet
  • 18. http://www.greenazibo.com/ Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.) Problem 9. Rio measures one side of a solar panel. The length is 8 feet and the width is one half of the length. What is the area, in square feet, of the solar panel? G-Zibo Tip, A = lw A = Area l = length w = width A. B. C. D. 4 16 32 108
  • 19. http://www.greenazibo.com/ How To Solve The length is 8 feet The width is given as ½ the length (8 feet) = 1/2 x8=4 A = lw Substitute the numbers for length and width; A = 8 x ½(8) A=8x4 A = 32 C is correct
  • 20. http://www.greenazibo.com/ Translate simple verbal expressions into algebraic expressions Problem 10. Demi brought 8 bottles of water to a picnic. Of those bottles of water, she and her friends opened a certain number of bottles, b. What expression can be used to determine the number of unopened bottles at the picnic? A. B. C. D. 8+b b+8 8–b b-8
  • 21. http://www.greenazibo.com/ How To Solve Demi started with 8 bottles and she and her friends drank some of the water. The number of bottles that were drunk is then subtracted from the total. Original total = 8 bottles Bottles she and her friends opened = b The number of bottles they drank is then subtracted from the original number. Choice C states that 8 – b is the answer, that is the correct choice.
  • 22. http://www.greenazibo.com/ Solve simple one-step equations using basic wholenumber facts Problem 11. Kennet brought 6 bags of cans to the recycling center. He received a total of $12. He used the equation below to determine the price per bag, b, which he received. 6b = $12.00 How much money did Kennet receive for each bag? A. $72.00 B. $18.00 C. $6.00 D. $2.00
  • 23. http://www.greenazibo.com/ How To Solve Isolate the unknown on one side of the equal sign. Then whatever action you perform must be performed on both sides of the equal sign. 6b = $12.00 Divide both sides by 6 6b ÷ 6 = $12.00 ÷ 6 b = $2.00 Answer D is the correct choice.
  • 24. http://www.greenazibo.com/ Substitute assigned values into variable expressions and evaluate using order of operations Problem 12. What is the value of the expression below when r = 2? 9 -3r = A. B. C. D. 0 3 6 12
  • 25. http://www.greenazibo.com/ How To Solve The formula provided is 9 – 3r = r was given a value of 2 r=2 Substitute 2 for r in the formula 9 – 3(2) = Multiply the -3 times 2, which will equal -6 The problem now becomes 9–6=3 Choice B is the answer.
  • 26. http://www.greenazibo.com/ Translate simple verbal expressions into algebraic expressions Problem 12. An aquarium has 30 kinds of salt-water fish. If f represents the number of tropical saltwater fish, which expression can be used to determine the total number of fish that are not tropical salt-water fish? A. 30f B. 30/f B. 30 – f D. 30 + f
  • 27. http://www.greenazibo.com/ How To Solve The aquarium has 30 kinds of fish f is the unknown number of tropical salt-water fish Whatever is not f would have to be the remaining kinds of fish 30 – f = Choice C has the correct formula.
  • 28. http://www.greenazibo.com/ Use substitution to evaluate algebraic expressions (may include exponents of one, two and three) Problem 13. What is the value of the expression 6m + 33 when m equals 7? Show your work
  • 29. http://www.greenazibo.com/ How To Solve The formula given 6m + 33 The value of m is 7. Substitute 7 for m in the formula 6(7) + 33 Solve the exponent first. 33 = 3 x 3 x 3 = 27 6(7) + 27 Solve the multiplication of 6 times 7 42 + 27 Add the result 69 is the answer
  • 30. http://www.greenazibo.com/ Solve and explain simple one-step equations using inverse operations involving whole numbers Problem 14. Urie is planting a garden. He has a total of 320 seedlings to plant. He has planted 14 so far. The equation below can be used to determine the number of seedlings, s, Urie still needs to plant. 14 + s = 320 What is the number of seedlings that Urie still needs to plant? Show your work
  • 31. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. 14 + s = 320 Subtract 14 from both sides 14 + s - 14 = 320 – 14 s = 306 Urie has to plant 306 more seedlings
  • 32. http://www.greenazibo.com/ Solve simple one-step equations using basic whole-number facts Problem 15. If 8n = 96, what value of n makes the equation true? A. B. C. D. 12 88 104 768
  • 33. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. 8n = 96 Divide both sides by 8 to isolate the n 8n ÷ 8 = 96 ÷ 8 n = 12
  • 34. http://www.greenazibo.com/ Substitute assigned values into variable expressions and evaluate using order of operations Problem 16. Gabija has been growing 5 containers of avocado seeds in his windows at home. Once they started to sprout he added 3 more avocado seeds. The expression below shows the total number of avocado seeds in Gabija’s window when a represents the number of avocado seeds in each container. Let a represent the number of avocado seeds per container. 3 + (a x 5) If each container holds 8 seeds, how many total avocado seeds are in Gabijo’s windows A. 18 B. 28 C. 43 D. 55
  • 35. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. 3 + (a x 5) = The number of avocado seeds per container is 8, represented as a a=8 Substitute 8 for a in the formula 3 + (8 x 5) = Perform the multiplication first 8 x 5 = 40 Then the addition 3 + 40 = 43 The answer is C
  • 36. http://www.greenazibo.com/ Use substitution to evaluate algebraic expressions (may include exponents of one, two, and three) Problem 17. Arlen wrote the expression below for 3 of his classmates to calculate the age of his tortoise. n2 x 7 - 4 If n represents the number of classmates, what is the age of Arlen’s tortoise? A. B. C. D. 12 18 36 59
  • 37. http://www.greenazibo.com/ How To Solve The formula given n2 x 7 – 4 The number of classmates, n, is given as 3 Substitute the number 3 for the n in the formula That gives 32 x 7 – 4 32 is the same as 3 x 3, which equals 9 The formula now reads as 9x7–4 Perform the multiplication operation first 63 – 4 Then the subtraction 63 – 4 = 59 Choice D is correct; the tortoise is 59 years old
  • 38. http://www.greenazibo.com/ Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.. Problem 18. Geena walks at a rate, r, of 4 miles per hour. What is the distance, d that she walks in the time, t, of 3 hours? G-Zibo Tip, d = rt d = distance r = rate of speed t = time A. B. C. D. 1 mile 7 miles 12 miles 43 miles
  • 39. http://www.greenazibo.com/ How To Solve The formula for calculating distance is provided d = rt The rate of speed, r, was provided, 4 miles per hour The time, t, was provided, 3 hours Substitute the provided numbers for the letter symbols Multiply the numbers; the “hours” cancel each other leaving just the unit of miles d = 12 miles Choice D is the correct answer
  • 40. http://www.greenazibo.com/ Solve simple one-step equations using basic whole-number facts Problem 19. A sixth grade class is wants to raise money to have an aquarium so they decide to have a bake sale. The students earn $6 for each cake they sell. To determine how many cakes they need to sell to reach their goal of $144, the class uses the equation below where c represents the unknown number of cakes the students need to sell. 6c = 144 Part A What is the value of c in the equation? Show your work Answer_________
  • 41. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. The formula provided 6c = 144 Divide both sides by 6 to isolate the c 6c ÷ 6 = 144 ÷ 6 On the left side 6 divided by 6 equals 1 leaving C alone on that side And on the right side there is, 144 ÷ 6 = 24 c = 24 24 cakes must be sold to earn $144 Part B The teacher wrote the equation shown below for her students to solve to find the number of angel fish, a, they could buy to add to the fish tank in their classroom using the $144, if each angel fish costs $9 144/a = 9
  • 42. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. The formula provided 6c = 144 Divide both sides by 6 to isolate the c 6c ÷ 6 = 144 ÷ 6 On the left side 6 divided by 6 equals 1 leaving C alone on that side And on the right side there is, 144 ÷ 6 = 24 c = 24 24 cakes must be sold to earn $144
  • 43. http://www.greenazibo.com/ Part B The teacher wrote the equation shown below for her students to solve to find the number of angel fish, a, they could buy to add to the fish tank in their classroom using the $144, if each angel fish costs $9 144/a = 9
  • 44. http://www.greenazibo.com/ How To Solve There are 2 basic rules to a problem like this. Isolate the unknown on one side of the equal sign. Whatever action you perform must be performed on both sides of the equal sign. 144/a = 9 a is the denominator on the left side Multiply both sides by a to remove it from the denominator 144/a x a = 9a The a’s on the left cancel each other out 144 = 9a Divide both sides by 9 to isolate the a 144 ÷ 9 = 9a ÷ 9 The 9’s on the right of the equal sign cancel each other 16 = a The class can buy 16 angelfish with their $144
  • 45. http://www.greenazibo.com/ Use substitution to evaluate algebraic expressions (may include exponents of one, two, and three) Problem 20. Jorja’s teacher asked the students to evaluate the expression 43 + 2y, when y = 8. Three of the students wrote their answer on the board Which student evaluated the expression correctly? Show your work
  • 46. http://www.greenazibo.com/ How To Solve The formula provided is 43 + 2y The value of y is given as 8 Substitute the 8 for y in the formula 43 + 2(8) Perform the action required by the exponent first 43 + 2(8) = (4 x 4 x 4) + 2(8) = 64 + 2(8) = Now perform the multiplication of 2 x 8 64 + 2(8) = 64 + 16 = 80 Govad had the correct answer with 80
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