Objective To demonstrate the use of decimal notation for metric measures and the conversion of centimeters to meters. 1 materials Teaching the Lesson Key Activities Children use metric units of length to model decimals through hundredths. Key Concepts and Skills ⵧ Math Journal 1, p. 119 ⵧ Student Reference Book, pp. 218 and 219 ⵧ Home Link 5 8 䉬 • Use base-10 blocks and a meterstick to model tenths and hundredths. • Use base-10 blocks and a meterstick to represent, compare, and order decimals through hundredths. [Number and Numeration Goal 6] ⵧ slates, tape ⵧ metersticks (1 per partnership, plus 3–4 more for meterstick “shelf,” if available) ⵧ base-10 blocks: longs and cubes Key Vocabulary decimeter See Advance Preparation [Number and Numeration Goal 1] • Find fractional parts of a region using a meterstick and base-10 blocks. [Number and Numeration Goal 2] Ongoing Assessment: Recognizing Student Achievement Use journal page 119. [Number and Numeration Goal 6] 2 Ongoing Learning & Practice Children simulate a shopping trip to practice calculating money. Children practice and maintain skills through Math Boxes and Home Link activities. 3 Children review metric units of measure. They estimate and measure the lengths of objects. ⵧ Math Journal 1, p. 120 ⵧ Student Reference Book, pp. 215–217 ⵧ Home Link Master (Math Masters, p. 148) ⵧ Teaching Master (Math Masters, p. 147) ⵧ calculator and bills and coins (optional) materials Differentiation Options READINESS materials ENRICHMENT Children explain decimal relationships. Additional Information Advance Preparation Tape together two or three metersticks and make a 1-meter-long shelf by taping the bundle to the board, centimeter side facing outward. See margin on page 365. ⵧ Math Journal 1, p. 60 ⵧ Student Reference Book, p. 141 ⵧ rulers, metersticks, tape measures ⵧ half-sheets of paper and base-10 blocks Technology Assessment Management System Journal page 119 See the iTLG. Lesson 5 9 䉬 363 Getting Started Mental Math and Reflexes Math Message Display the following sets of base-10 blocks or use base-10 shorthand to indicate the blocks. On slates, children write a decimal to represent the base-10 blocks shown and read it aloud. Turn to pages 218 and 219 in your Student Reference Book. What is the maximum length for a python? Home Link 5 8 Follow-Up 䉬 7 longs 0.7; seven tenths 1 long and 8 cubes 0.18; eighteen hundredths 9 cubes 0.09; nine hundredths 2 longs and 1 cube 0.21; twenty-one hundredths 1 flat, 1 long, 1 cube 1.11; one and eleven hundredths Partners orally read their counts to each other from Problems 8 and 9. Encourage them to extend the counts through whole numbers. 2 flats, 3 longs, 4 cubes 2.34; two and thirty-four hundredths 1 Teaching the Lesson 䉴 Math Message Follow-Up WHOLE-CLASS DISCUSSION (Student Reference Book, pp. 218 and 219) The maximum length of a python is 9 meters. Ask children to state the maximum length for each of the other animals. Show children a meterstick as a frame of reference. Be sure that they state a unit with each measurement; some of the measurements are reported in meters and others in centimeters. Use the information on Student Reference Book, pages 218 and 219 to pose additional questions: Student Page ● Which is the longest animal? python ● Which is the shortest? Queen termite ● Which is longer, the green turtle or the Mississippi alligator? Mississippi alligator ● Which is longer, the agama lizard or the Mississippi alligator? Mississippi alligator Data Bank Animal Clutches All of the animals shown lay eggs. A nest of eggs is called a clutch. Most birds, reptiles, and amphibians lay eggs once or twice a year. Insects may lay eggs daily during a certain season of the year. NOTE If children disagree on some of their answers or comparisons, it is most likely due to the inconsistent units (cm and m). Record their ideas on the board, and resolve their differences at the end of the lesson. Adjusting the Activity Green Turtle up to 1.5 meters long median of 104 eggs, as many as 184 eggs Pose ratio-comparison questions, such as: • About how many times longer is the green turtle than the giant toad? 5 times Ostrich more than 2 meters tall • About how many times longer is the python than the Mississippi alligator? 2 times up to 15 eggs A U D I T O R Y Giant Toad up to 30 cm long maximum of 35,000 eggs Student Reference Book, p. 218 364 Unit 5 Place Value in Whole Numbers and Decimals 䉬 K I N E S T H E T I C 䉬 T A C T I L E 䉬 V I S U A L 䉴 Exploring Decimals in WHOLE-CLASS ACTIVITY Metric Units 1. Show the class a meterstick, or point out the meterstick shelf mounted on the board. Explain that in previous lessons, a base-10 block flat was the ONE. For this lesson, a meter will be the ONE. All the fractions and decimals will be parts of a meter. 2. Place a long on the meterstick shelf so that one end is at the 0-mark. Ask: How many centimeters are in one long? 10 A meterstick shelf NOTE A decimeter is equivalent to 10 cm. Decimeters (dm) are not used as commonly as some other metric units of length (mm, cm, m, km). 3. Ask a volunteer to put enough longs on the meterstick shelf to reach the one-meter mark. How many longs are in 1 meter? 10 1 What fraction of 1 meter is 1 long? 1 0 Write 1 long (10 centimeters) 0.1 meter on the board. 4. Draw a number line under the meterstick while children count in unison: 1-tenth, 2-tenths, ... Remind them that each long is 1 meter. 10 Meterstick 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 long 0.1 of a meter 5. Replace the long at the 0-mark on the meterstick with cubes. How many cubes would be needed to reach the 1-meter mark? 100 How many centimeters are in 1 meter? 100 What fraction 1 of 1 meter is 1 centimeter? 100 Write 1 cube (1 centimeter) 0.01 meter on the board. 6. Make a chalk mark on the board above the 24-cm mark. Ask someone to place longs and cubes on the meterstick from the 0-cm to the 24-cm mark. 2 longs and 4 cubes How many hundredths of a meter does this show? 24 How would you write this as a decimal? 0.24 meter Record the information in a table on the board. length in centimeters longs cubes length in meters 24 cm 2 4 0.24 m ELL Adjusting the Activity Make and display a Metric Equivalencies chart in the classroom. Metric Equivalencies 10 centimeters = 0.1 meter 1 centimeter = 0.01 meter AUDITORY 䉬 KINESTHETIC 䉬 TACTILE 䉬 VISUAL Erase the chalk mark above the 24-centimeter mark. Repeat this routine with several other measurements. Include measurements that result in decimals with zeros in the tenths or hundredths places, such as 70 cm and 6 cm. Lesson 5 9 䉬 365 Student Page Date Time LESSON 䉴 Writing Metric Measurements in Decimals for Metric Measurements 5 9 䉬 1. Fill in the missing information. Put longs and cubes end to end on a meterstick to help you. Length in Centimeters Number of Longs Number of Cubes Length in Meters 2 3 4 6 cm 0 3 cm 0 3 8 0 0.24 m 0.36 m 0.03 m 0.08 m cm 4 3 24 cm 36 cm 3 8 cm 30 43 0.3 m 0.43 m PARTNER ACTIVITY Decimal Notation (Math Journal 1, p. 119) Children model and compare metric measurements by sharing metersticks and base-10 blocks with partners. They write the measurements as decimals and label a centimeter ruler for measurements given in decimal notation. Work with a partner. Each partner uses base-10 blocks to make one length in each pair. Compare the lengths and circle the one that is greater. 夹夹 2. 0.09 or 0.12 夹 3. 0.24 or 0.42 5. 0.18 or 0.5 4. 0.10 or 0.02 6. 0.2 or 0.08 Ongoing Assessment: Recognizing Student Achievement 7. 0.3 or 0.24 Follow these directions on the ruler below. Use base-10 blocks and a meterstick to help you. 8. Make a dot at 4 cm and label it with the letter A. 9. Make a dot at 0.1 m and label it with the letter B. 10. Make a dot at 0.15 m and label it with the letter C. 11. Make a dot at 0.08 m and label it with the letter D. A 0 1 2 3 4 D 5 6 7 B 8 9 C 夹 Journal Page 119 Problems 2–4 Use journal page 119 to assess children’s progress in comparing decimals. Children are making adequate progress if they successfully complete Problems 2, 3, and 4 with or without manipulatives. Some children may be able to complete Problems 5, 6, and 7 with or without manipulatives. [Number and Numeration Goal 6] 10 11 12 13 14 15 cm Math Journal 1, p. 119 2 Ongoing Learning & Practice NOTE Some children may prefer to use the flat as the ONE, rather than the meter, to complete Problems 2–7 on journal page 119. 䉴 Simulating a Shopping Trip PARTNER ACTIVITY (Math Masters, p. 147; Student Reference Book, pp. 215–217) This activity was introduced in Lesson 1-11. To buy items on the shopping trip, children can use either the Variety Store Poster, or one of the two Stock-Up Sale Posters in the Student Reference Book. Teaching Master Name Date LESSON Time A Shopping Trip 59 䉬 Use pages 215–217 in your Student Reference Book. 1. List at least 4 items you are buying in the space below. If you buy the same item 2 times, list it 2 times. Item Children select the items they want to buy; record the information on Math Masters, page 147; and estimate the number of bills to give the shopkeeper. They take turns acting out the transactions with bills and coins. After each partner completes the shopping trip, they work together to complete the Try This problem. Sale Price 䉬䉬䉬䉬䉬䉬䉬䉬䉴 Math Boxes 5 9 䉬 INDEPENDENT ACTIVITY (Math Journal 1, p. 120) 2. Estimate how many dollar bills you need to pay for these items. Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-11. The skill in Problem 6 previews Unit 6 content. 3. Give the clerk the dollar bills. 4. The clerk calculates the total cost. $ 5. The clerk calculates the change you should get. $ 6. Record your change. Use Î, Â, Í, ‰. Try This Use Stock-Up Sale Poster #1 in your Student Reference Book, page 216. 7. Justin wants to buy 5 ballpoint pens. How much money will he save by buying them at the “5-or-More Sale”? Regular price (for 5 ballpoint pens): $ “5-or-More Sale” price: $ Amount saved: $ 1.95 1.35 0.60 Writing/Reasoning Have children write an answer to the following: Explain why the area in Problem 4 is measured in square units. Sample answer: The area of the rectangle is covered with squares. I counted 21 squares so the area is 21 square units. Math Masters, p. 147 366 Unit 5 Place Value in Whole Numbers and Decimals Student Page 䉴 Home Link 5 9 INDEPENDENT ACTIVITY 䉬 (Math Masters, p. 148) Date Time LESSON Math Boxes 5 9 䉬 Write the number that has 6 in the ones place 4 in the tenths place 3 in the hundredths place 2 in the thousandths place 1. Home Connection Children fill in missing decimal numerals on number lines and mark metric measures on a ruler. 2. If each grid is ONE, what part of each grid is shaded? Write the decimal. 6.4 3 2 0.25 35 Use addition and subtraction to complete these problems on your calculator. 3. Enter 3 Differentiation Options READINESS 䉴 Reviewing Metric Measure INDEPENDENT ACTIVITY 1,366 966 627,581 628,581 43,775 43,175 33–35 Draw a 3 7 rectangle. How? 12,000 400 1,000 600 37 21 square units Number model: Area: 21 18 19 154–156 6. Draw an example of a cylinder. Sample answer: 4,000,000 3,000 1 1 means 60,000 6 means 9 means 900,000 4 means 5–15 Min 3 means To explore metric units of length and how to measure, have children estimate and measure the lengths of objects in the room. Children turn to page 141 in their Student Reference Books to review the relative size of millimeters, centimeters, and meters. After a brief review, have children use their personal references (Math Journal 1, page 60) to estimate the length of objects in the room to the nearest centimeter and meter and then measure the object to check their estimate. On a half-sheet of paper, children can make a table, such as the one below, to record their work. Have children describe the objects they measured. Encourage vocabulary like shorter, longer, estimate, actual, and so on. My Estimate 12,894 For the number 4,963,521 5. (Math Journal 1, p. 60; Student Reference Book, p. 141) Object Change to 894 4. 0.07 Peanut Butter Jar 18–21 112–114 Math Journal 1, p. 120 Actual Length Home Link Master Name Date HOME LINK 59 Family Note ENRICHMENT 䉴 Writing about Tenths and Your child has been using the metric system to practice measurements and to convert centimeters to meters. The following equivalencies will assist you in helping your child solve Problems 3–6. 1 cm 10 mm Please return this Home Link to school tomorrow. 1 m 100 cm 1 m 1,000 mm INDEPENDENT ACTIVITY Fill in the missing numbers. 5–15 Min 2. Hundredths To apply children’s understanding of tenths and hundredths, have them write a response to the following question: Vanna says that 0.10 m is more than 0.2 m because 0.10 m is 10 longs but 0.2 m is only 2 longs. How could you help Vanna see her mistake? Supply base-10 blocks and metersticks for children to use as needed. Sample answer: 0.10 represents 1 tenth and 0 hundredths, or 1 long; 0.2 represents 2 tenths and 0 hundredths, or 2 longs. So, 0.2 is more than 0.10. Time Practice with Decimals 䉬 137–140 1. 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Follow these directions on the ruler below. 3. Make a dot at 7 cm and label it with the letter A. 4. Make a dot at 90 mm and label it with the letter B. 5. Make a dot at 0.13 m and label it with the letter C. 6. Make a dot at 0.06 m and label it with the letter D. 0 1 2 3 4 5 D • A • 6 7 B • 8 C • 9 10 11 12 13 14 15 cm Practice 7. 3 9 10. 12 27 26 8. 5 8 11. 9 40 9. 0 8 33 12. 15 0 53 Math Masters, p. 148 Lesson 5 9 䉬 367