3-1. Enrichment. Expressions for Figurate Numbers

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1 NAME DATE PERIOD -1 Expressios for Figurate Numbers Figurate umbers are umbers that ca be show with dots arraged i specific geometric patters. Below are the first five square umbers. The expressio will give you the umber of dots i the th square umber. The variable takes o the values 1,,, 4, ad so o. So, to fid the 10th square umber, you would use 10 for. 1. Match each set of dot patters with its ame ad expressio. Write exercise umbers i the boxes to show the matchigs. a. Dot Patters for Secod ad Third Numbers Name of Figurate Number Expressio petagoal ( 1) b. c. hexagoal ( 1) triagular ( 1) Use the algebraic expressios o this page to compute each umber. The make a drawig of the umber o a separate sheet of paper.. 6th square. 4th triagular 4. 4th petagoal. 4th hexagoal 6. th triagular 7. th petagoal Chapter 14 Course

2 NAME DATE PERIOD - Equatio Hexa-maze This figure is called a hexa-maze because each cell has the shape of a hexago, or six-sided figure. To solve the maze, start with the umber i the ceter. This umber is the solutio to the equatio i oe of the adjacet cells. Move to that cell. The umber i the ew cell will the be the solutio to the equatio i the ext cell. At each move, you may oly move to a adjacet cell. Each cell is used oly oce Ed Start Here Chapter 0 Course

3 NAME DATE PERIOD - Direct Variatio Equatios of the form y ax ad y x a ca be used to show how oe quatity varies with aother. Here are two examples. Drivig at a speed of 0 miles per hour, the distace you travel d varies directly with the time you are oe the road t. The loger you drive, the farther you get. It is also the case that the time t varies directly with the distace d. The farther you drive, the more time it takes. Complete the equatio for each situatio. The describe the relatioship i words. 1. If you go o a diet ad lose pouds a moth, after a certai umber of moths m, you will have lost p pouds. d 0t d t 0. You ad your family are decidig betwee two differet places for your summer vacatio. You pla to travel by car ad estimate you will average miles per hour. The distace traveled d will result i a travel time of t hours.. You fid that you are spedig more tha you had plaed o retig video movies. It costs $.00 to ret each movie. You ca use the total amout spet a to fid the umber of movies you have reted m. 4. You sped $0 a moth to take the bus to school. After a certai umber of moths m, you will have spet a total of dollars d o trasportatio to school.. You are savig moey for some ew athletic equipmet ad have 1 weeks before the seaso starts. The amout you eed to save each week s will deped o the cost c of the equipmet you wat to buy. Lesso Chapter 7 Course

4 NAME DATE PERIOD - Equatios with Like Terms Some equatios cotai two or more expressios that are called like terms. For example, i the equatio a a 4 14, the expressios a ad a are like terms. Whe you see like terms, you ca combie them ito oe expressio. a a a Whe you solve a equatio cotaiig like terms, combie them first before cotiuig to solve the equatio. To solve a a 4 14, proceed as follows. a a 4 14 Combie like terms. a 4 14 a a 10 a 10 a Solve each equatio. The locate the solutio o the umber lie below. Place the letter correspodig to the aswer o the lie at the right of the exercise. 1. x 4x 9. x x 1. 4x 7x x 6x 0..4x 1. 1.x (6 x) x 4 x 8. 7x (x) x 4 9. (x x) W I H F L J O P N V G C D T M K A B R Lesso Chapter 7 Course

5 NAME DATE PERIOD -6 Perimeter ad Area Two shapes ca have the same area ad differet perimeters. Each of these shapes has a area of 16 square uits, but their perimeters are differet. Lesso 6 P 4 P 0 P 0 P 16 Amog rectagles that have a area of 16 square feet, rectagles that are log ad thi have the greatest perimeter. Rectagles with the least perimeter are more closely shaped to a square. The grid shows the basic floor pla of the Smith s house. The side of each grid represets feet. The three bedrooms all have the same area. 1. Which of the rectagular bedrooms has the greater perimeter? What is aother dimesio that will create a rectagle with the same area?. Lisa s bedroom has a irregular shape. How does the area of her bedroom compare to the other two bedrooms? How does the perimeter of her bedroom compare to the other two bedrooms? Mike's Bedroom. The Smith s are movig to a ew house. Desig two differet floor plas for them from which they may choose. Your floor plas must have five rooms icludig three bedrooms. Each bedroom must have a area of 16 square feet (18 squares) but ot the same perimeters. You may add ay other features to the house that you wat. Tim's Bedroom Kitche Livig Room Frot Hallway Lisa's Bedroom Chapter 4 Course

6 -7 NAME DATE PERIOD Fudraisig for Charity Jacqui is leadig a fud-raisig group for a charity. The group is goig to make buttos ad sell them at a couter for $6.00 each. Their goal is to raise $1000. Jacqui creates a table to predict their earigs. 1. Complete the table showig how much moey will be raised based o the umber of buttos sold.. Make a lie graph represetig the fuctios from Jacqui s table. Fud-Raisig Buttos Buttos Sold Moey Raised Moey Raised (i dollars) Buttos Sold. At this rate, how may buttos does Jacqui s group eed to sell to raise $1000? 4. Write a equatio that relates the amout of moey raised if there is a $0 couter fee.. If the group calculates i the $0 couter fee, how may buttos do they eed to sell i order to raise their goal of $1000? Chapter 0 Course

7 Aswers (Lessos -1 ad -) Lesso -1 Expressios for Figurate Numbers Figurate umbers are umbers that ca be show with dots arraged i specific geometric patters. Below are the first five square umbers. The expressio will give you the umber of dots i the th square umber. The variable takes o the values 1,,, 4, ad so o. So, to fid the 10th square umber, you would use 10 for. 1. Match each set of dot patters with its ame ad expressio. Write exercise umbers i the boxes to show the matchigs. a. Dot Patters for Secod ad Third Numbers Name of Figurate Number Expressio petagoal b ( 1) c b. - Lesso Readig Guide Solvig Additio ad Subtractio Equatios Get Ready for the Lesso Read the itroductio at the top of page 16 i your textbook. Write your aswers below. 1. What does x represet i the figure? umber of games iitially had. What additio equatio is show i the figure? x = 6. Explai how to solve the equatio. Fid the umber that whe added to is How may games did Max have i the begiig? 4 Read the Lesso. Match the method of solvig with the appropriate equatio. x 9 c a. add to each side y 1 a b. add to each side m 1 d c. subtract from each side r 9 7 e d. add 1 to each side k b e. subtract 9 from each side 6. Explai i words how to solve each equatio. a 10 Add te to each side ad simplify. 4 t 1 Subtract four from each side ad simplify Add seve to each side ad simplify. 7. Solve each equatio. a. w 11 4 b. z 1 0 c. 4 c 9 1 Remember What You Leared 8. Take turs with a parter explaiig the Additio ad Subtractio Properties of Equality i your ow words. The each of you write two additio ad two subtractio equatios. Trade equatios ad solve. Check your work by explaiig to each other the method you used to solve the equatios. See studets aswers. Chapter 1 Course c. hexagoal c ( 1) a triagular a ( 1) b Use the algebraic expressios o this page to compute each umber. The make a drawig of the umber o a separate sheet of paper.. 6th square. 4th triagular 4. 4th petagoal th hexagoal 6. th triagular 7. th petagoal 8 1 Chapter 14 Course Chapter A4 Course

8 Aswers (Lesso -) Lesso - Equatio Hexa-maze This figure is called a hexa-maze because each cell has the shape of a hexago, or six-sided figure. To solve the maze, start with the umber i the ceter. This umber is the solutio to the equatio i oe of the adjacet cells. Move to that cell. The umber i the ew cell will the be the solutio to the equatio i the ext cell. At each move, you may oly move to a adjacet cell. Each cell is used oly oce Ed Aswers - Scietific Calculator Activity Solvig Equatios A calculator may be helpful for solvig additio ad subtractio equatios with decimals. Example 1 Solve k k k ENTER Eter: So, k Example Solve 1.46 y y y ENTER Eter: So, y Exercises Solve each equatio. 1. k y b x m c g w v r f d j CHALLENGE Each week for eight weeks, Mr. Patel s sales commissio icreased his previous week s commissio by $ I the eighth week, his commissio was $6.84. What was his commissio eight weeks before this? $1.64 Chapter 1 Course Start Here Chapter 0 Course Chapter A7 Course

9 Aswers (Lesso -) Lesso - Word Problem Practice Solvig Multiplicatio Equatios 1. TRAVEL The speed limit o a Arizoa highway is 7 miles per hour. Suppose a truck travelig at the speed limit drives miles before the driver stops for a break. Write a multiplicatio equatio to fid the legth of time the truck has traveled. 7t. TRAVEL Solve the equatio you wrote i Exercise 1. How log did the truck travel? h. FLOWERS A gardeig expert recommeds that flower bulbs be plated to a depth of three times their height. Suppose Jea determies that a certai bulb should be plated at a depth of 4. iches. Write a multiplicatio equatio to fid the height of the bulb. h FLOWERS Solve the equatio you wrote i Exercise. What is the height of the bulb? 1. i. Chapter 6 Course - Direct Variatio Equatios of the form y ax ad y x a ca be used to show how oe quatity varies with aother. Here are two examples. Drivig at a speed of 0 miles per hour, the distace you travel d varies d 0t directly with the time you are oe the road t. The loger you drive, the farther you get. d It is also the case that the time t varies directly with the distace d. t The farther you drive, the more time it takes. Complete the equatio for each situatio. The describe the relatioship i words If you go o a diet ad lose pouds a moth, after a certai umber of moths m, you will have lost p pouds. p m; The loger you diet, the more weight you will lose.. You ad your family are decidig betwee two differet places for your summer vacatio. You pla to travel by car ad estimate you will average miles per hour. The distace traveled d will result i a travel time of t hours. d t ; The farther you drive, the more time it will take.. You fid that you are spedig more tha you had plaed o retig video movies. It costs $.00 to ret each movie. You ca use the total amout spet a to fid the umber of movies you have reted m. m a ; The greater the amout spet, the more movies reted. 4. You sped $0 a moth to take the bus to school. After a certai umber of moths m, you will have spet a total of dollars d o trasportatio to school. d 0m; The loger you ride the bus, the more you will sped.. You are savig moey for some ew athletic equipmet ad have 1 weeks before the seaso starts. The amout you eed to save each week s will deped o the cost c of the equipmet you wat to buy. s 1 c ; The more expesive the equipmet, the more moey must be saved each week. Chapter 7 Course. EXERCISE A 1-poud perso uses 4.4 Calories per miute whe walkig. Write a multiplicatio equatio to fid the umber of miutes of walkig it will take for a 1-poud perso to use 198 Calories. 4.4m ELECTRICITY The electric compay charges $0.06 per kilowatt hour of electricity used. Write a multiplicatio equatio to fid the umber of kilowatt hours of electricity for which the Estevez family was charged if their electric bill was $ k EXERCISE Solve the equatio you wrote i Exercise. How may miutes of walkig it will take for a 1-poud perso to use 198 Calories? 4 mi 8. ELECTRICITY Solve the equatio you wrote i Exercise 7. For how may kilowatt hours of electricity was the Estevez family charged? 764 kilowatt h Chapter A10 Course

10 Aswers (Lesso -) Lesso - Word Problem Practice Solvig Two-Step Equatios 1. GOLF It costs $1 to atted a golf cliic with a local pro. Buckets of balls for practice durig the cliic cost $ each. How may buckets ca you buy at the cliic if you have $0 to sped? 6 buckets. MONEY Paulo has $14 i his savigs accout. He ears $6 a week mowig laws. If Paulo saves all of his earigs, after how may weeks will he have $4 saved? 8 wk. RETAIL A olie retailer charges $6.99 plus $0. per poud to ship electroics purchases. How may pouds is a DVD player for which the shippig charge is $11.94? 9 lb 4. MONEY Caitli has a $10 gift certificate to the music store. She has chose a umber of CDs from the $7 bargai bi. If the cost of the CDs is $ after the gift certificate is credited, how may CDs did Caitli buy? 6 CDs Chapter 6 Course Aswers - Equatios with Like Terms Some equatios cotai two or more expressios that are called like terms. For example, i the equatio a a 4 14, the expressios a ad a are like terms. Whe you see like terms, you ca combie them ito oe expressio. a a a Whe you solve a equatio cotaiig like terms, combie them first before cotiuig to solve the equatio. To solve a a 4 14, proceed as follows. a a 4 14 a 4 14 a a 10 a 1 a 0 Combie like terms. Solve each equatio. The locate the solutio o the umber lie below. Place the letter correspodig to the aswer o the lie at the right of the exercise. 1. x 4x 9 F. x x 1 A. 4x 7x 1 C 4. 1 x 6x 0 T..4x 1. 1.x 4.8 O 6. 1 (6 x) 1 R x 4 x I 8. 7x (x) x 4 A 9. (x x) 0 L W I H F L J O P N V G C D T M K A B R Chapter 7 Course. EMPLOYMENT Mrs. Jackso eared a $00 bous for sigig a oe-year cotract to work as a urse. Her salary is $ per hour. If her first week s check icludig the bous is $1,04, how may hours did Mrs. Jackso work? h 6. PHOTOGRAPHY Morga subscribes to a website for processig her digital pictures. The subscriptio is $.9 per moth ad 4 by 6 ich prits are $0.19 each. How may prits did Morga purchase if the charge for Jauary was $1.8? prits Chapter A1 Course

11 Aswers (Lesso -6) -6 Perimeter ad Area Two shapes ca have the same area ad differet perimeters. Each of these shapes has a area of 16 square uits, but their perimeters are differet. Amog rectagles that have a area of 16 square feet, rectagles that are log ad thi have the greatest perimeter. Rectagles with the least perimeter are more closely shaped to a square. The grid shows the basic floor pla of the Smith s house. The side of each grid represets feet. The three bedrooms all have the same area. 1. Which of the rectagular bedrooms has the greater perimeter? What is aother dimesio that will create a rectagle with the same area? Tim s bedroom has the greatest perimeter; feet by 6 feet.. Lisa s bedroom has a irregular shape. How does the area of her bedroom compare to the other two bedrooms? How does the perimeter of her bedroom compare to the other two bedrooms? Lisa s bedroom has the same area as the other two bedrooms. The perimeter of her room is greater tha that of Mike s bedroom ad the same as that of Tim s bedroom.. The Smith s are movig to a ew house. Desig two differet floor plas for them from which they may choose. Your floor plas must have five rooms icludig three bedrooms. Each bedroom must have a area of 16 square feet (18 squares) but ot the same perimeters. You may add ay other features to the house that you wat. See studets work. Chapter 4 Course py g, p, Lesso 6-6 Word Problem Practice Measuremet: Perimeter ad Area 1. BUILD A FENCE Mrs. Che wats to build a fece aroud her yard so that her dog, Fluffy, ca ru free. The yard she wats to fece is 60 feet by 0 feet. The fecig is sold by the liear foot, so i order to figure out how much fecig she eeds, Mrs. Che eeds to kow the perimeter of the yard. Fid the yard s perimeter. 180 feet. WINDOWS Mrs. Johso was plaig to caulk aroud the frame of her patio doors that measure feet by 6 1 feet. I order to help her to kow how much caulk to buy, fid the perimeter of the doors. ft 1 6 ft ft. SOCCER The dimesios of a field for Me s ad Wome s NCAA soccer ca be o more tha 80 yards by 10 yards. If the field has those dimesios what is the perimeter of the field? 400 yards. CARPET Mr. Yuji plas o buyig carpet for his bedroom that measures 1 feet by 1 feet. So he will kow how much carpet to buy, fid the area of his bedroom. 144 ft 7. LOBBY A hotel lobby measures 40 yards by 60 yards. Fid the area ad perimeter of the lobby s floor.,400 yd ; 00 yd 4. FENCING Mr. Lao is plaig to build a rectagular cattle pe that measures 0 feet by 7 feet. Fid the total legth of fecig that he will eed to purchase. 0 ft 6. BORDER Mrs. Jackso is goig to put up a wallpaper border alog the top of the walls i her diig room. If the diig room measures 16 feet by 1 feet, how much border should she buy? 6 ft 8. MURAL A artist paited a mural measurig 9 feet by 0 1 feet. Fid the area ad perimeter of the mural ft ; 9 ft Chapter 4 Course Chapter A18 Course

12 Aswers (Lesso -7) Lesso 7-7 Fudraisig for Charity Jacqui is leadig a fud-raisig group for a charity. The group is goig to make buttos ad sell them at a couter for $6.00 each. Their goal is to raise $1000. Jacqui creates a table to predict their earigs. 1. Complete the table showig how much moey will be raised based o the umber of buttos sold.. Make a lie graph represetig the fuctios from Jacqui s table. Buttos Sold Moey Raised $60 $7 $84 $96 Fud-Raisig Buttos At this rate, how may buttos does Jacqui s group eed to sell to raise $1000? 167 buttos 4. Write a equatio that relates the amout of moey raised if there is a $0 couter fee. y 6x 0. If the group calculates i the $0 couter fee, how may buttos do they eed to sell i order to raise their goal of $1000? 17 buttos Chapter 0 Course -7 TI-7 Activity Table of Values Use the Table feature o your calculator to create a table of values from a equatio of a fuctio. The graph the fuctio. Example 1 Suppose you have $ saved ad you ear $10 for mowig a eighbor s law. Suppose you save all the moey you ear. How much moey would you have after mowig the law times? 0 times? Write a equatio i which x is the umber of laws you mow ad y is the total amout of moey you have saved. Make a table where x has the values 0 through 0. Graph the fuctio. Sketch the graph ad mark the poits (0, ), (, 7), ad (0, ) with their coordiates. Describe what each poit meas i terms of laws mowed ad dollars saved. The equatio is y 10x. Step 1 Eter the equatio. Y= CLEAR 10 Step Set up the table. View the table ad aswer the questios. d [TBLSET] 0 1 ENTER ENTER d [TABLE] Whe you mow laws, x. Whe x, y 7. You have saved $7. Whe x 0, y. Whe you mow 0 laws, you have saved $. Step Tur off ay other plots. View the graph. d [PLOT] 4 ENTER ZOOM 9 Step 4 Explore the graph usig the TRACE feature. The poit (0, ) represets 0 laws mowed ad $ saved. (, 7) is laws mowed ad $7 saved. (0, ) is 0 laws mowed ad $ saved. Exercises Create a table. Graph the fuctio. Sketch the graph ad label three poits with their coordiates. Describe what the poits represet i terms of classrooms ad studets. Suppose each classroom has 8 studets. The umber of studets i the whole school is give by the fuctio y 8x, where x represets the umber of classrooms. The umber of classrooms could be 1 up to 18. How may studets are i a school with 9 classrooms? 1 classrooms? See studets work for graph; 9 studets; 1 40 studets. Chapter 1 Course Moey Raised (i dollars) Buttos Sold Chapter A Course