Lesson 1C ~ The Four Operations

Transcription

1 Lesson C ~ The Four Operations Find the value of each expression. Show all work Mike hosted a fundraiser to benefit the Children s Hospital and the Cancer Societ. Twent people came and each paid $30 to enter the event. An additional $800 was raised before the event. a. Write a number expression to represent the total amount of mone raised. Find the value of our expression. b. Mike split the mone equall between the two organizations. How much did each organization receive? 6. Create an expression that equals each number in the table below. You can onl use the numbers,, 3, and. Use all five numbers in each expression. Each number cannot be used more than once in an expression. Use at least one operation (,, +, ) in each expression SM C Curriculum Oregon Focus on Introductor Algebra

2 Lesson C ~ Powers and Exponents The inverse (or opposite) of an exponent is a root. Roots undo the exponent. The smbol is called a square root. It undoes the operation of squaring a number. For example: 8 = 6 6 = 8 Find the square root of each number Fill in the values of each square root on the number line Some square root values are not whole numbers. Use the number line above to help determine the two numbers each square root falls between. 8. Between and 9. 9 Between and 0. 3 Between and. 6 Between and. a. What two integers is between? and b. Which integer is it closer to? c. Estimate the value of to the nearest tenth. 00 SM C Curriculum Oregon Focus on Introductor Algebra

3 Lesson 3C ~ Order of Operations with Powers Fill in the box with a number from to 0 that makes the equation true.. 3 = = = = = = 0 Use the numbers,, 3, and once in each expression to create an answer that meets each criteria. Each expression must use at least one exponent and at least two different tpes of operations. Uses each number Example: Has an answer that is even once and equals 8, which is even. 7. Has an answer that is odd. 8. Has an answer that is divisible b Has an answer larger than Has an answer that is a prime number.. Has an answer that is between 0 and 60.. Has an answer equal to. 00 SM C Curriculum Oregon Focus on Introductor Algebra

4 Lesson C ~ Order of Operations with Grouping Smbols Find the value of each expression. Show all work.. 7 (6 ) ( + 3) Kari had $. Her dad told her if she did all her chores for the entire ear, he would take her $ in exchange for the following i. Raise her mone to the power of. ii. Multipl the new value b 0. iii. Cut the new value in half. iv. Add $0 to the new value. a. How much mone would she end up with if she did all her chores? b. Her dad told her she could switch one of the steps with another step in the order above. Which steps should she switch? How much will she receive if he uses the new order? Insert operations (,, +, ) in each box in the numerical expressions to make it equal the stated amount. 6. (7 3) = = 6 8. (0 ) (3 ) = 7 00 SM C Curriculum Oregon Focus on Introductor Algebra

5 Lesson C ~ Number Properties Use the Commutative and/or Associative Properties to group numbers and solve the following problems. Explain our reasoning in words.. Burt purchased 3 comic books at one store. He purchased 79 comic books at another store. At the last store he stopped at, he bought 7 comic books. How man did he bu in all? Work and Answer: Reasoning for grouping/order of calculations:. Olivia gained.6 pounds in her first ear of life. In her second ear, she gained 0. pounds. From age to age 3, she gained 9.8 pounds. How much weight did she gain in her first three ears of life? Work and Answer: Reasoning for grouping/order of calculations: 3. Determine if each equation is true or false. If the equation is true, identif the propert shown. Equation True or False Propert 9 (7 3) = (9 7) 3 ( ) = ( ) = 9 + = + 9. Use the Commutative Propert to write three equivalent numerical expressions using the numbers, and 8.. Jack wants to find the perimeter of the rectangle at right. How should he use the Associative Propert to make his calculations easiest? 3 feet 3 8 feet 00 SM C Curriculum Oregon Focus on Introductor Algebra

6 Lesson 6C ~ Variables and Expressions Saul s Corner Market sells large cand bars for $ each. A bag of pretzels is $3. On Tuesda, the store sold twice as man cand bars as Monda but the same number of pretzels. On Wednesda, the store sold the same number of cand bars as Monda but onl half the amount of pretzels. On Thursda, the store sold three times as much as the sold on Tuesda. On Frida, the store sold fewer cand bars and more bags of pretzels compared to Wednesda. Let c represent the number of cand bars sold and p represent the number of pretzels sold on Monda. Write an expression for each da to show the amount of mone that the store brought in from cand bars and pretzels.. Monda. Tuesda 3. Wednesda. Thursda. Frida 6. Monda through Frida The store sold cand bars and 6 bags of pretzels on Monda. How much mone did the store bring in each da? 7. Monda 8. Tuesda 9. Wednesda 0. Thursda. Frida. Monda through Frida 00 SM C Curriculum Oregon Focus on Introductor Algebra

7 Lesson 7C ~ Evaluating Expressions Functions are used in most high school and college math courses. Function notation is a different wa to show what value ou are substituting into an expression. For example: f ( x) = x + is read f of x equals x + When a number is in the parentheses, this number is substituted for the variable it replaced. For example: f ( 9) =?? Substitute 9 in for x in the equation above. f ( 9) = 9 + = f ( 9) = Use the function f ( x) = x + 3. Find each of the following.. f (). f (7) 3. f (0). f ( ). f (.) 6. f (0) Use the function f ( x) = x + x. Find each of the following. 7. f () 8. f (7) 9. f () Sometimes, ou ma put a value through multiple functions. Alwas start with the function inside the parentheses and then use the new value in the second (outside) function. For example: Find g( f ()) when f ( x) = 3x and g ( x) = x + 7. First find f (). f ( ) = 3() = 6 Then plug 6 into g(x). g( 6) = = 3 Answer: g ( f ()) = 3 Use the function f ( x) = x 3 and g( x) = x +. Find each of the following. 0. g ( f ()). f (g(8)). g( f (0)) 00 SM C Curriculum Oregon Focus on Introductor Algebra

8 Lesson 8C ~ Evaluating Geometric Formulas h h w s h b b l b Triangle Parallelogram Rectangle Square Trapezoid Circle A = bh A = bh A = lw A = lw or s² A = h b + b ) A = πr² b ( r Calculate the area of each shaded region. Use 3. for π mm 6 mm 6 in 6 cm 6 cm cm in 3 cm.. 6 ft 3. m. m 6.9 m. m Use the formulas for the volume and surface area of a rectangular prism to answer the questions. h Volume = lwh Surface Area = ( lw + wh + hl) w l 6. A rectangular prism has a side length of. The width is twice the length. The height is two less than the width. What is the volume of the prism? 7. Find the surface area of the rectangular prism described in #6. 00 SM C Curriculum Oregon Focus on Introductor Algebra

9 Lesson 9C ~ Evaluating More Formulas Compound interest is mone that is paid on the starting amount as well as previous ears interest that has been added to the account. Use the annual compound interest formula, t N = p( + r), to determine the new value (N) in the account after t ears. Remember that p is the amount ou started with. Round our answer to the nearest cent.. Find the new value (N) in an account when p = $300, r = % and t = ears.. Find the new value (N) in an account when p = $00, r = 8% and t = 3 ears. 3. BreSha deposited $800 in an account that is compounded annuall at 3% interest. a. How much mone will she have after ears? b. How much total interest did she earn? c. If she had placed her mone in a simple interest account ( I = p r t ), how much interest would she have earned? d. How much more did she earn with compound interest? Man banks give compound interest each month. Use the monthl compound interest r t formula, N = p ( +, to find the new values in an account compounded monthl. ) Remember that t represents the number of ears.. Find the new value (N) in an account when p = $300, r = % and t = ears.. Find the new value (N) in an account when p = $00, r = 8% and t = 3 ears. 6. Compare the answers from # and # to the answers in # and #. Would ou prefer to have our mone compounded annuall or monthl? Wh? 00 SM C Curriculum Oregon Focus on Introductor Algebra

10 Lesson 0C ~ Simplifing Algebraic Expressions Match each expression on the left to its simplified expression on the right. Make sure to onl combine terms with the exact same variable combination.. 6x + x + A. x + 7x. x + 0x 7x + x B. 6x 3. x + 8x x x C. 3 x + 6x. x + 8x + x + x D. x. 9x + 3x + x x 0x + x E. x + 9x x x + x + x F. 0 x + 3x Write the word phrase to describe the given expression. Then simplif and write the word phrase to describe the simplified expression. Expression Simplified Expression Simplified Word Phrase x + x 8. x + 3x x 9. w w + 3w + w 0. x x + 3x 00 SM C Curriculum Oregon Focus on Introductor Algebra

11 Lesson C ~ The Distributive Propert The Distributive Propert can be used to help calculate products mentall. In some cases, numbers are separated into two parts. In other cases, ou can separate the number into more than two parts. Use place value to break down each number into its parts. Example:,9 = =. 3,07 = = = Use the Distributive Propert to evaluate each expression.. 3 (67) = 3(60 + 7) = + = (3) = ( + + ) = + + = 8 (9.8) = 8( + + ) = + + = (6.9) = ( ) = = Use the Distributive Propert to find each product. Break the second number into more than two parts as shown in # through #8. Show our work. 9. (7.3) 0. 6(8). (9.8). 8(36) 3. How is breaking a number up into its parts before multipling similar to the multiplication process taught to most students in elementar school? SM C Curriculum Oregon Focus on Introductor Algebra

12 Lesson C ~ Using the Distributive Propert with Variables The Greatest Common Factor (GCF) is the largest number that divides a set of numbers. The GCF can be used when factoring. Factoring is a process in which an expression is broken into smaller parts. This is done b pulling out the GCF. Look at the example below. Example: x + 6 GCF between x and 6 is. Divide from each term to get: (x + 3) Check our work b distributing: (x + 3) = x + 6 Factor each expression using the GCF. Check our work using the Distributive Propert.. 3 x +. 6x x 6. 0 x x 6. 7x 7. 36x x + 7 Simplif each expression. Then factor the simplified expression using the GCF. 9. ( h + 8) + h + h 7 0. ( + ) +. 3 ( p + ) + 9 p +. 0 x + ( x + ) + 00 SM C Curriculum Oregon Focus on Introductor Algebra

13 Lesson 3C ~ Equations and Solutions Match each equation on the left with its solution on the right.. x + = 7 A. x = 0. x = 36 B. x = 7 x 3. 8 = C. x = 9. 8 x = D. x =.. + x =. E. x = 3 6. x = 6 F. x = Some equations have two variables. In each row of the tables below, ou are given either the x or the value for the equation. Use this information to find the missing values in each table. 7. = x = x x x = 7 x 0. = + x x x SM C Curriculum Oregon Focus on Introductor Algebra

14 Lesson C ~ Solving Equations Using Mental Math Write an equation for each situation. Solve each puzzle using mental math.. Larr added to a number and got 33. What number did he start with?. Leslie opened a bank account. She took out $. She had $3 left in the account. How much did she put in the account when she opened it? 3. Klnn had some mone in her wallet. She bought an item for $.0 and had $3.7 left in her wallet. How much did she have in her wallet before buing the item?. Mrell had a bag of marbles. His mom added marbles to the sack and his dad put in 3. He ended up with 0 marbles. How man did he have to begin with?. Gina had $0. She spent some mone on a shirt and then earned $7 babsitting. She ended up with $. How much did she spend on the shirt? 6. The Steamboat Soccer Organization had people tr-out for a team. The cut some people at the beginning of the season and other people got injured during the season. At the end of the season, the had people. How man people did the cut at the beginning? 7. Kara divided all of her holida cand evenl between her friends. Each person received. pounds of cand. How man pounds of cand holida cand did she have to split between her friends? 8. Harle the Hound gained 7. pounds last ear. This ear he lost 3 pounds. Now he weighs. pounds. How much did he weigh at the beginning of last ear? 9. Tom tripled his mone b working all Saturda. He now has $96. How much did he have before Saturda? 00 SM C Curriculum Oregon Focus on Introductor Algebra

15 Lesson C ~ Solving Addition Equations Solve each equation or inequalit. Graph the solution on a number line. See the Tic-Tac-Toe activit on page 00 in Oregon Focus on Introductor Algebra for examples of inequalities. The first one is done for ou to show ou how to graph the solution to an equation.. x + 3 = 3 3 x = 9. f + < p +.7 = t + > > m w + 3 = < < x j +3. = SM C Curriculum Oregon Focus on Introductor Algebra

16 Lesson 6C ~ Solving Subtraction Equations Solve each equation using inverse operations. Write all fraction answers in simplest form. Check our solution.. 37 = 30. x. = = p. 3. =.09. m 3 0 x 6 = = w = g = d j 6 = 3 Write a word phrase for each equation. You must use each term in the box AT LEAST once. is equals less than subtract take awa minus 0. 6 =. = x. m = = p Find the solution for each equation in #0 through #3. 00 SM C Curriculum Oregon Focus on Introductor Algebra

17 Lesson 7C ~ Solving Multiplication and Division Equations Solve each equation using inverse operations. Check our solution. Remember, when dividing b a fraction, ou multipl b the reciprocal of the fraction. Example Solve for x: x = 6 Multipl both sides b the reciprocal of 3 (which equals 3 ): 3 3 x = 6 3 Multipl. x = 9 p. 7 x = 7. = = 3. 3 m. =... b = f = 33 c 7. = x = x = 7 Write our answer as a mixed number. Write an algebraic equation for each problem. Solve each equation. 0. Kristina is four-fifths as old as her sister. Kristina is ears old. Write a multiplication equation and solve the equation to determine her sister s age.. Keaton sold three-fourths as much as Jimm during a fundraiser. Keaton sold 60 products. How man products did Jimm sell? 00 SM C Curriculum Oregon Focus on Introductor Algebra

18 Lesson 8C ~ Mixed One-Step Equations Solve each equation using inverse operations. Write a second equation using a different operation that has the same answer. The first one is done for ou.. x + =7. Answer: x = 3 New Equation: x = 6 6 = 3. m 36 = p k =.9. 7x = 8 6. = 7. 6 = w 3 8. x + = h = 0 Solve each equation using inverse operations. Write three more equations, each using a different operation, that has the same answer as the first. Each problem should have one equation for each operation (,, +, ). 0. m =. 6 h = 96 x = = SM C Curriculum Oregon Focus on Introductor Algebra

19 Lesson 9C ~ Formulas and Equation-Solving Formulas to use in the exercises: h b Area = h w w l l bh Area = l w Volume = lwh Other Formulas I = p r t d = rt h B = a For each exercise, write a real-life stor problem that involves the specified formula. Write the problem so inverse operations must be used to solve the problem. Give the answer to each problem.. Triangle Area Answer:. Rectangle Area Answer: 3. Volume of a Rectangular Prism Answer:. Simple Interest Formula ( I = p r t ) Answer:. Distance Formula ( d = rt ) Answer: h 6. Batting Average Formula ( B = ) Answer: a 00 SM C Curriculum Oregon Focus on Introductor Algebra

20 Lesson 0C ~ Solving Two-Step Equations Solve each equation for the variable b using the Distributive Propert. Check our solution.. ( x + 8) = 0 Distribute first, then rewrite the equation and solve.. ( x ) = + = 0 3. ( x + 7) = 0. 6 ( x 3) =. 9 = 3( x ) 6. ( x ) = (8x + 0) = 8. 0 = ( x ) 9. (x ) = 0. 3 = ( x + ). Jacob has kept a food journal of the last das. He has eaten 00 calories less than his normal intake b not eating ice cream ever night. He calculated that he has eaten 30,800 calories over the last das. a. The equation ( x 00) = represents this situation. What does x represent in the equation? b. Solve the equation and determine what Jacob s normal calorie intake was before he stopped eating ice cream. 00 SM C Curriculum Oregon Focus on Introductor Algebra

21 Lesson C ~ The Coordinate Plane h h w s h b b l b Triangle Parallelogram Rectangle Square Trapezoid A = bh A = bh A = lw A = lw or s² A = h b + b ) ( Plot each set of points. Connect the points in order. Connect the first point to the last point. Name each shape and find the area of each figure using the formulas above.. (, 3), (, 8), (7, 8) and (7, 3). (9, 8), (9, ), (3, ) and (3, 8) 3. (3, ), (9, ) and (9, 6) b Name: Name: Name: Area: Area: Area:. (, ), (8, ), (0, 6) and (3, 6). (, 0), (7, 0), (0, 6) and (3, 6) 6. (, ), (8, ) and (, 9) Name: Name: Name: Area: Area: Area: 7. List the ordered pairs for four points that would create a trapezoid. What is the area of the trapezoid created b these points? (Do not use the trapezoid in the exercises above.) 00 SM C Curriculum Oregon Focus on Introductor Algebra

22 Lesson C ~ Input-Output Tables Complete the input-output tables for each equation.. = 3 x +. = x 3. = x x = 3 x x = x x 0 3 = x Fill in each table with the missing values that satisf the equation. Graph the ordered pairs on the coordinate planes below.. = + x. = x = x x 7 0 x x You should notice something similar about the sets of ordered pairs when ou plot the points in Exercises through 6. What is similar about the graphs? 00 SM C Curriculum Oregon Focus on Introductor Algebra

23 Lesson 3C ~ Writing Function Rules. Shasta owns 0 baseball cards. Each week she plans to add 6 cards to her collection. a. Create an input-output table that shows the number of cards in her collection over the first five weeks. Weeks x 0 3 b. Plot the points that show the number of cards in Shasta s collection over the first five weeks. Label both axes. Cards c. Write a function rule that describes the total number of baseball cards Shasta will own based on the number of weeks she has been collecting cards. d. Determine how man weeks it will take before Shasta has 76 cards in her collection.. Before Henr went on a diet, he weighed 60 pounds. Each month he diets, he loses pounds. a. Create an input-output table that shows Henr s weight over the first five months. b. Create a scatter plot that shows Henr s weight over the first five months. Label both axes. c. Write a function rule that describes Henr s weight based on the number of months he has been dieting. Months x 0 3 Weight d. Henr s doctor told him a good weight for his age is 0 pounds. How man months will it take him to reach this weight? 00 SM C Curriculum Oregon Focus on Introductor Algebra

24 Lesson C ~ Graphing Linear Functions Two points on a line are given. Graph the points and use the graph to help write the linear function that goes through the two points.. (3, 7) and (, ). (, 6) and (9, ) 3. (, 7) and (8, 0) Equation: = Equation: = Equation: =. (, ) and (, 3). (, 3) and (6, 0) 6. (,.) and (, 0) Equation: = Equation: = Equation: = 7. Some graphs form horizontal or vertical lines. Write the equation for each line. Equation: = Equation: x = 00 SM C Curriculum Oregon Focus on Introductor Algebra

25 Lesson C ~ Patterns and Functions Find the missing values in each sequence. Identif the start value (or first term) and the operation that must be performed to arrive at the next term.., 7, 0,, 6,, Start Value: Operation:. 6,,, 3, 37,,, Start Value: Operation: 3. 7,, 7,, 7,, Start Value: Operation:.,, 6,, 30, 37,, Start Value: Operation:. 0., 0.9,,,,., Start Value: Operation: 6.,,, 66,,, 3 Start Value: Operation: For each sequence below, describe the start value and the operation performed to get to the next term. Give the 8 th term in the sequence. 7. 3, 0, 7,, , 9., 8., 7.8, Start Value: Start Value: Operation: Operation: 8 th Term: 8 th Term: 9. 8, 0, 3,, 0. 30, 303, 86, 69, Start Value: Start Value: Operation: Operation: 8 th Term: 8 th Term:. 80, 7, 6, 6,.,, 3,, Start Value: Start Value: Operation: Operation: 8 th Term: 8 th Term: 00 SM C Curriculum Oregon Focus on Introductor Algebra