Linear Measures. Assessment Management

Transcription

1 Linear Measures Objectives To provide review for measuring with inches, feet, centimeters, and decimeters; and to guide children as they begin a table of equivalent linear measures. 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 Explore fractional parts of units of measurement. [Number and Numeration Goal 3] Compare U.S. customary and metric units. [Number and Numeration Goal 7] Measure objects to the nearest inch, foot, centimeter, and decimeter. [Measurement and Reference Frames Goal 1] Key Activities Children use a ruler to measure in inches, feet, centimeters, and decimeters. Children also begin to identify equivalent U.S. customary and metric measures. Ongoing Assessment: Recognizing Student Achievement Use journal page 212. [Measurement and Reference Frames Goal 1] Key Vocabulary inch centimeter foot decimeter Materials Math Journal 2, p. 212 Home Link 9 1 Math Masters, p. 255 pictures and items for the Measures All Around Museum base-10 longs tape measure Class Data Pad scissors slate Playing That Number My Reference Book, pp. 138 and 139 per partnership: 4 each of number cards 0 10 and 1 each of number cards (from the Everything Math Deck, if available) Children use addition and subtraction to name equivalent numbers and practice facts. Math Boxes 9 2 Math Journal 2, p. 213 Children practice and maintain skills through Math Box problems. Home Link 9 2 Math Masters, pp. 256 and 257 Children practice and maintain skills through Home Link activities. READINESS Measuring More or Less than One Foot Math Masters, p. 258 half-sheet of paper scissors Children measure various classroom items that are longer than and shorter than 1 foot. EXTRA PRACTICE Constructing a Display of Fish Lengths Math Masters, p. 259 index cards string tape yardstick or tape measure Children measure and cut lengths of string to correspond to the lengths of fish on the Fish Poster and then order the strings from shortest to longest. ELL SUPPORT Comparing Units of Measure Math Masters, p. 258 posterboard yardstick 1-inch square pattern block meterstick base-10 long centimeter cube Children compare the relative sizes of units. Advance Preparation Begin a display of the items and pictures you and the children have collected for a Measures All Around Museum. For the optional ELL Support activity in Part 3, create two posters using a yardstick, a foot-long foot (cut from Math Masters, page 258), a 1-inch square pattern block, a meterstick, a base-10 long, and a centimeter cube. (See page 671.) For a mathematics and literacy connection, obtain copies of Twelve Snails to One Lizard by Susan Hightower (Simon and Schuster, 1997) and Measuring Penny by Loreen Leedy (Scholastic Inc., 1997). Teacher s Reference Manual, Grades 1 3 pp. 157, Unit 9 Measurement

2 Getting Started Mental Math and Reflexes Have children record addition fact sums on their slates. For example: Doubles +1 Harder Facts Doubles Mathematical Practices SMP1, SMP2, SMP5, SMP6, SMP7 Content Standards 2.OA.2, 2.MD.1, 2.MD.2, 2.MD.3, 2.MD.4 Math Message Yards and meters are good units to use for measuring long lengths. What units are good to use for measuring short lengths? Home Link 9 1 Follow-Up Conduct a brief show-and-tell session. Ask children to talk about the items they brought from home and about the tools people at home use for measuring. Display items you collected for the Measures All Around Museum. Encourage children to bring in additional items for the museum over the next few days. Clothing sizes, temperatures, wind speeds, numbers on a camera lens, sizes of nails and screws, and weights of cars are all good sources. Have children share strategies for one of the Practice problems. 1 Teaching the Lesson Math Message Follow-Up Most children will name inches and centimeters because those units have been used previously in second-grade activities. Some children may remember measuring with the foot-long foot in First Grade Everyday Mathematics. 0 feet 1 foot Measuring to the Nearest Inch and Centimeter The foot-long foot used in First Grade Everyday Mathematics Ask children to describe how to measure to the nearest inch or centimeter. Their descriptions should include the following: Line up the 0-mark on the ruler with one edge of the object being measured. The inch (or centimeter) mark nearest to the other edge of the object is the measurement. Use the mark halfway between inches (or centimeters) to decide which mark the edge is closer to. Measure objects longer than the ruler by putting a mark on the object where the end of the ruler meets it and then moving the ruler so the 0-mark is at that mark. If one end of the object is not lined up with the 0-mark, the measurement is equal to the difference between the beginning and end numbers. Lesson

3 Links to the Future Activities in this lesson include children measuring to the nearest foot and decimeter. Describing the relationships among feet, inches, centimeters, and decimeters is a Grade 3 Goal. Remind the class that a measurement is meaningful only when it is labeled with an appropriate unit. Ask what is wrong with the statement, The average second grader is 46 centimeters tall. Children may show a length of 46 centimeters with their tape measures to illustrate their answers. Ask them to make up other silly statements that use inappropriate units. Revisiting Foot and Decimeter Remind children that in first grade they used two other units to measure length, the foot and the decimeter. Children may remember using the foot-long foot to measure lengths and that a foot is equal to 12 inches. The other unit they used was the base-10 block called a long. A long has a length of 10 centimeters. It is the same length as a decimeter, another metric unit. A decimeter is equal to 10 centimeters. Table of Equivalent Measures U.S. Customary System 1 yard (yd) = 36 inches (in.) Metric System = 3 feet (ft) 1 foot = 12 inches = 1_ yard 3 1 inch = 1_ foot 12 = 1_ yard 36 1 meter (m) = 100 centimeters (cm) = 10 decimeters (dm) 1 decimeter = 10 centimeters = 1_ meter 10 1 centimeter = 1_ decimeter 10 = 1_ meter 100 NOTE As children complete the Table of Equivalent Measures, point out how they can partition (or divide) each larger unit (e.g., yards) into smaller units (e.g., feet or inches). Beginning a Table of Equivalent Measures Adjusting the Activity Have children look at the inch side of their tape measures. Remind them that this side is numbered in inches and that the marks between inches show fractions of an inch. Ask: Does this side of the tape measure have any other marks? Some tape measures have a star (or other symbol) at the 12-inch and 36-inch marks. To support English language learners, ask questions like the following about equivalent measures and record the key ideas on the board. How many inches are in 1 foot? 12 inches How many inches are in 1 yard? 36 inches How many feet are in 1 yard? 3 feet (You can demonstrate this by laying three 12-inch rulers on top of a yardstick.) How many inches long is the tape measure? How many feet? Begin a Table of Equivalent Measures on the Class Data Pad. (See margin.) Save the table for future discussions. Plan to add equivalencies as they are introduced in subsequent lessons. Ask questions like the following: What part of a yard is 1 inch? 1_ 36 What part of a yard is 1 foot? 1_ 3 ELL What part of a foot is 1 inch? 1_ 12 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 Ask children to turn over their tape measures to the centimeter side. The numbers name whole centimeters, and the marks between centimeters are used to name fractions of centimeters. 668 Unit 9 Measurement

4 Ask: Are there any other marks on this side? There is probably a symbol at 100 centimeters to name 1 meter. Place longs from the base-10 blocks on a tape measure or meterstick to show that 1 meter is equal to 10 decimeters (10 longs). Tell children that the prefix deci- means one-tenth of and centimeans one-hundredth of in this case of a meter. To support English language learners, write these prefixes on the board along with their meanings. Ask: What fraction of a meter is 1 decimeter? 1_ 10 What fraction of a meter is 1 centimeter? 1_ 100 Finally, help children see that 1 meter is a little more than 1 yard, a decimeter is a little less than 4 inches, and 1 centimeter is less than 1_ inch by drawing and labeling lines on the board. For 2 example, draw and label lines that measure l meter and 1 yard next to one another. Children can compare these measurements by finding the metric measure on the tape measure, turning the tape measure over, and identifying the closest U.S. customary measure. Measuring in Feet and Inches, Decimeters and Centimeters (Math Journal 2, p. 212; Math Masters, p. 255) Children cut out the foot and decimeter rulers from Math Masters, page 255. Working in small groups, children estimate the length of objects or distances and then measure them to the nearest foot, inch, decimeter, and centimeter. Bring the class together to compare measurements. Help children see that using smaller units gives more exact measurements. Date 9 2 Student Page Time Units of Linear Measure Materials foot and decimeter rulers from Math Masters, p. 255 Directions 1. Select two objects or distances. 2. Estimate the length of each object or distance in feet, inches, decimeters, and centimeters. Write your estimates. 3. Measure the length of each object or distance in feet, inches, decimeters, and centimeters. Write your measurements. Answers vary. First Object My Actual or Distance Estimates Measurements about ft about ft about in. about in. about dm about dm about cm about cm Second Object My Actual or Distance Estimates Measurements Math Journal 2, p. 212 about ft about ft about in. about in. about dm about dm about cm about cm NOTE After children complete journal page 212 and share their answers, help them observe the inverse relationship between the size of a unit and the number of units needed to measure each object. Help children see that it takes fewer units to measure something with a larger unit (feet and decimeters) than with a smaller one (inches and centimeters). Ongoing Assessment: Recognizing Student Achievement Journal page 212 Use journal page 212 to assess children s ability to use a ruler. Children are making adequate progress if they align the 0-mark on the ruler with one edge of the object or at one end of the length to be measured. It may be helpful to use a class checklist as you observe children measuring. Some children may be able to measure to the nearest 1_ 2 inch. [Measurement and Reference Frames Goal 1] Teaching Master Date 9 2 A Foot and a Decimeter Ongoing Learning & Practice Playing That Number (My Reference Book, pp. 138 and 139) PARTNER This game was introduced in Lesson 2-9. See My Reference Book, pages 138 and 139 for game directions. s Math Masters, p cm Lesson

5 Date 9 2 Math Boxes 1. Fill in the missing numbers. 1,248 1,249 1,257 1,258 1,259 1, Dillon leaped 32 inches. Marcus leaped 27 inches. How many more inches did Dillon leap? 5 inches Fill in the diagram. Quantity 5. 3 insects. 6 legs per insect. How many legs in all? 18 legs Fill in the diagram and write a number model. insects Time 2. Draw a line segment that is 8 cm long. Now draw a line segment 5 cm shorter. 1, Quantity Difference legs per insect Student Page legs in all 3 6? Sample answer: = 18 Math Journal 2, p What is the chance that you will have two birthdays this year? Choose the best answer. unlikely likely certain impossible 6. Solve pennies = $2.00 nickels = $2.00 dimes = $2.00 quarters = $2.00 Math Boxes 9 2 (Math Journal 2, p. 213) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-4. The skill in Problem 6 previews Unit 10 content. Home Link 9 2 (Math Masters, pp. 256 and 257) INDEPENDENT Home Connection Children measure objects with rulers using U.S. customary and metric units. 3 Differentiation Options READINESS Measuring More or Less than One Foot (Math Masters, p. 258) 5 15 Min Home Link Master Date Time HOME LINK 9 2 Linear Measurements Family Today your child reviewed how to use a ruler to measure objects and distances in inches and Note feet and in centimeters and decimeters. Your child s class also began making a Table of Equivalent Measures for the U.S. customary and metric systems. Ask your child to show you how to measure some of the objects or distances that he or she selects to complete the tables below. Please return this Home Link to school tomorrow Cut out the 6-inch ruler on the next page. Measure two objects or distances. Measure to the nearest foot. Then measure again to the nearest inch. Some things you might measure are the width of the refrigerator door, the length of the bathtub, or the height of a light switch from the floor. Object or Distance Nearest Nearest Foot Inch length of bed 7 Sample answers 79 about ft about in. about ft about in. 2. Cut out the 10-centimeter ruler on the next page. Measure the same objects or distances. Measure to the nearest decimeter. Then measure again to the nearest centimeter. To explore the length of a standard foot, have children compare the lengths of objects to the foot-long foot on Math Masters, page 258. Children cut out the foot and compare it to objects in the room. They label one side of a half-sheet of paper Shorter than a Foot and the other side Longer than a Foot. On the appropriate side, they record the name of or draw 3 objects for each category. Date Time HOME LINK 9 2 Linear Measurements continued Complete each sentence. 3. One foot is equal to 12 inches. 4. One yard is equal to 3 feet. 5. One decimeter is equal to 10 centimeters. 6. One meter is equal to 100 centimeters. 7. Two feet are equal to 24 inches. 8. Three yards are equal to 9 feet. 9. Four decimeters are equal to 40 centimeters. 10. Seven meters are equal to 700 centimeters. Practice = = = = Home Link Master Object or Distance Nearest Nearest Decimeter Centimeter Math Masters, p. 256 about dm about cm about dm about cm inches cm Math Masters, p Unit 9 Measurement

6 EXTRA PRACTICE Constructing a Display of Fish Lengths (Math Masters, p. 259) Min To apply children s knowledge of measurement, have children measure and cut lengths of string that correspond to the lengths of fish on the Fish Poster. For example, since the poster reports Fish H s length as 30 inches, children use their tape measures or yardsticks to measure and cut a 30-inch length of string. They tape this string to an index card and write Fish H: 30 inches on the card. When children have repeated this routine for all the fish shown on the poster, display their string models in the classroom. Children arrange the strings from shortest to longest in the display. After children have completed the display of fish lengths, ask them to solve 1- and 2-step comparison number stories. Suggestions: Fish H is 6 inches shorter than which fish? Fish J The total of the lengths of Fish C and Fish D together is 30 inches more than which fish? Fish A The total of the lengths of Fish A and Fish B together is 10 inches less than which fish? Fish J What fish is 12 inches longer than the total of the lengths of Fish F and Fish I? Fish L What fish is 36 inches shorter than the total of the lengths of Fish D and Fish G? Fish C Suggest that they use a tape measure or number line to help. ELL SUPPORT Comparing Units of Measure (Math Masters, p. 258) 5 15 Min To provide language support for measurement, make two posters with representations for standard units of measurement. Title one poster U.S. Customary Units and tape a yardstick, a foot-long foot (cut from Math Masters, page 258), and a 1-inch square pattern block to the poster and label each. Title the second poster Metric Units and tape a meterstick, a base-10 long, and a centimeter cube to the poster and label each. Display the posters so that children can see the relative sizes of the units. yard foot U.S. Customary Units meter decimeter Metric Units Teaching Master 9 2 Foot-Long Foot Math Masters, p. 258 Date t 1 foot Planning Ahead Collect the boxes shaped like rectangular prisms that children have brought to school. Check that each box fits on a sheet of paper. Make sure children have written their names on the boxes. Remind children who have not yet brought in boxes to do so. The boxes will be used in Lesson 9-4. Date Time 9 2 Fish Poster Fish A 1 lb 12 in. Fish E 6 lb 24 in. Fish H 14 lb Teaching Master Fish B 3 lb 14 in. Fish F 8 lb Fish I 15 lb Fish C 4 lb 18 in. Fish J 24 lb 36 in. Fish D 5 lb 24 in. Fish G 10 lb inch centimeter Fish K 35 lb 42 in. Displays showing the relationships among U.S. customary and metric units Fish L 100 lb 72 in. Math Masters, p. 259 Lesson