Measuring with a Ruler

Transcription

1 Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Name the marks on a ruler that divide inches into halves, fourths, and eighths. [Number and Numeration Goal ] Use a ruler to find equivalent halves, fourths, and eighths. [Number and Numeration Goal 5] Select measuring tools and appropriate units for particular measuring tasks. Measure to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. [Measurement and Reference Frames Goal ] Key Activities Children select measuring tools and choose appropriate units of length. They measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. Ongoing Assessment: Informing Instruction See page 79. Ongoing Assessment: Recognizing Student Achievement Use journal page 58. [Measurement and Reference Frames Goal ] Playing Subtraction Top-It Student Reference Book, pp. 0 and per group: each of number cards 0 0 and each of number cards 0 (from the Everything Math Deck, if available) Children develop automaticity with basic subtraction facts. Math Boxes Math Journal, p. 59 Children practice and maintain skills through Math Box problems. Home Link Math Masters, p. 66 Children practice and maintain skills through Home Link activities. READINESS Making a Number Line sheet of paper Children create number lines and label with whole numbers and fractions. ENRICHMENT Beginning with a Nonzero Mark on a Ruler Math Journal, p. 58 Math Masters, p. (Ruler E) Children measure line segments from a nonzero mark on a ruler. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. Children add the terms inch, centimeter, and millimeter to their Math Word Banks. Key Vocabulary inch (in.) line segment centimeter (cm) millimeter (mm) Materials Math Journal, p. 58 Student Reference Book, pp. 7 9,, and Home Link Math Masters, p. transparency of Math Masters, p. 65 scissors red crayon (optional) Advance Preparation Cut the rulers from the bottom of the transparency of Math Masters, page 65. You may wish to precut the rulers on Math Masters, page for children who have difficulty cutting accurately. Teacher s Reference Manual, Grades pp. 57, Unit Linear Measures and Area

2 Getting Started Mental Math and Reflexes Write the following multiple-addend problems on the board. Encourage children to look for combinations that make the addition easier = = = = = = = = = Math Message Suppose you and your classmates are going to have a watermelon seed-spitting contest. How would you measure the distance the seeds travel? How would you pick the winner? Discuss with a partner Home Link Follow-Up Children show and discuss their lists and pictures of items with measurements. Remind children to continue to look at home for pictures that show measurements. Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Have children describe what they would do to measure the distances in a seed-spitting contest. Which measuring tool would they use to find the distances? Which unit of length would they choose? Probably inch or centimeter; someone might suggest fractions of an inch or millimeters. What other units of length do children know? Foot, yard, mile, meter, kilometer, and so on Why are larger units not as appropriate for measuring the distances in the contest? With larger units, it is harder to get precise measurements of shorter distances. Teaching Aid Master Name Date Time Reading a Ruler and Measuring to the Nearest Inch, _ Inch, and _ Inch (Math Journal, p. 58; Math Masters, pp. 65 and ; Student Reference Book, pp. and ) WHOLE-CLASS If children are fairly skilled at measuring with a ruler, you may want to omit parts of the following activity. Have children carefully cut out Rulers A, B, C, D, and E from Math Masters, page. Set aside Ruler D until later in the lesson. Ruler E is used in the optional Part Enrichment activity. Point out that Rulers A, B, and C are divided into inches. The inch, abbreviated in., is a standard unit of length in the U.S. customary system. Review reading an inch ruler with the class. Rulers Inches (in.) Ruler E Centimeters (cm) Ruler D Inches (in.) Ruler C Inches (in.) Ruler B Inches (in.) Ruler A Math Masters, p. Lesson 77

3 Date LESSON about in. about mm about in. 87 about 9 mm Time Measuring Line Segments about in. about mm Use Ruler D to measure to the nearest millimeter (mm).. Use Ruler C to measure to the nearest inch (in.). Ruler C Ruler D Try This about in. about cm about in. about 5 cm about in. about 9 cm Math Journal, p. 58 Use Ruler D to measure to the nearest centimeter (cm).. Use Ruler B to measure to the nearest inch (in.). Ruler B Ruler D about in. about 9 cm about in. about in. 5 about cm about cm 8 NOTE The measures of the line segments on journal page 58 are not exactly whole inches, _ inches, _ inches, whole centimeters, or _ centimeters. The focus of this lesson is to measure to the nearest or closest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. Use Ruler D to measure to the nearest centimeter (cm).. Use Ruler A to measure to the nearest inch (in.). Ruler A Ruler D Look at Ruler A. Each inch is divided into equal parts by a mark that is halfway between the inch marks. These _ -inch marks help when measuring to the nearest inch. Guide children to think of _ inch as one out of two equal parts of the inch. Using the transparency of Ruler A, have a volunteer measure a line segment to the nearest inch on the transparency of Math Masters, page 65. These line segments are the same length as those on journal page 58. Point out that the ruler and line segments on the screen are larger than real life. Ask children how the inches on the screen are different from the inches on their rulers. Tell them that the screen inch is at a different scale than a real inch and that they will explore more about scale at a later time. Review the following ideas: Line up one edge of the line segment with the 0-mark on the ruler. Caution children that sometimes the 0-mark is the edge of the ruler, and sometimes the 0-mark is away from the edge. Note that Rulers A, B, and C have an arrow at the 0-mark to help children line up one edge of the line segment. Remind children to use such phrases as about inches and between and inches to indicate that measurements are not exact. Adjusting the Activity Have children color the 0-mark with a red crayon to highlight it. ELL A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Name Date Time LESSON Measuring Line Segments Measure the line segments with the rulers.. Use Ruler A to measure to the nearest inch (in.).. Use Ruler B to measure to the nearest inch (in.).. Use Ruler C to measure to the nearest inch (in.) Inches (in.) Ruler A Inches (in.) Ruler B Inches (in.) Ruler C Math Masters, p. 65 Teaching Master in. 5 in. in. in. in. in. in. in. in. Children measure the first line segment in Problem on journal page 58 to the nearest inch. When most children have finished, have them share their measurements. When they agree that the measurement is about inches, have children continue measuring the other line segments in Problem. Circulate and assist as needed. Look at Ruler B. Ask children to identify the _ -inch marks and to write the fraction _ below each of those marks. The first one is done for them. What is the distance from the 0-inch mark to the _ -inch mark? _ inch What is the distance from that _ -inch mark to the -inch mark? _ inch Point out that each _ -inch distance on Ruler B is divided into two equal parts. How many equal parts does each inch have on the ruler? equal parts Think of _ as one out of four equal parts of the inch. Tell children that the _ -inch marks help when measuring to the nearest _ inch. 78 Unit Linear Measures and Area

4 Children should measure the first line segment in Problem to the nearest _ inch while a volunteer demonstrates how to make the measurement on the overhead with the transparency of Ruler B. When everyone agrees that the measurement is about _ inches, children should measure the other line segments. Ongoing Assessment: Informing Instruction Watch for children who have difficulty understanding that a measurement to the nearest _ inch can be at a whole-inch mark. Discuss the possibility that when measuring to the nearest _ inch, some lines may be a whole number of inches. NOTE These ruler activities can be summarized by reading Student Reference Book, pages and with the class. The second example on page can be used to clarify the skills needed to use Ruler C correctly. Look at Ruler C. Ask children to identify the _ -inch marks and to read the fractions _, _ or _, _, and (or _ ) below those marks between the 0-inch and -inch marks. Count the labeled marks in an inch space in unison. What is the distance between each of the labeled marks from the 0-inch mark to the -inch mark? _ inch Point out that each _ -inch distance is divided into two equal parts. Those marks help when measuring to the nearest _ inch. Repeat the procedure for measuring the line segments in Try This Problem to the nearest _ inch. Adjusting the Activity ELL Have children name the marks that divide the _ -inch spaces in half on ruler C. _ 8 inch Ask how many equal parts these marks divide each inch into. 8 equal parts Explain that each of the marks between consecutive whole inches names _ 8 of an inch. Ask children to name the marks that have more than one name. _ 8 and _ ; _ 8, _, and _ ; 6_ 8 and _ To support English language learners, write these fractions, using numbers and words, on the board. Guide children to think of _ 8 as one out of eight equal parts of the inch. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Links to the Future Problem on Math Journal, page 58 provides an opportunity for children to begin working with _ inches and millimeters when measuring. Children use rulers marked with _ 8 inches to measure to the nearest _ inch. They use rulers marked with millimeters to measure to the nearest millimeter. Measuring to the nearest _ inch is a Grade Goal. Measuring to the nearest millimeter is a Grade 5 Goal. Measurement What is the length of the eraser? Ongoing Assessment: Recognizing Student Achievement Journal Page 58 Problem Use journal page 58, Problem to assess children s progress with measuring line segments to the nearest _ inch. Children are making adequate progress if they are able to measure the line segments to the nearest inch in Problem. Some children may be able to measure to the nearest _ in., _ in., _ cm, and mm to complete Problems and successfully. [Measurement and Reference Frames Goal ] Always line up the end of the object with the 0-mark of the ruler. If the 0-mark is at the end of a ruler, the number 0 may not be printed on that ruler. There are small spaces between the -inch mark and the end of the eraser. Each small space is 6 inch long. So the eraser is 6 inches long. Because 6, 8 the length can be written as 6 in., or 8 in. There are times when you do not need an exact measurement. Measuring to the nearest inch or the nearest inch may be good enough. Find the length of the pencil to the nearest quarter-inch. The quarter-inch marks between and are written below the ruler. The tip of the pencil is closest to. The pencil is inches long, to the nearest quarter-inch. Student Reference Book, p. Lesson 79

5 Measuring Length in Centimeters and Millimeters Length is the measure of a distance between two points. Length is usually measured with a ruler. The edges of your Pattern-Block Template are rulers. Tape measures, yardsticks, and metersticks are rulers that are used for measuring longer distances. Rulers are often marked with inches on one edge and centimeters on the other edge. The side showing centimeters is called the centimeter scale. The side showing inches is called the inch scale. Each centimeter is divided into 0 equal parts called millimeters. A millimeter is 0 or 0. of a centimeter. The word centimeter is abbreviated cm. The word millimeter is abbreviated mm. The centimeter marks are numbered 0,,, and so on. Millimeter marks are not numbered. Student Reference Book, p. 7 Measurement In January 00, Chinese scientists found the body of a four-winged dinosaur that was about 75 centimeters long from head to tail. Measuring to the Nearest Centimeter, _ Centimeter, and Millimeter (Math Journal, p. 58; Math Masters, p.; Student Reference Book, pp. 7 9) WHOLE-CLASS Ruler D is marked in centimeters and millimeters. Remind children that centimeters, abbreviated cm, and millimeters, mm, are standard units of length in the metric system. The ruler also has marks to show half the distance between consecutive whole centimeters. These marks help when measuring to the nearest whole centimeter. Briefly discuss pages 7 9 in the Student Reference Book to review measuring with these units. Children use Ruler D to measure the nine line segments on journal page 58 to the nearest centimeter, _ centimeter, and millimeter. Ongoing Learning & Practice Playing Subtraction Top-It (Student Reference Book, pp. 0 and ) PARTNER Children play Subtraction Top-It to maintain and/or develop automaticity with basic subtraction facts. Review the rules for Subtraction Top-It on pages 0 and in the Student Reference Book. Measurement How long is the key? Always line up one end of the object with the 0-mark on the ruler. The other end of the key is at the -centimeter mark. The key is centimeters long. We write this as cm. If the 0-mark is at the end of a ruler, then the number 0 may not be printed on the ruler. When this happens, line up the end of the object with the end of the ruler. How many millimeters long is the arrow? The 0-mark is at the end of the ruler. Line up the end of the object with the end of the ruler. There are 0 millimeters from the end of the ruler to the cm mark. The arrow tip is another 5 millimeters past the cm mark. So the arrow is 5 millimeters long. We write this as 5 mm. Math Boxes (Math Journal, p. 59) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem 6 previews Unit content. Home Link (Math Masters, p. 66) INDEPENDENT Home Connection Children take body measurements of someone at home. Remind them to continue to collect and bring in pictures and lists of items that show measurements. Student Reference Book, p Unit Linear Measures and Area

6 Differentiation Options READINESS Making a Number Line SMALL-GROUP 5 5 Min To explore modeling fractions as equal parts on a number line, have children fold a strip of paper in half vertically and label the fractional parts. Along the folded edge, they make a tick mark, for 0 and near the edges of the paper and a tick mark for in the middle. (Children may fold the paper the opposite way to find the middle, if they wish.) Then children fold the number line and label tick marks to indicate the halfway points between 0 and and between and. Some children may be able to create markings for fourths and eighths. Children may use their number lines for reference as they identify fractional increments on a ruler. Date LESSON. Count by 6s.. Write <, >, or =. 69 < Math Boxes 57, 6, 69, 75, 8, 87, 9, 99, 05,, 7,, 9, 5,, 7 0 < 0 = 5Í,000 > 999 Number of Children 0 Books Read Maximum number of books read: books Time. Measure to the nearest } } inch. about _ in. Draw a line segment inches long.. Pamela had $8. She spent money on shoes. She has $5 left. Start Change End $8? $5 Number model: $8? = $5 Answer: $ 5 55 Book Club Totals 6. Courtney has 8 pennies. She shares them equally with Nicholas. How many pennies do they each get? Fill in the circle for the best answer. A. 6 pennies B. 8 pennies C. pennies D. pennies EMMJ_G_U0_55-78.indd 59 Math Journal, p. 59 /0/0 6: PM ENRICHMENT Beginning with a Nonzero Mark on a Ruler (Math Journal, p. 58; Math Masters, p. ) SMALL-GROUP 5 5 Min To apply children s understanding of measuring, have them remeasure the line segments on journal page 58 with Ruler E (from Math Masters, p. ), beginning with the 5-inch mark instead of the 0-inch mark. Discuss ways of measuring with such a ruler. Their measurements should match those recorded earlier. Some children may suggest counting unit segments. Others may suggest lining up the 5-inch mark with the left endpoint of a line segment, recording the number for the mark nearest the right endpoint, and subtracting 5 from that number. ELL SUPPORT SMALL-GROUP Building a Math Word Bank (Differentiation Handbook, p. ) 5 5 Min Name Date Time HOME LINK Family Note Body Measures Help your child measure an adult at home. Use a tape measure if you have one, or use a piece of string. Mark lengths on the string with a pen, and then measure the string with a ruler. Please return this Home Link to school tomorrow. Measure an adult at home to the nearest inch. Fill in the information below: Name of adult: Around neck: about inches Height: about inches Around wrist: about inches Length of shoe: about inches Distance from waist to floor: about inches Forearm: about inches Home Link Master Hand span: about inches Arm span: about inches To provide language support for units of measure, have children use the Math Word Bank template found on Differentiation Handbook, page. Ask children to write the terms inch, centimeter, and millimeter; draw pictures representing the terms; and write other related words that describe them. See the Differentiation Handbook for more information. forearm hand span arm span Reminder: Find more pictures that show measurements. Bring them to school if possible (ask an adult first) or write descriptions of them. Practice Write these problems on the back of this page. Fill in a unit box. Write number models for your ballpark estimates. Show your work Unit Math Masters, p. 66 Lesson 8