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5th GradeMeasurement Resources5.MD.1Grade 5Measurement Unit OverviewConcepts and StandardsTimeMetric Measurement (5.MD.15 daysCustomary Measurement (5.MD.1)4 daysAdditional ResourcesStandardsNC.5.MD.1 Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system.Teacher NoteOverview This unit was designed to address mathematics concepts embedded in 5.MD.1 in North Carolina. While the Grade 5 standards do not call for students to measure and estimate, this unit includes multiple hands-on experiences for students to develop measurement skills, and also develop a deep understanding of the various units of measure they are expected to work with. The tasks posed include multi-step situations that include both whole numbers and fractions. This unit is best done after students have done ample work in Grade 5 with whole number operations and fractions. Each lesson includes the following phases: Ten Minute Math- an activity focused on mathematical reasoning and computationExplore- a task that students should explore in pairs or small groups with minimal direction from the teacherExplain- a discussion of the explore taskElaborate/Extend- follow up tasks or mathematics activities; most are aligned to the topic being taught during the day, but some activities may be review of previously covered conceptsEvaluate- suggestions for assessment, including the Elaborate/Extend activity or an additional exit ticket Lesson: 1Concept: Metric LengthStandard(s):5.MD.1Academic Language and Vocabulary:Millimeter, centimeter, measure Materials: centimeter rulers that are marked in millimeters. Ten Minute Math (Engage) Counting MoneyI have 23 objects with the same value in my pocket. What is the value of my collection if my objects are:Pennies?Dimes?$1 bills?$10 bills? Ask students, “Look at the various answers. What do you notice?”“What do you notice about the value of the 3 in each of the answers?”“What influences the location of the 3 in each of your answers?”If time permits pose a follow up task with the same questions but involving 75 objects. ExploreDistribute the meter sticks and centimeter rulers to students. Also distribute the activity sheet- “Measuring Lengths in Metric Units” to students. Allow students time to find objects in the room and measure them in centimeters as well as in millimeters. As students are working, observe their process of measuring and pose questions such as:How are you measuring the length of that object? How do you know your measurement is accurate?What do you notice about the measurements of the same object in millimeters and centimeters? ExplainBring students together and make a two column table similar to the one on the activity sheet they recorded on. Have students share with you the objects that they measured as well as the measurements. The column should include data in which the measurement of the same object is 10 times greater for millimeters compared to centimeters. If the data does not reflect that as a class measure the length of a few objects in both millimeters and centimeters. During the discussion make sure you have students discuss the following questions:How did you know your measurements were accurate? What relationship do you notice between the measurements in millimeters and centimeters of the same object? Extend/ElaborateAllow students to look at page 2 of “Measuring Lengths in Metric Units.” Students may either complete these tasks with a partner or by themselves. If students need additional support pull students in small group to ask them questions to guide their thinking. Other activities or math games that could be included:24 Game- Product Compare- Students use number cards marked 0 through 9. Each student takes 4 cards from the deck and arranges them to make 2 2-digit numbers to get the largest possible product. They then find the product on paper and then compare them. The person with the largest product wins a point. The game continues with new cards. Alternative- try to get the smallest product. Quotient Compare- Students use number cards marked 0 through 9. Each student takes 4 cards from the deck and arranges them to make a 3-digit number and 1-digit number to get the largest possible quotient. They then find the quotient on paper and then compare them. The person with the largest quotient wins a point. The game continues. Alternative- try to get the smallest quotient. Evaluation/Assessment The work on the activity sheet could be collected as an assessment. A possible exit ticket could also be: Saul jumped 98 cm, Yani jumped 89 cm, and Ronald jumped 66 cm. Was their actual combined distance greater than 2,500 mm? How far was their combined distance from 2,500 mm? (10 mm = 1 cm). Measuring Lengths in Metric UnitsComplete the table below. Approximate measurements to the closest centimeter. ObjectLength (cm)Length (mm) Write 1 or 2 sentences about how you measured the length of one of your objects. Be specific about how you know that you measured accurately. Look at the centimeter and millimeter columns. What do you notice about the relationship between centimeters and millimeters for each of the objects? What is the difference between the longest and shortest objects in centimeters? What is the difference between those objects in millimeters? Apply your understanding of centimeters and millimeters to solve the following tasks:The width of a paper towel is 25 centimeters. How wide is the paper towel in millimeters? (1 cm = 10 mm). A case of juice boxes holds 6 juice boxes lined up in a row. If each juice box is 12 cm wide how wide is the juice box in centimeters? How wide is it in millimeters? (1 cm = 10 mm). In the gym the students in the table all competed in the standing long jump. StudentJump (cm)Devonte85 cmTyreisha76 cmTaylor79 cm Selena83 cm How long was the longest jump in millimeters? How long was the shortest jump in millimeters?In millimeters what was the difference between the longest and the shortest jumps? For a school project the class needs 30,000 centimeters of yarn. Based on the following information does the class have enough yarn? How far is their amount of yarn from the needed 30,000 centimeters?Yellow- 8 packs with 1,376 centimeters in each pack. Green- 9 packs with 4,216 millimeters in each pack. Blue- 76 packs with 68 centimeters in each pack.Orange- 8 packs with 1,254 centimeters in each pack. Lesson: 2Concept: Metric Length Standard(s):5.MD.1 Academic Language and Vocabulary:Millimeter, centimeter, measure Materials: centimeter rulers that are marked in millimeters. Ten Minute Math: Broken CalculatorYour target number is 3,523. Write an equation that equals 3,523 using the following conditions: 1) you may not use the number 3, 2) you must use at least two multiplication and two addition signs. In order to make this more difficult you could require students to use all 4 operations. Possible solutions:6 x 500 + 80 x 5 + 120 + 2 + 1 = 3,523 2 x 1,500 + 500 + 10 x 2 + 3 ExploreGive students the activity sheet “Longer or Shorter than a Piece of Paper” and either a ruler or meter stick that is marked in centimeters. Give students 10 minutes to find 10 objects around the classroom. They need to find 5 objects that are longer than a Piece of Paper and 5 objects that are shorter than a Piece of Paper. They should measure each to the nearest centimeter. As students are working observe them and pose questions such as:What process are you using to measure accurately?How do you know that the object is shorter than or longer than a piece of paper? ExplainBring the students together to discuss as a class what they measured and found. Use small group talking strategies such as turn and talk to have students fully engage in talking about the objects, their measurements, and the processes used to measure the lengths of objects. During the discussion pose questions such as:How do you know that your measurements were accurate?What are the important things to focus on when you measure length? Extend/ElaborateHave students look at the rest of the activity sheet “Longer or Shorter than a Piece of Paper.” If needed ask students to share ideas about how they may begin the first problem. During this phase you may have small groups of students to work on the activity sheet. Other possible center or workshop activities include Multiplication or Division activities from lesson 1 or the following:Drawing rays- Students need a 6-sided number cube, a pencil and their math notebook. Students roll the number cube and draw a ray that is the length of the number they roll in centimeters. They should label the first ray AB with 2 points. As students keep rolling they continue to draw rays and they decide to make the rays either parallel or perpendicular to the last ray that they drew and label them. Example: Students roll a 4 and then roll a 3. They draw a ray that is 4 cm long and one that is 3 cm long. The rays can either be parallel or perpendicular to each other. Drawing angles- Students need a 6-sided number cube, a protractor, and a set of number cards. Students roll the number cube and draw a ray that is the length of the number they roll in centimeters. Students then pull 2 number cards and make the largest number that they can. They then use the first ray that they drew and draw an angle that is the measure of the value of the number cards. Example: Students roll a 5 and draw the cards 7 and 4. They would draw a ray that is 5 cm long and then draw a 74 degree angle that includes the ray. Alternative: You can have students make the largest number possible and subtract it from 180 in order to do the activity with obtuse angles as well. Evaluation/Assessment The activity sheet can be used as an assessment. A possible exit ticket could also be: Tanya jumped 78 cm, Brianna jumped 95 cm, and Rita jumped 86 cm. Was their actual combined distance greater than 2,600 mm? How far was their combined distance from 2,500 mm? (1 cm = 10 mm). Longer or Shorter than a Piece of PaperMeasure objects and estimate to the nearest cm. ObjectLength (cm)Length (mm) Longer or Shorter than a Piece of PaperWrite a sentence to explain how you know you measured the lengths correctly. What is the difference in lengths between your longest object and your shortest object in millimeters? If you lined up the 3 longest objects in a line how long would that line be in millimeters? If you lined up the 3 shortest objects in a line how long would that line be in centimeters? More Problem Solving with Length In the gym the students in the table all competed in the standing long jump. StudentJump (cm)Bess71 cmHarriett 75 cmMaria69 cm Paola 74 cm How long was the longest jump in millimeters? (1 cm = 10 mm). How long was the shortest jump in millimeters?In millimeters what was the difference between the longest and the shortest jumps? At the craft store there are a variety of ribbon. Vicki needs 587 cm of ribbon. Using the list of packages below determine how she could buy enough ribbons if she buys between 2 and 9 packs of each color. (1 cm = 10 mm). ColorLength per packet Red29 cm Blue585 mm Green345 mm Yellow472 mm Lesson: 3 Concept: Metric Weight Standard(s):5.MD.1Academic Language and Vocabulary:Grams, kilograms, milligrams Materials: metric weights (grams kilograms)Ten Minute Math: Broken CalculatorYour target number is 1,555. Write an equation that equals 1,555 using the following conditions: 1) you may not use the number 5, 2) you must use at least two multiplication and two addition signs. In order to make this more difficult you could require students to use all 4 operations. Possible solutions:3 x 400 + 300 + 11 x 3 + 22 ExploreDistribute weights and the “Measuring Mass” activity sheet to students. Have students find 5 objects that weigh less than a kilogram and 5 objects that weigh more than a kilogram. As students work explore and pose questions such as:Do you think that object weighs more or less than a kilogram? Why or why not? How did you make sure that you accurately measured the weight of that object? ExplainBring students back together and discuss their work measuring objects. Facilitate the discussion by posing questions such as:For what objects was your estimate correct? How did you make sure that you accurately measured the weight of that object? Transition by asking students, “If we are measuring the weight of this pencil should we measure it in grams or kilograms? Explain to your neighbor/table and justify your thinking.”Extend/ElaborateAllow students time to work on the rest of the “Measuring Mass” activity sheet. If needed, pull students in small groups to ask questions and support them while they work on it. Other center/workshop activities could include ones from Lessons 1 and 2 in this unit or the activity below. Paper Clip Grab- Students need access to a large container of paperclips, a scale to measure in grams, and tools to record work. Students should grab a handful of paperclips and weigh them. Students should then complete the following by filling in the blanks and choosing the correct choice: . 1 handful was _____ paper clips. 25 handfuls would be __________ paper clips. 25 handfuls of paper clips would be _____ greater than/less than 800 grams. Evaluation/Assessment The activity sheet can be used as an assessment. A possible exit ticket could also be: You grab 39 grams of paper clips each time. If you grab the same amount 17 times how many paper clips would you grab? How much less than 1 kilogram would the entire group of paper clips weigh? (1 kg = 1,000 g). Measuring Mass ObjectMore or Less than a Kilogram (estimate)Actual Mass (grams) More or Less than a Kilogram (actual)List five items in the classroom that should be measured in kilograms instead of grams. Problem Solving with Metric MassThere are 4 books on the shelf that weigh a total of 4 kilograms. One book weighs 578 grams. The second book weighs 439 grams. The third book weighs 654 grams. How much does the last book weight? Two small dogs are on a large scale at the veterinary office. Their combined weight is 5 kilograms. If each dog weighs at least 2,000 grams and neither dog’s weight is a multiple of 10 how much could each dog weigh? Find at least 3 answers that work. Solve each task and show your work. Use the symbols >, <, or = to make each statement true. (1 kg = 1,000 g). 3 kilograms _________ 2,278 grams + 719 grams2 kilograms _________ 80 groups of pencils that weigh 25 grams each 7 kilograms _________ A pile of dirt that had 9 kilograms but had 2,050 grams removed2 kilograms _________ 12 groups of markers that weigh 16 grams each. 4 kilograms _________ 94 containers of juice that weigh 36 grams each. At a candy store candy is sold by the kilogram. Marco has enough money to buy up to 3 kilograms worth of candy. How much of each type of candy does he buy if he buys between 3 to 9 packs of each kind of candy. (1 kg = 1,000 g). Gumdrops: 137 grams per pack Gobstoppers: 358 grams per pack Sour Patch Pieces: 276 grams per pack How many grams away from 3 Kilograms is Marco’s candy? Write a sentence to explain your thinking. Lesson: 4 Concept: Metric Capacity Standard(s): 5.MD.1 Academic Language and Vocabulary:Milliliter, LiterMaterials: 2 Liter bottle, containers that will hold a Liter of water that are marked in milliliters Ten Minute Math: Examining 5 x ?Show the following equations to students in the order they appear below. 5 x ? = __ 5 x ? = __ 10 x ? = __ Have students draw pictures for each of the equations and find the solutions. Students should discuss with their partners and write about how each of the equations relates or compares to the equation before it. ExploreProvide students with a Liter of water in a container. Ask students, “If you had to divide this water evenly among yourself and 7 friends how much water would each person get? Tell them 1 L = 1,000 mL. Allow students time to work on the problem using whatever strategy they wanted. Even if students know the answer to 1 L or 1,000 mL divided by 8 they should use the water to explore and solve the problem. If students finish this problem while others are still working give them the task of sharing 1 L of water between themselves and 5 friends (6 people). ExplainBring students together and facilitate a discussion with questions such as:“How did you solve the problem of sharing a Liter of water?”“What did you notice about the relationship between milliliters and Liters?” “What mathematics did you do while working on that problem?”“Is there an equation we can write for the problem we solved?” 1,000 mL divided by 8Show students the following strategies and ask them to describe each one.Juan’s strategy Devonte’s strategy 1,000 divided by 8 1,000 divided by 8 8 x 100 = 800 1,000 - 800 = 200 8 x 1 = 88 x 10 = 80 200 - 80 = 120 8 x 2 = 168 x 10 = 80 120 - 80 = 40 8 x 3 = 248 x 5 = 40 40 - 40 = 0 8 x 4 = 32 8 x 5 = 40 It took me 100 + 10 + 10 + 5 groups of 8 to get 1,000. 8 x 50 = 400 so 8 x 100 = 800 I need 200 Each person gets 125 mL of water. 8 x 2 = 16 so 8 x 20 = 160 I need 40 8 x 5 = 40 so I have 800 + 160 + 40 = 1,000 8 x 100 + 8 x 20 + 8 x 5 = 1,000 so 8 x 125 = 1,000Extend/ElaborateDuring this phase students can work on a variety of activities:“Problem Solving using Metric Mass and Capacity” activity sheetCenter Activities from Lessons 1 and 2 Evaluation/Assessment The “Problem Solving using Metric Mass and Capacity” activity sheet can be used as an assessment. Copy of Juan’s and Devonte’s strategies Problem Solving with Metric Capacity A 2 Liter container currently holds 1 Liter and 327 milliliters of juice. Mrs. Rodriguez takes 576 milliliters out and puts it in a cup. The remaining juice is divided evenly between 3 students. How much juice does each student get? Is there any remaining juice? If so, how much? (1 Liter = 1,000 milliliters). A 5 Liter container holds 4 Liters and 211 milliliters of water. Bernie takes out 345 milliliters of water. The rest of the water is divided evenly among 7 students. How much water does each student get? Is there any remaining water? If so how much? (1 Liter = 1,000 milliliters). In class Nina and Taylor are talking about the prefixes they are learning about in measurement. Nina: There are 1,000 grams in a kilogram so I think kilo means 1,000. Taylor: If I have 3 Kiloliters how many Liters is that? Pretend you are Nina. Write an equation and write a sentence about how you would teach Taylor how to find the answer.Sarah jumps from the line in the gym and measures her jump at a distance of 72 cm and 6 mm. Taylor jumps and measures her jump at a distance of 70 cm and 27 mm. Who jumped the furthest? What was the difference in the two jumps? (1 cm = 10 mm). At the grocery store the following packages were weighed. There was a problem with the scale though so the weight was recorded as 1 kg and the rest of the mass was displayed in mg. Put them in descending order according to mass. (1 kg = 1,000 g, 1 g = 1,000 mg).PackageMassPack of Salmon Filets1 kg and 1,215 mg Pack of T-bone Steaks1 kg and 1,251 mgPack of Chicken Breasts1 kg and 1,300 mg Pack of Pork Chops1 kg and 1,220 mg For the Fall Festival, Mrs. Guerrero’s class had a large bowl with 1 L and 322 mL of punch. They scooped out 437 mL of punch for the teacher and then shared the rest of the punch equally among 7 students. How much punch did each student get? Was there any leftover punch? If so how much? (1 L = 1,000 mL). Lesson: 5Concept: Problem Solving with Metric UnitsStandard(s): 5.MD.1 Academic Language and Vocabulary:Materials: activity sheetsTen Minute Math: Number TalkPost the following equations on the board in the order that they appear.2 - 2/4 = __ 2 ? - 2/4 = __ 2 ? - 1 2/4 = __ Have students create representations for each of the equations and find the solutions. Students should discuss with their partners and write about how each of the equations relates or compares to the equation before it. ExploreProject the following task for students:“A worm is crawling down the street. It crawls a total of 4 meters and 56 cm. The worm takes a lot of breaks though and crawls the whole distance in 4 equally long lengths. Draw a picture to represent the story. How long was each length in centimeters? How long was each length in millimeters? 1 m = 100 cm.” Allow students time to work on this task. As they work observe them and ask them questions such as:“What did you draw to represent the problem?”“What do you need to find the answer?”“How do you know your strategy will work?” If students finish early feel free to give them the following task:If a different worm was crawling the same total distance but crawled the same distance of 4 meters and 56 cm but, in 8 equally long lengths how long was each length in centimeters? How long was each length in millimeters?ExplainAllow students to share their responses to the task. Facilitate the discussion with questions such as: “What did you draw to represent the problem?”“What do you need to find the answer?”“Once you found the length in centimeters what did you do to find the length in millimeters?” Extend/ElaborateDistribute to students the activity sheet “Problem Solving with Metric Units.” During this phase students may work on the activity sheet, activities from lessons 1-4 in this unit or other measurement activities. If students need support with the activity sheet, pull small groups and support them by asking them questions to support their reasoning. Evaluation/Assessment The “Problem Solving with Metric Units” activity sheet can be used for an assessment. Problem Solving with Metric Units Bracelet StringSally has various colors of string to make bracelets. She needs to know how much string she has in centimeters and millimeters though to plan her next set of bracelets. (1 cm = 10 mm). Color and LengthTotal Length in cmTotal length in mm3 packs of red:1 meter and 45 cm in each pack7 packs of yellow:3 meters and 86 cm in each pack6 packs of green:2 meters and 24 cm in each pack8 packs of blue:2 meters and 74 cm in each pack.7 packs of white:2 meters and 68 cm in each packWhat do you notice about the relationship between the total length in cm and mm for each color? Party DrinksFor the class party the following drinks are there. Find the total amount of each drink. (1 L = 1,000 mL). DrinkCapacity per ContainerNumber of ContainersTotal Amount of Drink Sprite3 L and 214 mL 3Fruit Juice4 L and 578 mL2Coca Cola7 L and 186 mL1Lemonade1 L and 787 mL5How many total milliliters of drink are there for the class party? How much more is there of the drink with the most amount compared to the drink with the least amount?If each of the drinks is going to divided into 3 separate containers how much of each drink will be in the containers? Lesson: 6 Concept: Customary Length Standard(s): 5.MD.1 Academic Language and Vocabulary:foot, inch, length, ruler, yard, Materials: Yard stick or rulers that are marked to at least the ? of an inch. Ten Minute Math: Number Talk Display the following tasks in the order that they appear.36 x 40 = __ 36 x 45 = __ 36 x 46 = __ Students should find the answers and discuss with their partners and/or write about how each of the equations relates or compares to the equation before it. ExploreDistribute the “How far can we…?” activity sheet. Make sure that students have access to yardsticks or rulers marked to at least the fourth of an inch. As students work ask questions such as:What is your process of measuring?How do you know that your measurement is accurate? When you measured to the nearest fourth of an inch how did you use your yardstick/ruler to help you? ExplainProvide opportunities for students to share their data either using a Google spreadsheet, sticky notes, or by recording their answers. Do this for at least 1 activity. This data will be needed by students in the Elaborate/Extend phase. Have students briefly share and/or discuss the answers to the following questions:What was your process of measuring?How do you know that your measurement is accurate? When you measured to the nearest fourth of an inch how did you use your yardstick/ruler to help you? Elaborate/Extend During this phase students can continue to measure if they did not get to every activity or complete the “Changing Between Units” activity sheet, “Close to 99,” or any of the activities from earlier in the unit. If students need support on the “Changing Between Units” activity sheet you can work with small groups by asking guided questions. Close to 99: In pairs or groups of 3, students use 1 set of Number Cards marked 0-9 with Wild Cards if possible. Students turn over 6 cards face up and will use 4 of them to make a 3 digit number and 1 digit number. The goal is for students to make a division problem that will have a quotient as close to 99 as possible. The score for each round is the difference between the quotient and 99. The goal is to get the lowest score. Evaluate/AssessmentThe “Changing Between Units” activity sheet can be used as an assessment.If you would like to use an exit ticket, pose this task:The yellow rope is 3 yards, 2 feet, and 8 inches long and the blue rope is 3 yards, 3 feet, and 1 inch long. How long is each rope in inches? Which rope is longer? How much longer is it compared to the other rope? How Far Can We ...?You are going to do the activities below in the table and determine the distance for each. Measure to the nearest fourth of an inch. ActivityDistance 1Distance 2Distance 3Greatest DistanceTotal DistanceStraw tossStanding jump (2 legs)Standing jump (1 leg)Blowing a paper ball Longest strideThumb to pinky stretch In the space below, find the total distance in feet of two of your measurements. (1 ft = 12 inches). Changing Between Units There are 3 pieces of rope available at the hardware store. The yellow rope is 5 ? feet long. The white rope is 6 and ? feet long. The green rope is 6 feet and 5 inches long. (1 ft = 12 inches). How long is each rope in inches?Which rope is the longest? How much longer is it than the second longest rope? If all of the ropes were placed end to end how many inches long would they be?The table below needs to be completed in order to determine the total length of different types of tape at Target. Fill in the missing blanks. (1 yard = 3 feet, 1 foot = 12 inches). ObjectLengthLength in Inches Duct tape2 yardsPainter tape3 yards, 2 feet, 2 inchesMasking Tape2 yards, 1 foot, 4 inchesOne sided scotch tape3 yard, 2 feet, 9 inchesTwo sided scotch tape2 yards, 2 feet, 8 inches Lesson: 7 Concept: Customary Length Standard(s): 5.MD.1 Academic Language and Vocabulary:Inch, foot, measure, ruler, yard, Materials: yardstick or ruler marked at least to the ? of an inchTen Minute Math: Broken CalculatorYour target number is 4,178. Write an equation that equals 4,178 using the following conditions: 1) you may not use the numbers 4 and 1, 2) you must use at least two multiplication and two addition signs. In order to make this more difficult you could require students to use all 4 operations. Possible solutions:2,000 x 2 + 50 x 3 + 28 2,000 x 2 + 50 + 50 + 50 + 20 x 4 -2 ExploreProvide students with the “Track and Field Meet” activity sheet.As students are working observe them and facilitate by asking the following questions: What steps are you using to change units of length? How do you know that your answer is correct? ExplainFacilitate a class discussion about students’ work on the “Track and Field Meet” tasks. Have students describe their strategies for changing the units of length.Also have the class discuss the following questions: What steps are you using to change units of length? How do you know that your answer is correct? Extend/ElaborateIn this phase students may complete the activity sheet, “Which Unit Makes More Sense?” If students need support with this activity you may pull a small group and use questions to facilitate their work.Also in this phase students may work on other activities from earlier in this unit, especially “Close to 99” and “How Far Can We…? From Lesson 6. Evaluation/Assessment The activity sheets can be used as an assessment. If you would like to give an exit ticket pose:On the high jump Nick jumped 1 yard, 2 feet, and 8 inches. Xavier jumped 5 feet, and 9 inches. Paul jumped 4 feet and 17 inches. How many inches high did each of them jump? Who jumped the highest? Track and Field MeetThe high jump bar is currently 62 inches off of the ground. In the next round the high jump bar will be 65 inches off the ground. Based on the table below which people will likely be able to jump over the bar for each round? (1 yard = 3 feet, 1 foot = 12 inches).NameTypical Jump Typical Jump (inches)Higher than the Bar at 62 inchesHigher than the Bar at 65 inchesSydney 1 yard, 2 feet, 2 and 1/2 inchesMarissa1 yard, 1 foot, 15 inchesTyrette3 feet, 29 inchesNina2 feet, 39 and 3/4 inchesKatie4 feet, 17 inchesA 30 yard race was run by a few different people. Using the times below determine how far each person ran per second. Name Time to run 30 yards Feet run in one secondInches run in one secondMarco8 seconds Stephan7 secondsVictor9 secondsGeorge6 seconds Tyrone5 secondsWhich Unit Makes More Sense? Does it make more sense to measure the following objects in inches, feet, or yards? ObjectUnitEstimateActual measurementMeasurement in inchesWidth of paper clipLength of paper clipLength of a large bookWidth of a large bookDistance from your desk to the classroom doorWidth of hallway Height of table or deskDistance from shoulder to pinkyDistance from elbow to pinky Width of your shoeLength of your shoe Length of a piece of paperSelect 2 lengths from the table. Describe your process of how you determined which unit to use to measure those lengths. Lesson: 8 Concept: Customary Mass Standard(s): 5.MD.1 Materials: Objects around the classroom with various massesObjects that weigh about a pound (e.g., canned vegetables) Scale that measures in pounds Academic Language and Vocabulary: mass, ounce, pound, unit Ten Minute Math: Number TalkPost the following equations on the board in the order that they appear.5 2/4 - 2/4 = __ 5 2/4 - 2 2/4 = __ 5 ? - 2 2/4 = __ Have students create representations for each of the equations and find the solutions. Students should discuss with their partners and write about how each of the equations relates or compares to the equation before it. ExploreGive students the “More or Less than a Pound” activity sheet.As students are working observe them. You may need to facilitate a discussion about how they would find the difference between the mass of objects and 1 pound as well as the mass of objects and 2 pounds. As students are working check for understanding by asking:“How do you know if this object has a mass greater than or less than 1 pound?” “Without measuring the mass can you estimate whether it is greater than or less than a pound?”“How do you know your measurements are accurate?” ExplainBring the students together to share some of their objects and their work in the table. Focus the discussion on how to determine the difference in the mass of the objects from 1 pound. Facilitate the discussion by asking questions: “What strategies did you use to determine the difference in the mass of <object> and 1 pound?”“How do you know your measurements were accurate?” Extend/ElaborateDuring this phase students should complete any of the work on the “More or Less than a Pound” activity sheet as well as the “Solving Problems about Length and Mass” activity sheet.If students need guidance you may work with students in small groups and support them by posing guided questions.Also during this phase students may work on the game “Close to 99,” “Close to 2,500” or other activities from earlier in this unit. Close to 2,500: In pairs or groups of 3, students use 1 set of Number Cards marked 0-9 with Wild Cards if possible. Students turn over 6 cards face up and will use 4 of them to make a 3 digit number and 1 digit number. The goal is for students to make a division problem that will have a quotient as close to 99 as possible. The score for each round is the difference between the quotient and 99. The goal is to get the lowest score. Evaluation/Assessment The “Solving Problems about Length and Mass” activity sheet can be used as an assessment. If you would like to give an exit ticket you can pose this task:Mrs. Murray needs 5 pounds of ham to make sandwiches for the party. If she already has 2 pounds and 7 ounces how many more ounces does she need to buy? More or Less than a Pound Find objects around the classroom. Measure them to determine their mass. Complete the table.ObjectMassGreater than a Pound?Difference from a Pound in Ounces (1 lb = 16 ounces). Find one of your objects that has a mass of more than 1 pound. Does that object have a mass more than 2 pounds? How much less or more is the mass of the object than 2 pounds? Write a sentence to explain how you determined the difference in the mass of the object and 2 pounds. Solving Problems about Length and Mass For each problem represent your work with an equation and show how you found your answer.Sylvia and Marquel have a large box of pencils that has a mass of 7 pounds and 3 ounces. They want to equally divide the pencils between themselves and their friend Tim. How many ounces will be in the group of pencils that each of them will receive? (1 pound = 16 ounces). Mrs. Turner has a bag of yarn for an art project. She has 6 feet and 3 inches of yellow yarn and 7 feet and 5 inches of blue yarn. She wants to share each color among the 7 groups of students in her class. How many inches of each color will each group get? If there is leftover yarn how much of each color will be left? (1 foot = 12 inches). Stevie gets to ride the roller coaster when he is 1 yard and 2 feet tall. Current Stevie is 1 yard and 8 inches tall. How much more does Stevie need to grow in order to be able to ride the roller coaster? (1 yard = 3 feet, 1 foot = 12 inches). To make sandwiches for the class, Mrs. Copeland needs 4 ounces of turkey and for each of the 22 students in her class. 8 ounces of turkey costs $2. How much will she spend on turkey? (1 pound = 16 ounces). Lesson: 9Concept: Customary Capacity Standard(s): 5.MD.1 Materials: measuring tools marked in cups, pints, quarts, half-gallons and Gallons Academic Language and Vocabulary: cup, gallon, half-gallon, pint, quartTen Minute Math: Number Talk Post the following equations on the board in the order that they appear.9 x ? = __ 9 x ? = __9 x 1 ? = ___ Have students create representations for each of the equations and find the solutions. Students should discuss with their partners and write about how each of the equations relates or compares to the equation before it. ExploreGive students the “Making Sense of Customary Capacity” activity sheet and access to water and the measuring tools. You may need to have a discussion to remind or teach students proper ways to measure liquid. Observe students as they work. You may check for understanding by asking questions such as: “What do you notice about the different sized measuring tools?”“What do you notice about the relationship in the units you are measuring with?”ExplainBring students back together and have them share their strategies and answers from the “Making Sense of Customary Capacities.” Have students give you their answers for the various problems. Facilitate a discussion by asking students questions such as:“What do you notice about the relationship in the units that you measured with?”“How do you know that you are correct about the relationships between units?” Extend/ElaborateDuring this phase students may work on the “Working with Customary Capacities” activity sheet. If students need guidance you may work with students in small groups and support them by posing guided questions.Also during this phase students may work on the game “Close to 99,” “Close to 2,500” or other activities from earlier in this unit. Evaluation/Assessment The “Working with Customary Capacities” activity sheet can be used as an assessment. If you want to give an exit ticket consider posing the following task:2 ? quarts = _______ pints2 ? quarts = _______ cups Making Sense of Customary CapacityMark each box with Cup, Half-Gallon, Gallon, Pint, or Quart. 1 Gallon = 2 Half-Gallons, 1 Half-Gallon = 2 Quarts, 1 Quart = 2 Pints, 1 Pint = 2 Cups Working with Customary Capacities Complete the equations below. Use the equations below to help you. 1 Gallon = 2 Half-Gallons, 1 Half-Gallon = 2 Quarts, 1 Quart = 2 Pints, 1 Pint = 2 Cups 2 half-gallons = ___ Cups; 2 half-gallons = ___ Pints15 Quarts = ___ Cups; 15 Quarts = ___ Pints? Gallon = __ Cups; ? Gallon = ___ Pints; ? Gallon = ___ Quarts4 ? Quarts = ___ Pints; 4 ? Quarts = ___ Cups 12 ? half-gallons = __ Cups; 12 ? half-gallons = __ Quarts The punch bowl for the class party holds 6 Gallons worth of liquid. If the following ingredients are used to make punch, how much room will be left in the punch bowl?3 containers of Sherbet; each container holds 1 ? half gallons 2 containers of Sprite; each container holds 1 Gallon and 1 Pint1 Quart and 5 cups of strawberry juice3 containers of orange juice; each container holds 2 ? Pints Based on the units of customary capacity complete the following tables. CupQuartGallonPintPintQuartHalf- GallonPint11/43/81 ? 21/23/42 33/41 ? 2 ? 411 ? 3 ? 51 ? 1 ? 4 ? Lesson: 10 Concept: Customary Capacity Standard(s): 5.MD.1 Materials: Copy of More Punch Please Activity Sheet Academic Language and Vocabulary: cup, gallon, half-gallon, pint, quartTen Minute Math: Number TalkPost the following equations on the board in the order that they appear.4 x 1 ? = __ 8 x 1 ? = __ 8 x 4 ? = ___ Have students create representations for each of the equations and find the solutions. Students should discuss with their partners and write about how each of the equations relates or compares to the equation before it. ExploreDistribute the “More Punch Please” task to students. If students need support working through this task you may pull them in small groups to support them by asking guided questions. It is recommended that you do not support students as a whole class to start this task. As students work observe them and support them by asking questions such as:“What information in the problem helped you to solve it?” “Why did you choose that strategy to solve the problem?”ExplainBring students together to discuss the first page of the More Punch Please task. Have students share their answers and strategies for solving each problem. Facilitate a discussion using questions such as: “What information in the problem helped you to solve it?” “Why did you choose that strategy to solve the problem?”Extend/ElaborateDuring this phase, students should continue to work on the “More Punch Please” task. If students need support working through this task you may pull them in small groups to support them by asking guided questions.If time permits, students may also work on other games and activities from earlier in the unit. If students need more practice with customary capacity they may also work on the “Customary Match Up” activity sheet. Evaluation/Assessment The “More Punch Please” task should be used as an assessment. Customary Match Up1 Gallon = 2 Half-Gallons, 1 Half-Gallon = 2 Quarts, 1 Quart = 2 Pints, 1 Pint = 2 Cups Part 1___ 2 ? Quarts____ 12 Pints___ 3 ? Quarts____ 22 Cups___ 3 half-gallons____ 5 Pints ___ 5 ? Quarts____ 32 Cups___ 2 Gallons____ 9 Pints ___ 3 ? Pints____ 13 Cups ___ 4 ? Quarts____ 6 ? CupsPart 2 ___ 5 ? Quarts and 3 Pints____ 26 1/2 Cups___ ? Gallon and 2 ? Quarts____ 9 Pints ___ 3 1/4 Pints and 5 Quarts____ 28 Cups ___ 4 ? Quarts and ? Gallon____ 24 ? CupsExtra Activities and Tasks Concept: Problem Solving with MeasurementStandard(s): 5.MD.1 Academic Language and Vocabulary: vocabulary from lessons in this unitMaterials: Activity sheets, Task Cards Ten Minute MathPost the following equations on the board in the order that they appear.6 3/4 - 2/4 = __ 7 - 2/4 = __ 7 ? - 2/4 = __ 7 ? - 4 2/4 = __ Have students create representations for each of the equations and find the solutions. Students should discuss with their partners and write about how each of the equations relates or compares to the equation before it. ExplorePass out the “Complete the Table” activity sheet to students. As students are working facilitate by asking questions such as: What is the problem asking?What strategies are you using to solve the problem? ExplainBring students together to facilitate a discussion about some of the tasks on the “Complete the Table” activity sheet. Pose questions such as: What strategies did you use to solve the problem?How do you know that your strategies worked? Extend/ElaborateStudents may continue to work on the “Complete the Table” sheet, the “Time Match Up” sheet from the previous lesson or start to work on some of the task cards in this lesson. Students may also work on math games that the teacher feels are appropriate. Evaluation/Assessment The “Complete the Table” activity sheet can be used as an assessment. If you want to give an exit ticket you may pose one of the task cards as an exit ticket. Complete the Table1 Gallon = 2 Half-Gallons, 1 Half-Gallon = 2 Quarts, 1 Quart = 2 Pints, 1 Pint = 2 Cups 1 Yard = 3 feet, 1 foot = 12 inches 1 Pound = 16 ounces1 Liter = 1,000 milliLiters1 kilogram = 1,000 grams1 meter = 100 centimeters 1 centimeter = 10 millimetersFeetInchesPoundsOuncesYardsInches2433743 and 1/29 and 1/47 ? 4 and 1/29 and 3/49 1/45 and 1/47 and 7/89 3/4 LiterMillilitercmmmGramsmillligrams31411525157371894924125331 QuartsCupsGallonsPintsQuartsPints33/83/43 and 1/47/813 and 1/211 5/84 and 3/81 1/41 7/84 and 7/81 7/8 2 5/8Task Cards: Set 1 AThere are 4 and ? gallons of milk in the cafeteria. If the milk is poured into containers that hold 1 pint of liquid, how many containers will be filled? If the milk is poured into containers that hold 1 quart of liquid, how many containers will be filled? BMandy jumps 2 meters in the long jump in the track and field meet. She jumped 32 centimeters longer than Kristen who finished in 2nd place. Kristen jumped 80 millimeters longer than Sonya who finished in 3rd place. How far did Kristen jump?How far did Sonya jump? CThere are 3 containers of water on the counter. The blue container has 2 Liters of water. The green container has 1,320 milliliters of water. The red container has 255 milliliters in it of water. There is 5 times more water than there is juice on the counter. How much juice is there? D There are 3 and ? yards of yarn in the bag. If ? of the yarn is used for a class project how many inches of yarn are left? How many inches of yarn were used for the project? EAt 6:57 a.m. Aimee woke up. She spent 19 minutes showering and getting dressed. Then she spent 56 minutes eating breakfast and reading before going to school. What time did Aimee go to school? FSchool gets out at 2:45 p.m. Manny decided to play outside until 4:13 p.m. Then Manny did homework until 6:05 p.m. How long did he play outside? How long did he do homework? GA 6 Liter container holds 5 Liters and 211 milliliters of water. Bernie takes out 345 milliliters of water. The rest of the water is divided evenly among 8 students. How much water does each student get? Is there any remaining water? If so how much? HThere are 27 3/8 gallons of milk in the cafeteria for lunch. Half of the containers are drank on Monday and Tuesday. If the rest of the milk is in containers that hold 1 cup each how many containers are there? Task Cards: Set 2 AThere are 6 containers of juice on the counter. Four containers have 1 Liter and 215 milliLiters in each of them. The other 2 containers have 1 Liter and 118 milliliters in each of them. How much juice is there total? If the juice were going to be evenly poured into 5 containers how much liquid would be in each container? Would there be any left over liquid? If so, how much? BFor a party punch is being made. In a 5 gallon punch bowl the following is combined: 5 containers of frozen orange juice, each container is 1 1/4 pints. 2 containers of sherbet and each container is 3 1/4 quarts5 containers of Sprite, each container is 2 ? quarts How much total liquid is in the punch bowl?How much room is left in the punch bowl? CThere are 5 quarts and 2 pints of milk on the counter. Mrs. Sanchez needs 3 gallons of milk to make cookies. Does she have enough milk? How do you know? D There are 5 quarts and 2 pints of milk on the counter. Mrs. Sanchez uses ? of a cup of milk for each dozen of cookies. How many dozens of cookies can she make? EThere are 3 and ? gallons of milk in the cafeteria. If the milk is poured into containers that hold 1 quart of liquid, how many containers will be filled? If the milk is poured into containers that hold 1 pint of liquid, how many containers will be filled? FVenus jumps 2 meters 71 centimeters in the long jump in the track and field meet. She jumped 98 centimeters longer than Serena. Serena jumped 235 millimeters longer than Ellie. How far did Serena and Ellie jump? How much further did Venus jump than Ellie? GThere are 16 and 1/2 quarts of juice in Mrs. Jones’ classroom. One fourth of that juice is used for snack. How much cups of juice were used for snack?Mrs. Hernandez had 14 1/3 quarts of juice. Half of that juice was used for snack. How many cups of juice were used for snack? HThere are 2 ? gallons of milk in the cafeteria. The milk is poured into 7 containers that each hold 1 pint and the rest of the milk was poured into smaller containers that hold 1 cup each. How many smaller containers were used ? ................
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