Fifth Grade. California Common Core math problems featuring Santa Monica stories and the ways we move around our community.

Transcription

1 MA in my World Fifth Grade California Common Core math problems featuring Santa Monica stories and the ways we move around our community. For complete details visit: santamonicasaferoutes.org Safe Routes to santa monica

2 Math in My World Explore like never before. The City of Santa Monica has created a series of Kindergarten through 5th grade math problem sets that meet California Common Core Standards and teach critical skills while incorporating stories about life in Santa Monica. The ways in which we move around the city greatly impact our own wellbeing as well as the quality of our environment. Santa Monica believes healthy communites thrive on clean air and active lifestyles, so it is creating a network of transportation choices for all people to get to where they re going and back, without needing to sit in traffic or produce greenhouse gas emissions. My Common Core State Standards Write and interpret numerical expressions. Operations and Algebraic Thinking 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product. 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. 1

3 Numbers and Operations in Base Ten Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Numbers and Operations - Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Apply and extend previous understandings of multiplication and division. 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 5.NF.B.7c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Explore like never before. 2

4 Represent and interpret data. Measurement and Data (Pages) 5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Geometric measurement: understand concepts of volume. 5.MD.C.5b Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. 5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). 3

5 4 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 x (8 + 7). Recognize that 3 x ( ) is three times as large as , without having to calculate the indicated sum or product. Problem 1: The Expo Line The new Expo Line extends the railway line from Culver City to Santa Monica. There are 7 new stations (see photo below) from Downtown Santa Monica to Culver City. Use the map above, what you know about the Expo Line, and your knowledge of mathematical expressions to write an expression that represents the story below. a. Jose took the Expo Line from Downtown Santa Monica to Westwood/Rancho Park so he could go to the movie theater. That ride took 11 minutes. When he got off the train, he walked 6 minutes to the movie theater, where he waited for 10 minutes, for his friend who was coming from downtown LA. Once his friend arrived, they got their tickets and watched the movie, which took 103 minutes in all. Jose invited his friend to sleepover at his house and they walked back to Westwood/Rancho Park station and took the 11 minute ride back to the Downtown Santa Monica station. Write an expression that represents the amount of time from the moment Jose left the Santa Monica station to when he returned. b. Write your own story about the Expo Line and an expression with at least 3 numbers that represents that story. Think of measuring things in minutes, the number of stops, or distance. Use a set of parentheses at least once in your expression.

6 5 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 x (8 + 7). Recognize that 3 x ( ) is three times as large as , without having to calculate the indicated sum or product. Problem 2: Counting the Metro Passengers Sarah decided to play a game based on her observations of the passengers on the Expo Line. When she got on the Expo Line at the 26 th St./Bergamont station, she noticed that there were 38 people in the car. At Expo/Bundy, 13 more passengers got on the train, and 4 passengers got off the train. At the next stop, Expo/Sepulveda, the number of passengers doubled. When the train arrived at Westwood/Rancho Park, another 10 passengers got on the train, while no passengers departed. Write an expression that represents the number of passengers on the train at the end of the ride. *Challenge: When the train arrived at Palms station, the number of passengers on the train halved. How would you change the expression above to represent the number of passengers at Palms? Can you think of two ways to manipulate the expression?

7 6 5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply by 2 as 2 x (8 + 7). Recognize that 3 x ( ) is three times as large as , without having to calculate the indicated sum or product. Problem 3: Bike Extension A fifth grade math class decided they wanted to beat the world record for a tandem bicycle that had enough seats for 52 riders that was built in Augusta, Maine. They decided that they wanted to build a bike that their entire 5 th grade class could ride. There were 72 students in their 5 th grade class. They started off with a 2-wheel bike, and added one more wheel for each additional person who was riding. There were 36 spokes on each bicycle wheel, including the first two wheels. Once they built the bike, they decided each wheel needed an additional 12 spokes to support the weight of all the people on the bike. Write an expression that shows the total number of spokes on the bicycle after they added the additional 12 spokes to each wheel.

8 7 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Problem 1: Saturday and Sunday Bicycle Trip Anita is going on a bicycle trip this weekend and wants to see how biking a certain distance every hour will change the total number of miles she bicycles. On Saturday, she decided to bicycle 4 miles every hour. In other words, she added 4 miles to her total trip for every hour that went by. On Sunday, she decided to bicycle 8 miles every hour. In other words, she added 8 miles to her total trip for every hour that went by. Day Start Hour 1 Hour 2 Hour 3 Hour 4 Hour 5 Hour 6 Hour 7 Hour 8 Saturday 0 4 Sunday 0 8 1) Fill in the table above with the number of miles Anita biked by the time each hour passed by adding 4 for every hour on Saturday and adding 8 for every hour on Sunday. 2) In Hour 5, how many times greater is the distance that Anita biked on Sunday than the distance she biked on Saturday? How many times greater is the distance she biked on Sunday than Saturday in Hour 7? Hour 8? Show your work below. 3) Is there a pattern based on your answers in #2? If so, what is it, and why does it happen? 4) If Anita continues to bike at the same rate, and she bikes 96 miles on Saturday by hour 24, how far will she bike on Sunday by hour 24?

9 8 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Problem 2: Miles the Bus Goes Ms. Nguyen is a bus driver in Santa Monica. Her routes on the weekdays and weekends are different, and Ms. Nguyen wants to know how many miles she drives her bus on the weekdays and the weekends during her work shift. On the weekdays, Ms. Nguyen drives her bus 22 miles every hour during her 8 hour shift. On weekends, Ms. Nguyen drives her bus 11 miles every hour during her 8 hour shift. Day Start Hour 1 Hour 2 Hour 3 Hour 4 Hour 5 Hour 6 Hour 7 Hour 8 Weekdays 0 22 Weekends ) Fill in the table above with the total number of miles Ms. Nguyen has driven her bus by the time each hour has passed given the information above. 2) In Hour 3, how many times greater is the distance that Ms. Nguyen drove her bus on weekdays than the distance she drove her bus on weekends? How many times greater is the distance Ms. Nguyen drove her bus on weekdays compared to weekends in Hour 6? Hour 8? Show your work below. 3) Is there a pattern based on your answers in #2? If so, what is it, and why does it happen? 4) If Ms. Nguyen works a 10 hour shift on Sunday and drives her bus 110 miles by the time Hour 10 is over, how many miles would she drive in Hour 10 on a Thursday?

10 9 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 and the starting number 0, and given the rule Add 6 and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Problem 3: Number of Riders on the Expo Line Extension The Los Angeles Metro Expo Line Extension opened up on May 20, During the first 10 minutes of the opening on Friday, the employees of the L.A. Metro measured the number of passengers entering the Extension station. They did the same thing again on Monday and started recording their information below. Minutes Day Start Friday 0 4 Monday ) 4 more passengers entered the Extension station on Friday with every minute that passed by. 12 more passengers entered the Extension station on Monday with every minute that passed by. Fill in the table above based on this information 2) In Minute 4, how many times greater is the number of passengers on Monday compared to Friday? How many times greater is the number of passengers on Monday compared to Friday in minute 7? minute 10? Show your work below. 3) Is there a pattern based on your answers in #2? If so, what is it, and why does it happen? 4) The employees continued to measure the number of passengers for 60 minutes total on Friday. They measured that 240 passengers entered the station by 60 minutes on Friday. Using the pattern you found above, how many passengers entered by minute 60 on Monday?

11 10 5.NBT.B.7 Add, subtract, multiply, and divide decimals to the hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Problem 1: Buying Expo Line Tickets Below is a chart with the costs of Expo Line tickets. College or Vocational Student Metro Fares Regular 62 years+ or Disabled 1 Ride $1.75 $0.75 $1.75 $ Day Pass $7.00 $ Day Pass $ Day Pass $ $20.00 $43.00 $24.00 Student K-12 1) Nanci is in 5 th grade and skateboards to and from school everyday and likes to perform tricks at The Cove Skatepark every weekend near the 17 th St/Santa Monica College Station in Santa Monica. She takes the Expo Line to get there. Her grandparents are visiting from out of town and she would like to show them her new tricks. Nanci, both of her grandparents (who are 70 and 72 years old), her little sister who is in Kindergarten, and her older brother who goes to Santa Monica City College, are going to take the Expo Line to and from Memorial Park where The Cove Skatepark is located. Each person will need two 1-ride tickets. What will the total cost be? 2) Josie s extended family is visiting from out of town and she and her brother, Ky rie, who are both in 5 th grade, are going to help them buy their Expo Line tickets for the visit. Josie and Ky rie s visiting family members include their two uncles (both 47 years old), 3 cousins who are in 1 st through 9 th grade, and their 87 year old grandmother. Each of the extended family members needs a 30-Day pass for their visit, and Josie and Ky rie need two 1-ride tickets each for when they go to the Westside Pavilion Shopping Mall with their extended family. What is the total cost for all of the tickets that Josie and Ky rie need to buy? 3) What would the cost of Josie and Ky rie s extended family visit be if every person had to buy 1-ride tickets for 30 days, instead of the 30-day pass? 4) Why do you think the cost for a 30-day Pass at the regular price, $100, is more expensive than 30 1-ride tickets?

12 11 5.NBT.B.7 Add, subtract, multiply, and divide decimals to the hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Problem 2: Getting The Right Change Below is a chart with the costs of Expo Line tickets. College or Vocational Student Metro Fares Regular 62 years+ or Disabled 1 Ride $1.75 $0.75 $1.75 $ Day Pass $7.00 $ Day Pass $ Day Pass $ $20.00 $43.00 $24.00 Student K-12 1) Theo is in 5 th grade. He and his 4 friends are going to visit Theo s older sister, Raven, who goes to Santa Monica City College. Raven is going to take Theo and his friends on a tour of Santa Monica City College and then go back home with her brother and his friends for dinner. Theo and his friends are taking the Expo Line to Santa Monica City College and they are all coming back on the Expo Line with his sister. If Theo s mother gave him $20.00 to spend on tickets for everyone, how much money will Theo receive in change after he buys the tickets? 2) Molly is in 4 th grade. Her 3 grandparents are going to explore Los Angeles over the weekend. They need to get two 1-day passes each. Molly and her mother are going to go with Molly s grandparents and will need three 1-ride tickets each. How much money will Molly s mother have in change if she uses two 20- dollar bills?

13 12 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Problem 1: Mural on Santa Monica Boulevard Mayor Vazquez has commissioned all 5 th graders in Santa Monica and Malibu to paint a mural on Santa Monica Boulevard. He made the following speech at a town hall meeting about the mural. Good afternoon! I am very pleased to announce the Santa Monica Mural. My hope is that only the colors red, orange, yellow, green, and blue be used on the mural and that 8 of the mural be orange, 3 of the mural be green, 12 of the 1 1 mural be red, of the mural be yellow, and of the wall be blue Consider Mayor Vazquez s statement. Is it accurate? 2. Draw a picture below that shows Mayor Vazquez s request and your findings from Number If you were Mayor Vazquez, how would you rewrite your statement?

14 13 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Problem 2: Dancers on the Expo Line Sometimes on the Expo Line people will enter a train and perform a dance routine. Some people watch, some people donate money to the dance group, some people film the dancing, and others don t watch at all. Answer the following questions about the dance performances below. RIDE 1: Electronic Music For the first ride, the dancers performed to electronic music. Of all the passengers on the train, passengers watched the performance and didn t give money, 1 3 of the of the passengers watched and donated money, and of the passengers filmed the dancing on their phones. What fraction of passengers on the train watched the dance performance to electronic music? RIDE 2: Disco Oldies Music For the second ride, the dancers performed to old disco music. Of all the passengers on the train, passengers on the train watched and didn t give money, 3 10 of the passengers watched and donated money, and of the passengers filmed the dancing on their phones. What fraction of passengers on the train watched the dance performance to disco oldies? of the RIDE 3: Hip-Hop Music For the third ride, the dancers performed to hip-hop music. Of all the passengers on the train, 1 of the passengers were reading their books, 6 of the passengers were asleep, and 12 of the passengers had headphones in their ears and did not watch. What fraction of passengers on the train watched the dance performance to hip-hop music? 1 3 8

15 14 5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Problem 3: The Regular Passengers Mr. Hernandez is a bus driver for the Big Blue Bus. He is very friendly to his passengers and has come to know all of his regular passengers, who ride the big blue bus at least 3 or 4 times a week. He computed some calculations to figure out what fraction of his passengers are regular passengers, but can t figure out why his solution seems incorrect. Help him by analyzing his work and writing your thoughts beneath it. Mr. Hernandez s work: On Monday, 2 of my passengers are regular passengers who I recognize on the bus. 15 On Tuesday, 1 of my passengers are regular passengers who I recognize on the bus. 3 On Wednesday, 1 of my passengers are regular passengers who I recognize on the 5 bus. On Thursday, 3 of my passengers are regular passengers who I recognize on the bus. 5 On Friday, 2 of my passengers are regular passengers who I recognize on the bus. 3 M T W Th F What is the error in Mr. Hernandez s work? How do you know? Therefore, of my passengers are regular passengers who I know. But this just doesn t seem right 29 15

16 15 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people, each person has a share the size of 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Problem 1: Birthday Bus! Mr. Hernandez drives the #18 Big Blue Bus and it is his birthday today! His tradition for his birthday is to bake an extremely large strawberry banana birthday cake and share it with all of the riders on the bus at 9:38am, the time when he was born. When 9:37am rolls around, Mr. Hernandez notices that there are 24 people on the bus, but his cake was already split into 8 slices. 1) What should Mr. Hernandez do so that everyone can have an equal piece of birthday cake? 2) What fraction of the original slice will each person get to eat? Show your work. 3) If Mr. Hernandez realizes he counted wrong and there are 28 passengers, what fraction of the original slice would each person get to eat?

17 16 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people, each person has a share the size of 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Problem 2: From Santa Monica to Santa Barbara This summer it is Ryan s goal to bike from Santa Monica to Santa Barbara. He knows that the trip is 88 miles long, and that it will take him 2 days to do the trip. If he wants to bike the distance in no more than 10 hours total (5 hours on each day), how many miles should he bike per hour as his goal? Provide your answer as a mixed fraction, improper fraction, and decimal. Ryan knows that he may or not be able to make his mile goal per hour, but as long as he gets close he will be able to make it to Santa Barbara in 10 hours. Between what two number of miles should Ryan aim to bike per hour? Ryan is about to leave on his trip and wants to just double check that his mile per hour goal is correct. Can you show him at least one way to verify that his mile per hour goal is correct in order for him to make the 88 miles in 10 hours?

18 17 5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4,noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people, each person has a share the size of 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Problem 3: Sidewalk Trees The Santa Monica Sidewalk Department is planting trees along a new sidewalk area. The department has 45 trees to plant across 180 sidewalk blocks. 1) How many trees will be planted per sidewalk block? 2) Does your answer make sense? In other words, is it possible to plant that number of trees per sidewalk? How might you interpret your answer to number 1 in a way that makes sense in real life? 3) The Santa Monica Sidewalk Department put out an advertisement asking for volunteers to prune the trees. They expected somewhere between people to express interest, but were surprised to see that 135 people responded to the advertisement! While this was extremely exciting, there are only 45 trees to take care of. Assuming all of the volunteers will be involved with pruning the trees, how could you make sure to include everyone? How many trees should be taken care of per person? Show your mathematical work below.

19 18 5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Problem 1: New Sidewalk Designs Use your knowledge of fractions to answer the questions below about new sidewalk designs in Santa Monica. 1) One of the new sidewalks has 1 of the sidewalk area as green space, with 2 of the green space 3 5 being flowers. What fraction of the sidewalk will be flowers? 2) Another one of the new sidewalk designs is designating 1 of the sidewalk to be decorated with 2 art, where 1 of that area will have a mural designed by 6 5th graders. What fraction of the sidewalk will have the mural designed by 5 th graders? 3) The third sidewalk design has 3 of the sidewalk set aside for seating area, with 1 of the seating 7 2 area being benches. What fraction of the sidewalk will have benches? 5) The fourth sidewalk design has 2 of the sidewalk designated for bicycle racks. 2 of those 13 3 bicycle racks will be designed by Santa Monica City College. What fraction of the sidewalk will have bicycle racks designed by Santa Monica City College?

20 19 5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Problem 2: New Street Designs 100 city block streets in Malibu and Santa Monica are being redesigned. The entire area that is being redesigned is 3 square miles. 10 For each of the following problems, use the diagram and/or write an equation that shows how you achieved your answer. 1) If the new designs include 6 of the redesigned streets being car lanes, how many square 5 miles will be car lanes? 2) If the new designs include 1 of the redesigned streets being bicycle lanes, how many square 8 miles will be bicycle lanes? 3) If the new designs include 2 of the redesigned streets being lined with trees, how many square 3 miles of streets will be lined with trees? 4) If the new designs include 1 of the redesigned streets having post boxes, how many square 4 miles of street will have a post box?

21 20 5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Problem 3: Soccer Field A soccer field is being built near the Westwood/Rancho Park stop on the Expo Line. The soccer field will be easily accessible by both those who live in downtown L.A. and those who live in Santa Monica, so that teams from both areas may compete, as well as the local schools. The soccer field is being built in a new park, where the size of the park is 6 4 acres. At a residential meeting, some of the residents who will be 5 playing on the soccer field make the suggestions below. For each of the following problems, draw a diagram and/or write an equation that shows how you achieved your answer. 1) Some of the athletes in the area would like the soccer field to be 2 2 acres, which is the size of a 3 large regulation-sized soccer field and is of professional status. They make the suggestion at the residential meeting that the park set aside 1 of its space for the soccer field. What do you think of 3 their suggestion? Is it a good suggestion considering the size of the soccer field they desire? Show your work below and then provide a brief explanation. 2) Parents in the area would like the soccer field to be 1 1 acres, which is the size of the smallest size 10 soccer field because they would like a soccer field that caters to the kids in the area, since most other soccer fields are too large for children s teams. They make the suggestion at the residential 1 meeting that the park set aside 6 of its space for the soccer field. What do you think of their suggestion? Is it a good suggestion considering the size of the soccer field they desire? 3) Some of the dog owners in the area would like the park to set aside a section for the dog park. They suggest the soccer field to be 1 1 acres, which is the size of the smallest size soccer field. 10 Then, 7 of the park could be used for the dog park. What do you think of their suggestion? Is it a 8 good suggestion considering the size of the dog park they desire, and the size of the soccer field they suggest?

22 Time of Day Number of People Density (Acres per person) 9:00AM 8 10:00AM 15 11:00AM 26 12:00PM 25 1:00PM 42 2:00PM 19 3:00PM NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Problem 1: Measuring Sidewalk Density The City of Santa Monica is interested in measuring the sidewalk density on Santa Monica Boulevard on the weekends. Fill in the following table with the density at each moment during a typical Saturday in the area of Santa Monica in front of the Santa Monica Public Library. The area 1 in front of the library is 4 square acres. Show your work in the Density section of the table.

23 22 5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Problem 2: How Many Bikes? Ms. King is taking an inventory at her bike store. She knows some information about each type of bike and needs help figuring out how many bikes are in her store at the beginning of each day. MONDAY Ms. King counts 12 mountain bikes in the store. If she knows 1 of her bikes are mountain bikes, how many bikes are 3 in her store on Monday? TUESDAY Ms. King counts 15 gray bikes in the store. If she knows 3 of her bikes are gray bikes, how many bikes are in her store 5 on Tuesday? WEDNESDAY Ms. King counts 22 children s bikes in the store. If she knows 1 of her bikes are children s bikes, how many bikes are 4 in her store on Wednesday? THURSDAY Ms. King counts 7 blue bikes in the store. If she knows 7 on Thursday? (*BONUS Notice anything interesting?) 30 of her bikes are blue bikes, how many bikes are in her store FRIDAY Ms. King counts 28 adult bikes in the store. If she knows 4 9 of her bikes are adult bikes, how many bikes are in her store on Friday?

24 23 5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Problem 3: Community Park Some community groups in Santa Monica and the greater Los Angeles area are interested in designing parts of the Expo Line Bike Path. The Expo Line Bike Path covers 18 acres of land and runs along the Expo 5 Line. Answer the questions below based on the community groups. Community Art Group The community art group would like to divide the path into 8 different sections where each section would be a different mural created by students in grades 1 through 8. How large would each section be in acres of land? Community Athlete Group The community athlete group would like to divide the path into 6 different sections where each section would be designated for different murals of sports that are popular in the area. How large would each section be in acres of land? Community Youth Group The community youth group would like to divide the path into 20 different sections where each section would be designated for different murals of youth and their visions for the future. How large would each section be in acres of land?

25 QUESTIONS 1) How many miles did the students bike collectively (all together)? 2) Considering this total number of miles, and how many students are in Ms. L Orange s class, how far would each student need to bike in order to reach the same collective total, but where all students bike the same distance? You may represent your answer as a fraction or a decimal MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Problem 1: Biking Distance Around the Track Some 5 th grade students in Ms. L Orange s class measured how far each student can bike in 90 seconds and represented the data in the line plot below. Each X represents how far one student was able to bike. Use the line plot to answer the questions underneath the line plot, which measures from 0 miles to 1 mile. X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

26 QUESTIONS 1) How many miles did the students walk collectively (all together)? 2) Considering this total number of miles, and how many students are in Mr. Bleu s class, how far would each student need to bike in order to reach the same collective total, but where all students bike the same distance? You may represent your answer as a fraction or a decimal MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Problem 2: Miles of Sidewalk Traveled Some 5 th grade students in Mr. Bleu s class measured how far each student would walk during 45- minute class period and represented the data in the line plot below. Each X represents the distance one student was able to bike. Answer the questions based on the line plot, which measures from 0 miles to 2 miles. X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

27 26 5.MD.C.5b Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Problem 1: Public Recycling Bins The city of Santa Monica is installing new recycling bins. The city s transportation department is assisting by letting the city know the best and busiest streets to put the recycling bins, so the most residents see them. The city decides to start with Santa Monica Boulevard, and wants to choose the recycling bin design that has the largest volume. For each of the designs below, draw a rough sketch of the bin according to the length, width, and height inside the box provided, and then find the volume. DESIGN 1 The Skinny This design is tall and skinny. It has a length of 14 inches, width of 16 inches, and height of 52 inches. What is the volume? DESIGN 2 The Equalizer This design is equal on all sides. It has a length of 35 inches, width of 35 inches, and height of 35 inches. What is the volume? DESIGN 3 The Shallow This design is short. It has a length of 45 inches, width of 32 inches, and height of 14 inches. What is the volume? DESIGN 4 The Wide This design is tall and skinny. It has a length of 53 inches, width of 20 inches, and height of 30 inches. What is the volume? Which design should they use?

28 27 5.MD.C.5b Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Problem 2: Which One is right? The city of Santa Monica is installing new trees along Santa Monica Boulevard. The area of the sidewalk where they are installing the trees has a restriction where the base area for the tree cannot be larger than 864in 2. However, the trees will need at least 72,400 in 3 in volume in order to grow properly. For each of the designs for the tree spaces below, help complete the design with the missing length, height, or width that would allow the tree to grow properly with a base area of no more than 864in 2 and a volume of at least 72,400 in 3. Round to the nearest whole number. This activity is appropriate for calculator use. DESIGN 1 The tree space could have a length of 21 inches, width of inches, and height of 90 inches. What is a width that could work? Prove your answer below by solving for the volume and base with your suggestion. DESIGN 2 The tree space could have a length of inches, width of 34 inches, and height of 88 inches. What is a length that could work? Prove your answer below by solving for the volume and base with your suggestion. DESIGN 3 The tree space could have a length of 32 inches, width of inches, and height of 100 inches. What is a length that could work? Prove your answer below by solving for the volume and base with your suggestion.

29 28 5.MD.C.5b Apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Problem 3: New Busses The Big Blue Bus is getting a new fleet of busses in Find the volume of each of the busses, and then pick which bus you think is the best model and say why, based on your opinion of what makes a great size bus. 1) Bus #1 has a length of 43 feet, width of 9 feet, and height of 20 feet. What is the volume of Bus #1? 2) Bus #2 is a double-decker bus that has two stories. Its length is 30 feet, width is 10 feet, and height is 38 feet. What is the volume of Bus #2? 3) Bus #3 fits 2 people per aisle and is very long. Its length is 80 feet, width is 7 feet, and height is 12 feet. What is the volume of Bus #3? 4) Bus #4 is like a large room where bus passengers can socialize easily. Its length is 44 feet, width is 23 feet, and height is 9 feet. What is the volume of Bus #4? Which bus is the best model for the new Big Blue Bus fleet? Why?

30 29 5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Problem 1: Schools in Santa Monica In the problem below, the X-axis represents the direction from East to West and the Y-axis represents the direction from North to South. The following is a list of schools and their coordinates in Santa Monica. Plot them on the graph. Edison Language Academy: (3, -2) John L. Webster Elementary: (-6, 6) Grant Elementary School: (4, -3) Juan Cabrillo Elementary: (-7, 3) Roosevelt Elementary School: (-2, 2) Franklin Elementary School: (1, 6)

31 30 5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Problem 2: Path of the Expo Line In the problem below, the X-axis represents the direction from East to West and the Y-axis represents the direction from North to South. The following is a list of stations along the Expo Line. Plot the points and then connect them to draw the Expo Line Extension from downtown Santa Monica to downtown LA. Downtown Santa Monica Station: (-7, -2) Expo/Crenshaw: (2, -2) Culver City: (-2, -1) Westwood/Rancho Park: (-4, 1) 7 th Street/Metro Center: (7, 4) 23 rd Street: (6, 1)

32 31 5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Problem 3: Path of the Big Blue Bus Route #18 In the problem below, the X-axis represents the direction from East to West and the Y-axis represents the direction from North to South. The following is a list of stops Big Blue Bus #18 makes. Plot the points and then connect them to draw Bus #18 s route from Venice Beach to UCLA Windward & Main: (-4, -7) Lincoln & Montana: (0, 5) Rose & Ruth: (0, -6) Montana & Barrington: (1, 5) San Vicente & Barrington: (1, 4) UCLA Hilgard Terminal: (3, 7)

33 NOTES

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35 NOTES

36 This project is funded in partnership between Metro and the City of Santa Monica.