Lesson 1C ~ Order of Operations

Transcription

1 Lesson C ~ Order of Operations Fill in the bo with a number from to 0 that makes the equation true. If there are two boes in a problem, both boes must contain the same number ( ) =. 5 + =. 0 + = 7.. 6(7 ) + = = 7 6. ( + ) + = Use the numbers,,, and 5 once in each epression to create an answer that meets each criteria. Each epression must use at least one eponent and at least two different tpes of operations. You can make an of the values negative (e.g.,, etc). Uses each number once and equals 8, Eample: Has an answer that is even which is even. 7. Has an answer that is odd. 8. Has an answer that is divisible b. 9. Has an answer less than Has an answer that is a prime number.. Has an answer that is between 0 and 0.. Has an answer equal to. 00 SM C Curriculum Oregon Focus on Linear Equations

2 Lesson C ~ Evaluating Epressions Functions are used in most high school and college math courses. Function notation is a different wa to show what value ou are substituted into an epression. For eample: f ( ) = + is read f of equals + When a number is in the parentheses, this number is substituted for the variable it replaced. For eample: f ( 9) =?? Substitute 9 in for in the equation above. f ( 9) = (9) + = 8 f ( 9) = 8 Use the function f ( ) = 9. Find each of the following.. f (). f (7). f ( ). ( ) f 5. f ( 8) 6. f (0) Use the function f ( ) = +. Find each of the following. 7. f () 8. f ( 5) 9. f (7) 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 eample: Find g( f ()) when f ( ) = and g ( ) = + 7. First find f (). f ( ) = () = 6 Then plug 6 into g(). g( 6) = = Answer: g ( f ()) = Use the function f ( ) = + and g( ) = 0. Find each of the following. 0. g ( f ( )). f (g(5)). g( f ()) 00 SM C Curriculum Oregon Focus on Linear Equations

3 Lesson C ~ The Distributive Propert 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 epression is broken into smaller parts. This is done b pulling out the GCF. Look at the eample below. Eample: + 6 GCF between and 6 is. Divide from each term to get: ( + ) Check our work b distributing: ( + ) = + 6 Factor each epression using the GCF. Check our work using the Distributive Propert Simplif each epression. Then factor the simplified epression using the GCF. 9. ( h + 8) + h + h 7 0. ( + 5) +. ( p + ) + 9 p ( + 5) + 00 SM C Curriculum Oregon Focus on Linear Equations

4 Lesson C ~ Solving 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.. + =7. Answer: = New Equation: = 6 8 =. m. =. 7 5 p. + k = = = = w 8. = 8 9. h = 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. h = 5. = 5. = 6 Write an algebraic equation for each problem. Solve each equation.. 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. 5. 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 Linear Equations

5 Lesson 5C ~ Solving Two-Step Equations Write an equation for each situation. Solve the problem. Show our work and check our solution.. AJ started the da with $90. He bought three used video games and had $7 remaining. If each video game cost the same amount, what was the price of each game?. Sara took a large bag of flour and put the same amount into four different containers. She had.7 pounds of flour remaining. If she started with 6. pounds of flour, how much flour is in each container?. Maria is thinking of a number. If she divides her number b si and then subtracts, she gets. What is Maria s number?. Ivan bought a new television. He was able to pa $0 at the time he received the television. He will pa $ each month on the balance. The original cost of the television was $76. How man months will it take Ivan to pa off the television? 5. The zoo fed the large animals,0 pounds of food last week. Nine large animals each received the same amount while the elephant ate 95 pounds of the food. How much did each of the nine large animals receive? 6. Rick is ears older than half his brother s age. Rick is ears old. How old is his brother? 7. Luc ate eight more than three times as man pretzels as Matt. Luc ate 56 pretzels. How man pretzels did Matt eat? 00 SM C Curriculum Oregon Focus on Linear Equations

6 Lesson 6C ~ Solving Multi-Step Equations Solve each inequalit. Graph the solution on a number line. See the Tic-Tac-Toe activit on page 7 in Oregon Focus on Linear Equations for eamples of solving and graphing inequalities f + < 5 f ( p + ) > p m > ( m + ) w 7 9w < ( h ) ( h + ) > SM C Curriculum Oregon Focus on Linear Equations

7 Lesson 7C ~ The Coordinate Plane and Scatter Plots A reflection flips a point or figure over a line. The figures will be mirror images of each other. A translation is also called a slide. A translation moves a figure from one position to another on a coordinate plane without turning it. Find the coordinates of the point (, ) that has undergone each of the following.. Reflection over the -ais.. Translation of to the right.. Translation of down.. Reflection over the -ais. Graph the original figure and the image under the given transformation on a separate sheet of graph paper. Label the vertices correctl. 5. Triangle M(, ), N(, ) and P(0, 5) A translation of units to the left. 6. Square A(, ), B(, ), C(, ) and D(, ) A reflection over the -ais. 7. Rectangle J(0, ), K(0, ), L(5, ) and M(5, ) A translation of unit to the right and units down. 8. Describe the translation that maps Δ DEF onto Δ D E F. D E D E F F 9. Describe the reflection that maps Δ HJK onto Δ H J K. H J J H K K 0. What are the new coordinates of the point (, 5) that has undergone a reflection over the -ais followed b a translation of units up? 00 SM C Curriculum Oregon Focus on Linear Equations

8 Lesson 8C ~ Recursive Routines Create a recursive routine that fits each description. List the start value, operation and first 6 terms.. Start value is a teen number and ever other term is odd. Start Value: Operation: First Si Terms:. Start value is a 0 and the fifth term is 5. Start Value: Operation: First Si Terms:. Start value is divisible b 6 and the fourth term is divisible b.. Start Value: Operation: First Si Terms:. Start value is a positive even number and terms alternate between positive and negative numbers.. Start Value: Operation: First Si Terms: 5. Start value is a decimal number less than and the fifth term is. Start Value: Operation: First Si Terms: 6. Start value is a prime number which is four less than a multiple of nine. The third term is 5. Start Value: Operation: First Si Terms: 7. Start value is a negative multiple of seven. The sith term is 9. Start Value: Operation: First Si Terms: 8. Start value is an odd number which is three more than one-half squared. The fourth term is. Start Value: Operation: First Si Terms: 9. Start value is the largest prime number less than one-hundred. The fifth term is 0. Start Value: Operation: First Si Terms: 00 SM C Curriculum Oregon Focus on Linear Equations

9 Lesson 9C ~ Linear Plots Determine the linear relationship shown b two points on the coordinate plane b stating the start value and operation. Create an input-output table for the -values of 0 through 5.. Start Value: Operation: 0 5. Start Value: Operation: 0 5. Start Value: Operation:. Create a linear relationship that includes the point on the coordinate plane below. Start Value: Operation: 00 SM C Curriculum Oregon Focus on Linear Equations

10 Lesson 0C ~ Recursive Routine Applications. After three weeks on the market, the AdMi stock was at.5 points After five weeks on the market, it was at 9.5 points. Each of the first five weeks, it fell an equal amount. a. Create an input-output table that shows the value of the stock over the first five weeks. Weeks 0 5 Value b. Write a recursive routine (start value and operation) that describes the value of the AdMi stock based on the number of weeks it has been on the market. c. Create a scatter plot that shows the stock s value over the first five weeks. Label both aes. d. Assuming the stock continues to decrease at this rate, how man weeks until it is worth onl points?. When Suzi finished her 6-week eercise program, she weighed 8 pounds less than when she started. After weeks of the program, she weighed 5 pounds. Each week she lost the same amount. a. Create an input-output table that shows Suzi s weight Weeks over the si weeks using the table at the right. 0 b. Write a recursive routine that describes Suzi s weight based on the number of weeks she has been participating in the program. 5 6 c. Create a scatter plot that shows Suzi s weight over the si weeks. Label both aes. Weight d. How man more weeks should she continue with the program if she would like to weigh 5 pounds? 00 SM C Curriculum Oregon Focus on Linear Equations

11 Lesson C ~ Rate of Change Each table shows three terms in a recursive routine. Determine the rate of change and start value for each table. Find two more terms in the routine Rate of Change: Rate of Change: Rate of Change: Start Value: Start Value: Start Value: Rate of Change: Rate of Change: Rate of Change: Start Value: Start Value: Start Value: Complete each table using the rate of change and the start value for each problem Rate of Change: Rate of Change: Rate of Change:.7 Start Value: Start Value: Start Value: SM C Curriculum Oregon Focus on Linear Equations

12 Lesson C ~ Recursive Routines to Equations Determine the rate of change and the start value for each table. Write an equation in slopeintercept form Rate of Change: Rate of Change: Rate of Change: Start Value: Start Value: Start Value: Equation: Equation: Equation: Rate of Change: Rate of Change: Rate of Change: Start Value: Start Value: Start Value: Equation: Equation: Equation: Use the given information to fill in the blanks in the each table and below the table Rate of Change: Rate of Change: Rate of Change:. Start Value: Start Value: Start Value: Equation: = 6 + Equation: = Equation: 00 SM C Curriculum Oregon Focus on Linear Equations

13 Lesson C ~ Input-Output Tables from Equations Complete the input-output tables for each equation. Graph the points on a separate sheet of graph paper to determine if the equation is linear (forms a straight line) or non-linear.. = ( ). = = 0 = ( ) 6 9 = = Tpe: Tpe: Tpe:. = 5. = + 6. = = 6 = + = 0 0 Tpe: Tpe: Tpe: 7. Write an equation for a non-linear curve (different than the ones above). Create a table of values including input-output pairs. Graph the curve. Equation: 00 SM C Curriculum Oregon Focus on Linear Equations

14 Lesson C ~ Calculating Slope from Graphs The line at the right has seven integer points shown. Use the graph to answer the questions.. List the seven ordered pairs. A (, ) B (, ) C (, ) E F G D (, ) E (, ) D F (, ) G(, ) A B C. Find the slope of the line using different slope triangles as designated below. Write each slope in simplest form. a. D and E b. B and D c. C and F d. A and G. Does it matter which two ordered pairs ou choose to use on a line when determining the slope of the line? Support our answer with evidence.. Similar triangles are triangles that have the same shape but not necessaril the same size. Similar triangles have side lengths that are proportional. Two quantities are proportional if the have the same ratio. Are the four slope triangles ou drew in Eercise # similar triangles? Wh or wh not? 00 SM C Curriculum Oregon Focus on Linear Equations

15 Lesson 5C ~ The Slope Formula Determine the slope of the line that passes through each pair of points. Write in simplest form. Then use the slope to find three other points on the line formed b the given points. Points on Line Slope Three Additional Points on the Line. (5, ) and (, ). (, 6) and (, ). (0, ) and (, 5). (, 6) and (6, 5) 5. ( 5, ) and (, ) 6. (, 0) and (, 7) 7. (6, ) and (, 6) 8. (, 5) and (6, 5) 9. Some lines are horizontal or vertical lines. You can determine this b finding the slope using the slope formula. You can also tell this b eamining the ordered pairs on a line. How can ou tell b looking at the ordered pairs for two points if a. the line is a vertical line? b. the line is a horizontal line? c. Give an eample of a set of ordered pairs for two points that form a vertical line. 00 SM C Curriculum Oregon Focus on Linear Equations

16 Lesson 6C ~ Graphing Using Slope-Intercept Form Graph each set of equations on the same coordinate plane. Determine the point where the lines intersect.. = 5. = +. = 8 = + 5 = + 8 = Intersection Point: Intersection Point: Intersection Point:. = + 5. = 6. = + = 9 = 5 = = = 8 = 6 Intersection Point: Intersection Point: Intersection Point: 7. Wh would it be difficult to find the intersection point of a set of equations if the coordinate pairs were not integers? 00 SM C Curriculum Oregon Focus on Linear Equations

17 Lesson 7C ~ Writing Slope-Intercept Equations for Graphs Three lines are given on each graph that intersect at one point. Find the slope-intercept equation of each line. Graph and write an equation for one additional line that intersects at the same point. Vertical and horizontal lines are not permitted.. Equation of Line a: Equation of Line b: c Equation of Line c: Equation of New Line: a b d. Equation of Line d: Equation of Line e: f Equation of Line f: Equation of New Line: e. Write the slope-intercept equations of three lines that all intersect at a point in Quadrant. 00 SM C Curriculum Oregon Focus on Linear Equations

18 Lesson 8C ~ Writing Linear Equations from Ke Information Write the slope-intercept equations for the lines that form each side of the quadrilaterals below. Label each line with the line segment it corresponds to (i.e. JK : = ).. C B D A. G F H E 00 SM C Curriculum Oregon Focus on Linear Equations

19 Lesson 9C ~ Different Forms of Linear Equations STANDARD FORM: A + B = C where A and B are not both zero. POINT-SLOPE FORM: = m( ) + where m represents the slope and (, ) is a point on the line. Find an equation in standard form that creates the same line as the slope-intercept equation given. The A and B values should be integers.. = +. =. = = + 5. = 6. = 5 Find an equation in point-slope form that creates the same line as the slope-intercept equation given. 7. = 8. = = 0. = + 9. = +. = Find two equations (one in point-slope form and the other in standard form) that create the same line as the slope-intercept equation given.. = + 5. = + 5. = 00 SM C Curriculum Oregon Focus on Linear Equations

20 Lesson 0C ~ More Graphing Linear Equations Equations in standard form can be graphed using the intercept method. Find the - and - intercepts for each equation. Substitute 0 for and solve for to find the -intercept. Substitute 0 for and solve for to find the -intercept.. + = = 5. 9 = = 0 5. = = = = 8 9. = C 00 SM Curriculum Oregon Focus on Linear Equations

21 Lesson C ~ Introduction to Non-Linear Functions Functions can be linear, non-linear or a combination of both. Sketch a graph for each situation and label the aes. Write a few sentences eplaining each graph. In our eplanations, use terms such as linear, nonlinear, continuous, discrete, increasing, and decreasing. (Look up the terms before starting the activit if ou do not know their meanings.). The temperature of water in ice cube tras from the time it is placed in a freezer.. The number of cars on the freewa and the level of pollution in the air.. The temperature of a kettle of water as it is heated.. The distance from a Ferris-wheel rider to the ground during two revolutions. Sketch a graph of a continuous function to fit each description. a. Linear and increasing, then linear and decreasing b. Neither increasing nor decreasing c. Increasing but non-linear d. Decreasing, discrete 00 SM C Curriculum Oregon Focus on Linear Equations

22 Lesson C ~ Parallel, Intersecting or the Same Line Perpendicular lines cross at a 90 angle. Two lines are perpendicular if the have slopes that are opposite reciprocals. A few eamples are shown below. Eamples of Slopes of Perpendicular Lines: and and 5 and 5 Determine if each pair of lines is perpendicular. Show our work. = 5 8 = = =. = = 6. In geometr, some coordinate proofs use items such as slopes, distances and midpoints to prove that points form a specific tpe of quadrilateral. a. Prove that quadrilateral ABCD is a parallelogram b using slopes. A(, 5) B(5, 7) C(6, 5) D(, ) b. Using slopes, determine if quadrilateral ABCD is a rectangle. Eplain our reasoning. 00 SM C Curriculum Oregon Focus on Linear Equations

23 Lesson C ~ Solving Sstems b Graphing Create a sstem of equations that has the given solution. You ma not use horizontal or vertical lines. Graph and record our equations.. SOLUTION: (, 5). SOLUTION: (, ). SOLUTION: (, 8) EQUATIONS: EQUATIONS: EQUATIONS:. SOLUTION: (6, 0) 5. SOLUTION: ( 7, ) 6. SOLUTION: (, ) EQUATIONS: EQUATIONS: EQUATIONS: 00 SM C Curriculum Oregon Focus on Linear Equations

24 Lesson C ~ Solving Sstems Using Tables Each sstem of equations has a solution whose -value is not an integer. Use input-output tables to determine what two integers the -value of the solution lies between.. = + = +. = 5 = Solution () between and. Solution () between and.. = 0. + = +.. = + = Solution () between and. Solution () between and. 5. = = =. = 5 Solution () between and. Solution () between and. 7. How could ou use the information in each of the above eercises to narrow in on the solution? Give an eample using the information from one of the eercises above. 00 SM C Curriculum Oregon Focus on Linear Equations

25 Lesson 5C ~ Solving Sstems b Substitution Each set of three lines intersects to form a triangle. Use the substitution method to find the intersection point of each pair of lines in the set. List the three vertices of the triangle. Graph the triangle.. Line A: =. Line D: = + Line B: + = Line E: = Line C: = 7 Line F: =. Create a sstem of three equations that intersect to form a triangle with integer coordinates for the vertices. List the three equations and the three ordered pairs of the vertices. 00 SM C Curriculum Oregon Focus on Linear Equations

26 Lesson 6C ~ Solving Sstems Using Elimination Solve each sstem of equations using the elimination method. Both equations will need to be multiplied b a constant in order to solve. Check the solution. =.. + = = 7 + = 8 + = = = 0 + = 6 = = = + = 0 00 SM C Curriculum Oregon Focus on Linear Equations

27 Lesson 7C ~ Choosing the Best Method. Solve the following sstem of equations using all four methods. Ever method should provide the same solution. = + + = GRAPHING TABLES SUBSTITUTION ELIMINATION. Which method do ou like best? Wh? 00 SM C Curriculum Oregon Focus on Linear Equations

28 Lesson 8C ~ Applications of Sstems of Equations Define the variables and develop a sstem of equations for each problem. Solve the sstem and check our solution. Write our answer in a complete sentence.. The Garrison s minivan gets miles per gallon for cit driving and 9 miles per gallon for highwa driving. At the beginning of the week, the -gallon tank was full. The famil drove miles before running out of gas. How man gallons were used for cit driving and how man were used for highwa driving?. A pigg bank contains dimes and quarters. There are a total of 6 coins in the bank with a total value of $0.0. How man of each tpe of coin are there in the pigg bank?. In triangle EFG the measure of angle E is four times the measure of angle F. The measure of angle G is 8 less than the measure of angle E. What is the measure of each angle? (Hint: the sum of the angles in a triangle is 80.). Dave, Frank and Kath can process,00 catalog orders per da when all three of them are working. Dave and Frank can do 780 orders per da and Frank and Kath can do 850 orders per da. How man can each do in a da? 00 SM C Curriculum Oregon Focus on Linear Equations