MR. STURDIVANT'S CLASS



Name Date ______________8.NS.2Class Square RootsKey Takeaways:Standard:8.NS.2- Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.Finding the square of a number means multiplying a given number by itself. To find the square root of a given number, x, you must find a number, n, where n?n=x. To estimate the square root of a non-perfect square, you determine the two perfect squares that the non-perfect square is in between, and it will be in between those square roots.A perfect square is a number that is the square of an integer, that is, the product of an integer and itself.The square root of a perfect square, x, is an integer, n, such that n?n=xThe area of a square is A=s2Vocabulary:Square root, Inverse Operations, Square, Perfect Square, non-perfect square, Area, Whole numbers, Exponent, Equation________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 1: Activation of Prior KnowledgeSquare rootPlace the following numbers on the number line below:81, 11, 25, πWhich numbers were easy to place on the number line? Why?__________________________________________________________________________________________________________________________________________________________Which numbers were harder? Why? How did you end up placing them?_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________2. The area of a square football field is 78 square feet. Which of the following gives the best estimate for the side length of the football field?Between 7 and 7.5 feetBetween 7.51 feet and 8 feetBetween 8 and 8.5 feetBetween 8.51 feet and 9 feetHow did you determine the answer to this question?_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 2: Guided PracticeWhen finding the square root of a non-perfect square:Determine what two ___________________ squares it is _____________________.Determine the two ______________________ it is ______________________.Example 1:The area of a square is 54 square meters. Which of the following gives the best approximation of the side length of the square?It is 27 metersIt is between 6 and 7 metersIt is between 7 and 8 metersIt is between 8 and 9 metersExample 2: Which of the following is not equal to the expression below?64162641664164Example 3: Place the numbers on the number line below.22, 3324, 34Is 34 closer to 5 or to 6? How can you tell?________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 3: Independent Practice (MILD)1.The solution to the equation below is between which two whole numbers?x2=34Between 4 and 5Between 5 and 6Between 6 and 7Between 7 and 82. The area of a square is 87 square meters. Which of the following is the best estimate for the side length of that square?(1) between 7 and 8 meters(2) between 8 and 9 meters(3) between 9 and 10 meters(4) between 10 and 11 meters3. Which of the following is equivalent to the expression below? SELECT ALL THAT APPLY.8199381981993994. Which of the following statements is true?(1) 75>9(2) 10<3(3) 8 < 3(4) 10<915. The square root of a given number, x, is between 7 and 8. Which of the following could be that number?(1) 42(2) 48(3) 57(4) 646. Which of the numbers below could not go on the line seen in the inequality?5<________<76273548Part 4: Independent Practice (MEDIUM)7. Place the following numbers on the number line:32, 92 , 5223, 88. The area of a square is 97 square meters. Which two whole numbers is the length of the square in between? Which is it closer to and why? Explain your answer along with the rationale on the lines below:____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________9. The equation below has a solution that is between two whole numbers:x2=12What two whole numbers is the value of x in between? Explain your answer on the lines below:___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Part 5: Independent Practice (SPICY)11. Mandi has a collection of 64 seashells. She finds an average of 8 seashells every hour she spends looking for them.Part A: Suppose Mandi wants to have at least 100 seashells by the end of summer. Write an inequality she could solve to find x, the number of hours she will need to spend looking for seashells.Inequality:__________________________Part B: Solve the inequality you wrote in part A.Answer:_____________________________12. Solve the equation below for r7r+3-r+4=27Answer:__________________________13. At Costco the monthly fee for a membership is $75 and the sign-up fee is $100. Write an equation that could be used to calculate the total cost (y) of a membership over a certain number of months, (x).Part B: Another company uses the equation y=58x to represent the cost of their services. What does the 58 represent in the equation? Explain on the lines below.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________445516048895I’m a mathlete00I’m a mathlete4377690-194310“”00“”5776595-19748500MathletesName Date ______________8.NS.2Class Square RootsExit TicketDirections: Complete each problem by showing ALL work. Don’t forget to use MOLE! 1. In the equation below, the value of x is in between what two whole numbers?x2=927 and 88 and 99 and 1010 and 112. The area of a square is 43 square centimeters. Which of the following gives the best estimate of the side length of the square?(a) Between 6 and 7 centimeters(b) Between 7 and 8 centimeters(c) Between 8 and 9 centimeters(d) Between 9 and 10 centimeters3. Place and label the numbers below on the number line.4.6,26, 3.4, 233On the lines below, please explain how you determined where 26 should be placed______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Name Date ______________8.NS.2Class Square RootsHomeworkDirections: Solve each problem. Show all work using MOLE. 1. Which of the following is equal to 6? Circle all that apply(a) 14412(b) 1444(c)1444(d) 1444(e)222. Which of the following numbers has a value between 8 and 9?(1)58(2)64(3)68(4)893. Which of the following is a true statement?(1) 74=8(2)35<6(3)22>4(4) 9>3On the lines below, explain how you determined your answer to #3.________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Mixed Review4. Below is an equation:3x+7+9=12x+6If Malik subtracted 9 from both sides to start, which property could he use to justify this step?Associative property of multiplicationDistributive propertyMultiplicative property of equalityAdditive property of equality5. What is the value of x in the equation below?-2x+3x-1=5818-826. What is the value of x in the equation below?3x+54=8-9919-197. The perimeter of a rectangle is 70 meters. The length of the rectangle is five more than twice the width. Which of the following expressions could be used to calculate the perimeter if the width is w?2 2w-5+2w=7022w+5+2w=7022w+5+2w2w+5+2w8. Mr. Thomas went to the store and bought a certain number of pounds of chicken (c) and a certain number of pounds of beef (b). The equation below represents his total cost:4.50c+3.25b=yPart A: What does the 4.50 represent in this equation?Part B: If he buys 3 pounds of chicken and 5 pounds of beef, how much will it cost? ................
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