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

Transcription

1 MA in my World Third 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 Operations and Algebraic Thinking (Pages 4-12) Represent and solve problems involving multiplication and division. 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 1

3 Operations and Algebraic Thinking (Pages 13-15) Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Numbers and Operations in Base Ten (Pages 16-21) Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. Numbers and Operations - Fractions (Pages 22-27) Develop understanding of fractions as numbers. 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Explore like never before. 2

4 Solve problems involving measurement and estimation. 3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. 3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Represent and interpret data. Measurement and Data (Pages 28-43) 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.C.7 Relate area to the operations of multiplication and addition. 3

5 4 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. Problem 1: Field Trip to the L.A. Philharmonic All Santa Monica-Malibu Unified District third and tenth graders are going on a field trip to see the L.A. Philharmonic perform. Students from every school are planning to meet at the Downtown Santa Monica Station so they can take Expo Line to downtown L.A., where the L.A. Philharmonic will play at the Walt Disney Concert Hall. Teachers and chaperones are trying to calculate the costs with regard to the Expo Line Tickets and need your help. 1) Suppose 863 students will be attending the performance at the Walt Disney Concert Hall. Each Expo Line Ticket will cost $3 per student to get to and from the Walt Disney Concert Hall, including the short bus ride from the downtown station to the hall itself. How could you mathematically express the total cost for all of the Expo Line Tickets? 2) If there are 4 adults going with every class and there are 22 different classes, how could you mathematically express the total number of adults going? 3) If there are 26 students in each class and 30 classes are going to the show, how could you mathematically express the total number of students going?

6 5 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. Problem 2: Expressing Groups Write multiplication expressions that represent the following groups of objects for each section below. Multiplication Expression: x Multiplication Expression: x Multiplication Expression: x

7 6 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. Problem 3: Thinking About Transit For the following mathematical expressions, describe a situation that represents the numerical expression and its product by writing a story that involves the written theme of transportation. Story 1: Busses Expression: 20 x 3 Story 2: Bicycling to School Expression: 4 x 52 Story 3: Walking Expression: 7 x 34 Story 4: Riding Rollerblades Expression: 6 x 26

8 7 3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 divided by 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 divided by 8. Problem 1: Biking Groups Use your knowledge of the meanings of multiplication and division to answer the questions below each set of bikers. Biker Set #1 The number of bikers above can be expressed as 5 x 4 = 20, because there are 5 bikers in each group, and 4 groups of bikers. a. What would the equation 20 4 = 5 mean for this problem? b. What would the equation 20 5 = 4 mean for this problem? Biker Set #2 The number of bikers above can be expressed as 2 x 6 = 12, because there are 2 bikers in each group, and 6 groups of bikers. a. What would the equation 12 6 = 2 mean for this problem? b. What would the equation 12 2 = 6 mean for this problem?

9 8 3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 divided by 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 divided by 8. Problem 2: How many groups? vs. How many are in each group? Read the following sentences and circle the correct answer. 1. Akol s teacher asked him to set out helmets for the bike field trip his class is going on tomorrow. He has 26 helmets and is supposed to put 2 helmets next to each bike until he runs out. What is a question that Akol might be asking? How many bicycles will my class use? or How many helmets go with each bicycle? 2. Tania is helping her teacher get everyone ready for the busses for their upcoming field trip by making a list of students in each bus. Tania s teacher asks her to put one student s name in each bus until she runs out of student names. There are 27 students and 3 busses. What is a question that Tania could be considering? How many busses are we using? or How many students will be on each bus? 3. Roberto wants to bike a total of 60 miles to and from school before he finishes the school year. He knows that his ride to and from school is 4 miles total each day. Which question makes sense for Roberto to ask? How many days will it take to bike 60 miles total? or How many miles will I bike each day? 4. Nia is walking around Santa Monica. She knows it takes her about 2 minutes to walk each block when she walks along Montana Avenue. She wants to walk for 94 minutes. What is something she might be asking? How long will it take me to walk my goal? or How many blocks will I walk in all?

10 9 3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 divided by 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 divided by 8. Problem 3: How many? For the following problems, fill in the blanks and write an equation that matches the picture or scenario. Show your work. 1. Ms. Jones is buying skateboards for the families in her neighborhood. She decides to give 2 skateboards to each family and buys 16 skateboards. How many families are in her neighborhood? 2. The Santa Monica Transportation Department is putting up pedestrian signs. They are putting up 18 signs and have to put 3 on each block. How many blocks will have new pedestrian signs? = There are families in Ms. Jones s neighborhood. = There are blocks that have new signs. 3. Santa Monica and Malibu Schools are considering buying Expo Line TAP passes for every teacher so they can get to work using public transportation. If they start off with 42 passes and want to give an equal number to 6 schools, how many TAP passes will each school get? = There are passes for each school.

11 10 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Problem 1: Santa Monica Streets Use your knowledge of Santa Monica and of multiplication and division to solve the following problems. Show your work by drawing a picture or writing down a multiplication or division equation. Problem Set A 1) There are 5 major boulevards of equal length in the City of Santa Monica, and their combined length is about 15 miles long. How long is each boulevard? 2) There are 5 boulevards in the City of Santa Monica, and each Boulevard is 3 miles long. How long is their combined length? 3) What is the difference between Question 1 and Question 2? What is the difference in your strategy to solve? Problem Set B 4) You have 60 minutes to spare and decide to walk the length of 14 th Street from 14 th St. & Ashland Avenue to 14 th St. & San Vicente Boulevard. If the length of your walk is 3 miles and you want to walk each mile at the same pace, how long does it take you to walk each mile? 5) You have 60 minutes to spare and decide to walk the length of 14 th Street from 14 th St. & Ashland Avenue to 14 th St. & San Vicente Boulevard. If it takes you 20 minutes to walk 1 mile, how many miles are you able to walk in those 60 minutes? 6) What is the difference between Question 4 and Question 5? What is the difference in your strategy to solve?

12 11 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Problem 2: Getting to the L.A. Philharmonic Use your knowledge of Santa Monica and of multiplication and division to solve the following problem. Show your work by drawing a picture or writing down a multiplication or division equation. Your class is going on a trip to see the L.A. Philharmonic at the Walt Disney Concert Hall. Your teacher has up to $90 to spend on transportation for students, and there are 15 students in your class. The leftover money will be used on a pizza party at the end of the year. There are two ways that you can get to the L.A. Philharmonic: Way #1: Take Bus R10. The cost is $5 per student and the entire trip takes 66 minutes. Way #2: Take the Expo Line and the Dash Downtown Bus. The cost is $3 per student and the entire trip takes 80 minutes. If you were your teacher, would you choose Way #1, or Way #2 to get all students to the Walt Disney Concert Hall? How much money does each way have left over after the cost of the tickets? Show your work, and then explain your decision in the blank lines provided below.

13 12 3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Problem 3: Santa Monica Streets The following table shows how much a day pass and a 7-day pass cost to ride on the Big Blue Bus. Use the table to answer the questions Day Pass $4 below. 7 Day Pass $14 1) If you have $70 to spend on yourself and your 4 siblings, can each kid get a 7 Day Bus Pass? 2) How much does the 7 Day Pass cost per day if you split up the cost for each of the 7 days? 3) Leila s grandmother wants to buy her and all of her cousins Day Passes on the Big Blue Bus so they can travel around Santa Monica together on a Saturday. If there are 17 grandchildren, how much money will Leila s grandmother spend? 4) If you have $84, how many 7 Day Passes can you buy? How many Day Passes can you buy? Would it be better to buy the 7 Day Passes with your money or the Day Passes?

14 13 3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Problem 1: Getting Around Santa Monica Solve the following problems by writing equations and drawing pictures or diagrams in the boxes provided to the right of the problem. 1) Joshua lives 12 miles from the beach. If he bikes half of the distance and then walks 1 more mile, how many more miles does he have left until he reaches the beach? 2) Omar s family is going on vacation to L.A. and they are going to visit Santa Monica for a week. They have $150 dollars to spend on transportation. If a 7-Day Big Blue Bus pass costs $14, and there are 8 people in his family, how much money will they have leftover if they buy each person in his family a bus pass? 3) Rico picks up his little brother from Grant Elementary School every day. It takes him 36 minutes to walk from Santa Monica High School to Grant Elementary School. It takes half that amount of time to take the bus and walk. If he walks for 7 minutes when he takes the bus, how long is he on the bus for? 4) Elizabeth s uncle picks her up at Mar Vista Recreation Center 150 minutes after school gets out every day. It takes Elizabeth 22 minutes to bike to Mar Vista from Edison Language Academy, where she goes to school. Then, she plays soccer for 70 minutes, and spends half of the rest of her time doing homework and the other half playing jumprope. How long does she spend on homework every day?

15 14 3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Problem 2: Matching Transportation Problems Match the following problems to the correct formulas on the right hand side by drawing a line from the problem to the set of equations. 1) Xena takes the school bus every day to school. From the moment she leaves her house, to the moment she steps in school takes 80 minutes. She spends 26 of those minutes walking to the bus stop and then from the bus to the front of school. The rest of the time she spends on the bus, and half of that time she spends reading her favorite book. How much time does she spend reading? 6 x 4 = x 3 = = W W = 60 2) Darren was biking near the Santa Monica Pier with 25 of his friends for his 8 th birthday party. 7 of his friends had to leave, and Darren decided to count how many bicycle wheels were left. How many did he count? 8 x 2 = = M M = 30 3) Abukar and his 5 neighbors like to skateboard. Abukar s brother, Manuel, likes to ride his tricycle with his 11 neighborhood friends. If Abukar and Manuel and all of their neighbors go on a skateboard and tricycle ride around the neighborhood, how many wheels are on the ground? (There are 4 wheels on a skateboard and 3 on a tricycle) 26 7 = x 2 = W W = 38 4) Muslima bought herself a 7-Day Pass on the Big Blue Bus for $14. Then, she spent half of what she had leftover on some ice cream. She counted and had 8 dollars left in her pocket. How much did she have to begin with? 5) All students can get a 30 day pass TAP card to ride on the L.A. Metro for $24 each. They can also ride 2 trips for $2. If 5 students want to buy one 30 day pass and one 2-trip ride each, how much money will they spend all together? 5 x 24 = x 2 = = M M = = = R R= 27

16 15 3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Problem 3: At the Bike Store You and your friends are going on a bike ride this weekend and see the following prices at the bike store for a daily rental. Adult Bikes Cost Blue Road Bike $25 Green Mountain Bike $17 Red Cruiser $15 Kid Bikes Cost Purple BMX $15 Orange Trainer $10 Yellow Tricycle $8 1) If 4 adults decide to rent the green mountain bike and 2 kids decide to rent the orange trainer bike, how much will the total cost be? 2) You saved up $105 to rent some bicycles for you and your friends for your birthday. If you rent only purple BMX bikes, how many kids can you invite to your birthday? If the parent chaperones get 3 green mountain bikes, how much will the total cost be? 3) A family of 5 spent $87 at the bike store. If the parents rented the blue road bike and the green mountain bike, and each of the three kids rented the same kind of bike, which kind of bike did the 3 kids rent? 4) Another family of 7 spent $79 at the bicycle store. Of the 6 children, three rented the orange bicycles and three rent the yellow tricycles. What kind of bike did their parent rent?

17 16 3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Problem 1: I live about Change the following statements from I live exactly to I live about by rounding each number to the nearest ten. 1) I live exactly 11 kilometers from Roosevelt Elementary School. I live about kilometers from Roosevelt Elementary School. 2) I live exactly 37 miles from the Los Angeles National Forest. I live about miles from Los Angeles National Forest. 3) I study exactly 94 feet from my school library. I study about feet from my school library. 4) I walk exactly 28 kilometers every month. I walk about kilometers every month. 5) I ride my bike for exactly 55 minutes every day. I ride my bike for about minutes every day. 6) I live exactly 83 feet from the bus stop. I live about feet from the bus stop. 7) I live exactly 79 miles from San Clemente Island. I live about miles from San Clemente Island. 8) I live exactly 62 meters from my neighborhood friend. I live about meters from my neighborhood friend.

18 17 3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Problem 2: I live about #2 Change the following statements from I live exactly to I live about by rounding each number to the nearest hundred. 1) I live exactly 187 kilometers from San Diego. I live about kilometers from San Diego. 2) I bicycle around my neighborhood for exactly 568 minutes every month. I bicycle around my neighborhood for about minutes every month. 3) I ride the bus for exactly 797 kilometers every month. I ride the bus for about kilometers every month. 4) I live exactly 923 feet from Grant Elementary School. I live about feet from Grant Elementary School. 5) I ride the Expo Line for exactly 149 minutes. I ride the Expo line for about minutes. 6) I spent exactly 276 minutes at Clover Park this month. I spent about minutes at Clover Park this month. 7) I spent exactly 344 minutes riding the bus to school this month. I spent about minutes riding the bus to school this month. 8) I live exactly 838 feet from Malibu High School. I live about feet from Malibu High School.

19 18 3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Problem 3: I live about #3 Change the following statements from I live exactly to I live about by rounding each number to the nearest tens or hundreds place 1) I have had my skateboard for exactly 483 days. Round to Tens Place: I have had my skateboard for about days. Round to Hundreds Place: I have had my skateboard for about days. 2) I have biked to school for exactly 127 days. Round to Tens Place: I have biked to school for days. Round to Hundreds Place: I have biked to school for days. 3) I live exactly 659 feet from my local bus station. Round to Tens Place: I live about feet from my local bus station. Round to Hundreds Place: I live about feet from my local bus station. 4) I like to spend exactly 792 minutes in a park each month Round to Tens Place: I like to spend about minutes in a park each month. Round to Hundreds Place: I like to spend about minutes in a park each month. 5) There are exactly 921 people who ride my bus. Round to Tens Place: There are about people who ride my bus. Round to Hundreds Place: There are about people who ride my bus. What are the similarities and differences in rounding to the tens and hundreds place? Similarities Differences

20 19 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. Problem 1: The 90-Day Challenge Each bus in Santa Monica and Malibu is going to try to pick up more passengers for 90 days straight. For each bus, figure out how many more passengers the bus will have to pick up over the entire 90-Day Challenge to meet their goal. 1) Bus Route #9 Bus Route #9 is going to pick up 8 more passengers per day. How many more passengers will the bus have to pick up for the entire 90-day challenge? 2) Bus Route #7 Bus Route #7 is going to pick up 4 more passengers per day. How many more passengers will the bus have to pick up for the entire 90-day challenge? 3) Bus Route #8 Bus Route #8 is going to pick up 3 more passengers per day. How many more passengers will the bus have to pick up for the entire 90-day challenge? 4) Bus Route #5 Bus Route #5 is going to pick up 9 more passengers per day. How many more passengers will the bus have to pick up for the entire 90-day challenge? 5) Bus Route #1 Bus Route #1 is going to pick up 2 more passengers per day. How many more passengers will the bus have to pick up for the entire 90-day challenge?

21 20 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. Problem 2: Most Passenger Challenge The city of Santa Monica is challenging each bus driver and their math skills! Each bus driver gets to create their own goal for picking up passengers this time. Whoever gets the most passengers wins! Before you begin, read each bus driver s goal and circle the bus number that you think will get the most passengers. 1) Bus Route #14 GOAL: Pick up 9 passengers for 30 days straight. How many passengers will Bus Route #14 get? 2) Bus Route #7 GOAL: Pick up 5 passengers for 50 days straight. How many passengers will Bus Route #7 get? 3) Bus Route #9 GOAL: Pick up 1 passenger for 90 days straight. How many passengers will Bus Route #9 get? 4) Bus Route #18 GOAL: Pick up 7 passengers for 20 days straight. How many passengers will Bus Route #18 get? 5) Bus Route #1 GOAL: Pick up 8 passengers for 40 days straight. How many passengers will Bus Route #1 get? Which bus won the challenge?

22 21 3.NBT.A.3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. Problem 3: Buying Bulk Tickets The Richardsons are a family of four. It costs them $10 to buy their tickets to ride a Rapid Big Blue Bus. For the following problems, help the Richardsons calculate their expenses for the number of rides they will need to take. 1) If the Richardsons have a week vacation and go to downtown L.A. and back to Santa Monica a couple of times, needing to buy 8 tickets for the entire time. How much will that cost them? 2) The Richardsons buy 4 tickets for each member of their family in a pack for $40 total, and they need to buy 7 packs of them, how much money will they spend? 3) The Richardsons buy 9 tickets a day for 6 days in a row. How much money did they spend? 4) The Richardsons need 2 groups of tickets on Monday, 4 groups of tickets on Tuesday, and 8 groups of tickets on Wednesday. How much money do they need?

23 22 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Problem 1: Walking the Sidewalks with Siblings Younger siblings walk more slowly than their older siblings. In each of the following problems, use a pencil or crayon to draw in the sidewalk lines and shade how far each sibling walked, making sure that your lines and the sections you shade represent the fractions of the problem. 1 1) Suzanne is 6 years old and walked of the sidewalk. 5 James, Suzanne s older brother, is 9 years old and walked 4 5 of the sidewalk. 2) Sheila is 4 years old and walked of the sidewalk. 1 8 Patrick, Sheila s older brother, is 10 years old and walked 6 8 of the sidewalk. 3) Kevonte is 7 years old and walked of the sidewalk. 1 3 Marigold, Kevonte s older sister, is 11 years old and walked 2 3 of the sidewalk. 4) Carl is 2 years old and walked of the sidewalk. 1 6

24 23 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Problem 2: Bassam s Bike Store The bikes in Bassam s bike store are shown below. 1) Count the number of bikes. How many are there? 2) What fraction of the bikes is yellow? 3) What fraction of the bikes is blue? 4) What fraction of the bikes is red? 5) What fraction of the bikes is orange? 6) What fraction of the bikes is green? 5 7) If someone wants to rent of the bikes in the store, can they rent only blue bikes? Why, or 26 why not? 6 8) If someone wants to rent of the bikes in the store, and wants all their bikes to be the same 26 color, which color bikes can they rent? 7) If someone wants to rent half of the bikes in the store, how many bikes in the store do they want to rent?

25 24 3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Problem 3: Missing Bike Spokes The following bicycle wheels need their bicycle spokes before they re assembled! For the following problems, add the number of bicycle spokes designated and then shade the fraction that is shown on the bicycle wheel, with all of the spaces inside the bicycle wheel representing a whole. Add 5 spokes Shade 2 5 of the wheel. Add 6 spokes Shade 5 6 of the wheel Add 8 spokes Shade 6 8 of the wheel Add 9 spokes Add 11 spokes Add 10 spokes Shade 7 9 of the wheel. Shade 3 11 of the wheel Shade 2 10 of the wheel

26 25 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Problem 1: Expo Line Reading Contest Use your knowledge of equivalent fractions to read the following scenario and answer the question below. Amanda and Nicole are friends who signed up for the Expo Line reading contest, where kids are encouraged to read as much as possible while on the train. It takes the same amount of time for Amanda and Nicole to get home from school, but Amanda has 8 stops and Nicole has 12 stops on the way home. One day, Amanda and Nicole took their trains home a little later, closer to rush hour, and couldn t read for the entirety of the ride because the trains were more crowded. The next day, Amanda told Nicole that she read for 6 stops, and Nicole told Amanda that she read for 9 stops. Nicole decided that she read for longer since she read for 3 more stops. Is she right? Defend your answer using mathematics. Work Space: Explanation:

27 26 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Problem 2: Who lives closer? (Same Denominator) For the following problems, decide who lives closer to the bus stop by using the 1-mile boxes to help draw the fractions. Circle the name of the student who lives closer. 1) Isabel and Ray 4 3 Isabel lives of a mile away from the bus stop. Ray lives of a mile away from the bus stop. 5 Isabel: 5 Ray: Who lives closer to the bus stop? 2) Jonas and Ezra 2 6 Jonas lives of a mile away from the bus stop. Ezra lives of a mile away from the bus stop. 8 Jonas: 8 Ezra: Who lives closer to the bus stop? 3) Princess and Alejandra Princess lives of a mile away from the bus stop. Alejandra lives of a mile away from the bus stop. Princess: Alejandra: Who lives closer to the bus stop? **Is there an easy way (or a pattern) to tell which fraction is smaller when both fractions have the same denominator?

28 27 3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Problem 3: Who lives closer? (Same Numerator) For the following problems, decide who lives closer to the bus stop by using the 1-mile boxes to help draw the fractions. Circle the name of the student who lives closer. 1) Latoya and Billy 3 3 Latoya lives of a mile away from the bus stop. Billy lives of a mile away from the bus stop. Latoya: 7 4 Billy: Who lives closer to the bus stop? 2) Rema and Kenia 4 4 Rema lives of a mile away from the bus stop. Kenia lives of a mile away from the bus stop. 5 Rema: 7 Kenia: Who lives closer to the bus stop? 3) Kevin and Cecilia 2 2 Kevin lives of a mile away from the bus stop. Cecilia lives of a mile away from the bus stop. 8 Kevin: 3 Cecilia: Who lives closer to the bus stop? ***Is there an easy way (or a pattern) to tell which fraction is smaller when both fractions have the same numerator?

29 28 3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Problem 1: Bus Schedules Use your knowledge of time and of the busses in Los Angeles to answer the following questions. 1) The #1 Marina Del Rey to UCLA bus picks up passengers at Admiralty & Vista Marina at 8:20am and arrives at the UCLA Hilgard Terminal at 9:22am. How long does the bus ride take? 2) The #2 Santa Monica to Century City/Palms Station Expo Line bus picks up passengers at 4 th & Arizona at 2:43pm and drops them off at Manning & National (Palms Station) at 3:41pm. How long does the bus ride take? 3) The #16 Wilshire Boulevard/Bundy Drive to Marina Del Rey bus picks up passengers at Lincoln & Mindanao at 7:20pm and drops them off at Wilshire & Bundy at 7:55pm. How long does the bus ride take? 4) The #8 UCLA/Westwood & Ocean Park Blvd. picks up passengers at Ocean Park & Bundy at 2:03pm and drops them off at 7 th & Olympic at 2:22pm. How long does the bus ride take? 5) The #10 Downtown Santa Monica to Downtown L.A. bus picks up passengers at 2 nd & Broadway at 12:40pm and drops them off at Main & Alameda at 1:43pm. How long does the bus ride take?

30 29 3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Problem 2: Who biked for the longest? The following students went on day-long bike trips around the Santa Monica District. Who was physically on their bike the longest (not including snacks or breaks)? 1) Sofia started riding her bike at 10:08am along the Santa Monica Pier. At 11:40pm she got off her bike to get a snack. At 12:05pm, she continued biking along San Vicente Boulevard until she arrived at home around 2:45pm. She got off a few times to check out some stores along San Vicente, which added up to 30 minutes off her bike. How long was Sofia riding her bike for? 2) Paul started riding his bike at 4:02pm. He rode his bike to Will Rogers State Park, where he got off at 5:08pm to go on a walk. At 5:34pm he stopped his walk and ran into a friend of his in the parking lot. 6 minutes later, he got back on his bike, and continued riding until he reached the Santa Monica Pier at 7:12pm. How long did he ride his bike for? 3) Lissandro started riding his bike at 8:55am. He rode his bike for 1 hour and 13 minutes, until he got to an ice cream store. The ice cream store was closed, so Lissandro decided to wait until 11am when they opened by riding his bike around the neighborhood. At 11:10am he returned to the ice cream store, where he spent 25 minutes. Then, he rode his bicycle home, and arrived back at 12:14pm. How long did he ride his bike for? rode their bike for the longest period of time.

31 30 3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Problem 3: How much longer? A few of your friends are waiting for the bus. Use the clocks in each problem to help you tell your friend how much longer they have to wait until their bus arrives. 1) Lisa is waiting for the #43 bus that arrives at 2:31pm. How much longer does she have to wait? 2) Hussein is waiting for the #8 bus that arrives at 1:29pm. How much longer does he have to wait? 3) Guss is waiting for the Rapid #12 bus that arrives at 8:59am. How much longer does he have to wait? 4) Nikki is waiting for the #14 bus that arrives at 7:55pm. How much longer does she have to wait? 5) Heather is waiting for the #16 bus that arrives at 2:42pm. How much longer does she have to wait?

32 31 3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiple, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Problem 1: Big Blue Bus Gas Usage Use your knowledge of the Big Blue Bus and of addition and subtraction to answer the following questions about the Big Blue Bus and its gas usage. 1) One Big Blue Bus holds about 378 liters of gas. If a Route #3 bus currently has 129 liters of gas, how many more liters does it need to have a full tank of gas? Draw a picture of the gas tank and label it as a part of your solution. 2) The Route #18 bus holds 378 liters of gas and has one half of a tank of gas left. How much gas is in the tank? Draw a picture of the gas tank and label it as a part of your solution. 3) Gas costs $2 for every liter of gas. How much would it cost to fill up a Big Blue Bus gas tank, if it still holds 378 liters? Draw a picture of the gas tank and label it as a part of your solution.

33 32 3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiple, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Problem 2: Bicycle Weights Use your knowledge of bicycles and of addition and subtraction to answer the following questions about bicycles and how much they weigh. 1) A small child s tricycle has a mass of 3 kilograms, while a kid s bike has a mass of 10 kilograms. How much more mass does the kid s bike have than the tricycle? 2) If 8 friends go on a bicycle ride and each of their bikes has a mass of 12 kilograms, how much mass do all of their bikes together have? 3) Considering a tricycle has a mass of 3 kilograms and a bicycle has a mass of 10 kilograms, which group would have more mass? (1) A group of 16 tricycles (2) A group of 5 bicycles

34 33 3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiple, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Problem 3: Comparing Gas Usage Use your knowledge of liters and addition and subtraction to answer the following questions about gas usage. 1) A bus uses 378 liters of gas in one tank, and a car uses 44 liters in one gas tank. Suppose a bus had 63 passengers over the course of one tank of gas, and a car had 4 passengers over the course of one tank of gas. If you divide the liters of gas by the number of passengers, how many liters of gas did each person use in the bus versus the car? What do you think about your answer? Reflect on it in the lines provided below. Work Space: Answer & Reflection: 2) You want to go on a trip to San Diego. If you drive your car, you will have to buy gas, which costs $2 per liter. Your gas tank holds 35 liters of gas and you will have to fill it up once with gas on your trip to go to San Diego and back. If you don t drive, you could take the bus for $12 each way from Los Angeles to San Diego. Which is the better option? Work Space: Answer & Reflection:

35 34 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Problem 1: Favorite Places to Bike in Santa Monica The following data was recorded about bicyclists favorite places to bike in Santa Monica. People were asked What is your favorite place to bike in Santa Monica? Use the following data to create a bar graph, then label your graph with a title that represents the data. 345 people said around the Santa Monica Pier. 298 people said along Montana Avenue. 120 people said along San Vicente Boulevard. 483 people said the Expo Line Bike Path. 71 people said they liked to bike in their neighborhood ) How many people were interviewed in the survey? 2) How did you decide how to scale your vertical axes? 3) How many more people liked biking along the Expo Line Path than the least popular path?

36 35 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Problem 2: Santa Monica City Planner You are a city planner for Santa Monica and are deciding how to spend $1,000. Use the information in Appendix 3A to decide how you would like to spend the money. On a separate sheet of paper, add up the cost for the things you choose to buy and write down the total cost for each category below. Parks - $ Bicycling - $ Busses - $ Sidewalks - $ Use the total amounts above to create a bar graph that shows your data ) 2How much money did you spend all together? Did you have money leftover? If so, how much? 0 2) Compare and contrast your bar graph with a partner and consider these questions: Compare your graph with someone else in the class. How much did they spend on each category? How much more or less money did they spend than you on each category? Where did your partner spend the most money? Where did they spend the least? How might your partner s city look different than yours? What did your partner value when making their choices? What did you value?

37 36 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Problem 3: How do we get to school? As a class, write down the different categories for the transportation that students use to get to school, and collect data for the number of students in the class that use those different categories by writing the total number of students on the board. Then, use Appendix 3B to individually draw a bar graph that represents the data on the board, and answer the questions below. 1) Were students allowed to answer for more than one category? How did your class come to this decision? 2) What two categories had the largest difference between them? What was the difference in number of students who used that kind of transportation? 3) How many more people used the most common form of transportation compared to the second most common form of transportation? 4) What is the total when you add up all of the categories? What does that number represent? 5) How do you think your data might change by the time your class reaches high school, when students can drive themselves to school? Be specific.

38 37 3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in an appropriate units whole numbers, halves, or quarters. Problem 1: Half the Class s Shoes Directions for the Teacher: Split the class into two separate groups and give each group a tape measure. Also distribute Appendix 3C to each student. Directions for the Students: As a group, take turns using the tape measure (each student should use the tape measure once) to measure everyone s shoes in the group once. Measure the length of the shoe to the nearest ½ inch, and record the data using the line plot on Appendix 3C by marking an x in the appropriate horizontal category. Then, answer the questions below. (Set up Appendix 3C before beginning.) 1) What was the most popular shoe size? 2) What was the least popular shoe size? 3) How did you ensure that students only had their shoe measured once? Are you sure that you included everyone? How could you check? 4) What are the similarities and differences between bar graphs and line plots?

39 38 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units.) Problem 1: The Different Areas of a Bus Use the diagram of a Big Blue Bus below, where each square represents a square foot, to answer the following questions. The light gray area represents where people can walk on the bus. The white area represents where passengers can sit on the bus. The dark gray area represents where the bus driver sits. The medium gray area represents the handicapped seating area. Find the following solutions without counting the unit squares one by one. 1) How large is the seating area in a Big Blue Bus in square feet? 2) How large is the driver s seat in a Big Blue Bus in square feet? 3) How large is the bus handicapped seating area in a Big Blue Bus in square feet? 4) How large is the walking area in a Big Blue Bus?

40 39 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units.) Problem 2: View of the Street The diagram below is an overhead view of a street block in Santa Monica, where each square represents a square meter. are used for the road? // ::: == = Street Businesses = Sidewalk = Bicycle Lane = Car Parking = Road Without counting each square individually, answer the following questions about the areas of a street. 1) In a Santa Monica Street, how many square meters do street businesses use? 2) How many square meters do sidewalks take up? 3) How many square meters do bicycle lanes take up? 4) How many square meters are reserved for parking? 5) How many square meters

41 40 3.MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units.) Problem 3: Bike Friendly Streets The boxes below represent some of the streets in Santa Monica that have bike lanes. San Vicente Blvd. Akta Ave. Montana Ave. Washington Ave. California Ave. Arizona Ave. Broadway Michigan Ave. 16 th Street 14 th Street 11 th Street 7 th Street 6 th Street Main Ave. Ocean Avenue Ocean Front Walk 1) Each square represents a square city block in Santa Monica. If the green and shaded squares represent city blocks that have bike lanes, how many city blocks have bike lanes? Describe your strategy to find the answer below. 2) Without counting all of the white squares, find out how many city blocks in this area do not have bike lanes.

42 41 3.MD.C.7 Relate area to the operations of multiplication and addition. Problem 1: The Areas in Our Streets Answer the following problems based on your knowledge of area. 1) The City of Santa Monica plans to put in a new bike lane on Santa Monica. They want the bike lane to be 2 meters wide and 32 meters long. How many square meters do they need to set aside for the bike lane? 2) A new set of bike racks on Broadway in downtown Santa Monica takes up about 15 feet along the sidewalk and is 7 feet wide. How many total square feet does the bike rack take up on the sidewalk? 3) A can of bicycle lane paint is enough to paint 100 square meters of bike lanes. a) If Montana Avenue s bike lanes are 2 meters wide and 40 meters long for each block, how many cans of paint will they need to paint one block? b) Draw a picture below of 4 blocks of Montana Avenue s bike lanes, and then find out how many cans of paint the city will need to repaint the bike lanes.

43 42 3.MD.C.7 Relate area to the operations of multiplication and addition. Problem 2: Designing a Street Use colored pencils or crayons to answer the questions below and then design your ideal street. The City of Santa Monica has hired you to build a street for them! You can put in car lanes, bus lanes, sidewalks, bike lanes, benches, trees, and anything else you think belongs on your street. The street is 15 meters wide and 20 meters long. 15 meters 20 meters 1) How large is your street in square meters? 2) Draw a grid onto your street to show each square meter. 3) Decide what type of spaces will be on your street (car lanes, bus lanes, trees, etc.) and create a key below with the colors you will use for each type of space. Then, color in your street to show the design, and write down how many square meters each type of space occupies.

44 43 3.MD.C.7 Relate area to the operations of multiplication and addition. Problem 3: How Big Is the Street? Below is an image of the street, where the green area represents the bike lanes, and the grey area represents the car lanes, and every square represents a square meter. 1) How large is the street in square meters? Use an equation to explain your thinking. 2) One possible way of solving is to find the area of the car lanes and then find the area of the bike lanes and then add them together. Find the total are of the street in square meters using this strategy and show your work below. 3) Another possible way of solving is to see the image as 11 columns and 6 rows of squares. Find the total area of the street in square meters using this strategy. 4) Which method is easier? Which method makes more sense to you?

45 APPENDIX 3A Santa Monica City Options 3.MD.B.3 Bench - $25 Television in the Bus - $130 Breeze Bike Station - $ 140 Sidewalk Bench - $30 Soccer Field - $500 Reclining Seats - $120 Bicycle Lane - $90 Swings - $60 Basketball Court - $340 Phone Chargers in the Bus - $45 Bike Locks - $70 Sidewalk Mural - $220 Playground - $395 Rapid Bus Lanes - $80 Tree - $5 Flowers - $5 Math in My World: K-5 Common Core for Angeleno Students Park Costs Bus Costs Bicycling Sidewalks

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47 3.MD.B.3 Math in My World: K-5 Common Core for Angeleno Students APPENDIX 3B How We Get to School Graph

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49 APPENDIX 3C Line Plot of Our Shoes 3.MD.B.3 Create a line plot below with the space in between data points being ½ inch. First, find out who has the longest shoe size and the shortest shoe size in class. Then, label those points on either end of the line. Finally, fill in every ½ inch in between before you measure your peers shoes. Math in My World: K-5 Common Core for Angeleno Students

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51 NOTES

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