Assessment Management

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1 Weight Objectives To review grams and ounces as units of mass and weight; and to guide the estimation and measurement of weight in grams and ounces. 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 Estimate weight with and without tools. [Measurement and Reference Frames Goal 1] Describe relationships among metric units of mass and weight. [Measurement and Reference Frames Goal 3] Convert between metric and customary units of mass and weight. [Measurement and Reference Frames Goal 3] Extend numeric patterns. [Patterns, Functions, and Algebra Goal 1] Key Activities Students review measuring weight in ounces and grams and start a classroom Gram and Ounce Museum. They estimate weights and practice converting between grams and ounces. Ongoing Assessment: Informing Instruction See page 851. Key Vocabulary gram ounce Materials Math Journal 2, pp. 286 and 287 transparency of Math Masters, p. 448 (optional) balance or scale standard masses index cards nickels pennies and quarters (optional) liter bottles of water (optional) chart paper (optional) Updating the World Tour Math Journal 2, pp , 340, and 341 Student Reference Book, pp. 276, 277, 281, 292, 293, 297, and Math Masters, pp (optional) Students continue the World Tour, traveling to Region 5. Math Boxes 11 1 Math Journal 2, p. 288 Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 1a. [Geometry Goal 3] Study Link 11 1 Math Masters, p. 327 Students practice and maintain skills through Study Link activities. READINESS Ordering Weights Math Masters, p objects to weigh balance or scale Students order objects by weight. EXTRA PRACTICE Estimating Weights objects to weigh scale Students estimate weights of objects. EXTRA PRACTICE 5-Minute Math 5-Minute Math, p. 134 Students convert among units of weight. Advance Preparation Give each student a nickel to use in the Math Message. In preparation for the Gram and Ounce Museum in Part 1, gather different kinds of scales, balances, and standard mass sets. See the note on page 850 for additional information. Teacher s Reference Manual, Grades 4 6 pp. 13, 44 46, , 225, 236, Unit 11 3-D Shapes, Weight, Volume, and Capacity

2 Getting Started Mental Math and Reflexes Write pairs of fractions on the board. Have students indicate thumbs-up if the fractions are equivalent. Suggestions: 1_ 2 and 2_ 4 up 1_ and up _ 1 5 and 3_ 10 down _ 1 10 and 20_ 100 down 3_ 4 and 6_ 8 up 4_ 5 and 9_ 10 down _ 2 3 and 3_ 9 down _ 7 8 and 70_ 80 up 14_ 21 and 2_ 3 up 12_ 20 and 2_ 5 down 8_ 40 and 1_ 5 up 18_ 54 and 1_ 3 up Math Message A nickel weighs about 5 grams. Look around the classroom. Find objects you think weigh about: 1 gram 10 grams 25 grams 100 grams 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS Interactive whiteboard-ready epresentations are available at to help you teach the lesson. Demonstrate or have students demonstrate how to use a scale or balance to weigh some of the objects identified by students for the weights given. For example: 1 gram centimeter cube 10 grams hexagon pattern block 25 grams compass 100 grams calculator For greater accuracy in weighing small objects, weigh several at once and divide to find the weight of a single object. Review the relationship betwen grams and kilograms (1,000 grams = 1 kilogram) and other metric units of mass, including the milligram ( 1_ gram) and the metric ton (1,000 kilograms). Ask: 1,000 What might be measured in milligrams? Sample answer: medicine In grams? Sample answer: food In kilograms? Sample answer: body weight NOTE In everyday language, the terms weight and mass are used more or less interchangeably. One may, for example, try to lose weight in order to improve one s body mass index. But in technical and scientific contexts, weight and mass are quite different. In such contexts, weight refers to the force of gravity on an object, whereas mass is a measure of the amount of matter in an object. Mass and weight are proportional an object with twice the mass, for example, weighs twice as much so the distinction between them is subtle and was not understood even by scientists until relatively recently. So, for example, units such as grams and pounds, which have been in use for hundreds of years, are often used for both mass and weight, and the context must be used to sort out what is being measured. See Section 14.6 of the Teacher s Reference Manual for a further discussion of the differences between weight and mass. In metric tons? Sample answer: whale Discuss the difference between weight and mass. Ask questions such as the following: If you went to the moon and weighed yourself, would you weigh more or less than you do on Earth? less Why? Gravity is weaker on the moon than it is on Earth. If your weight on the moon is not the same as on Earth, what does remain the same? mass Would you rather have a bowling ball dropped on your toe on Earth or on the moon? Explain. On the moon, because the weight of the bowling ball is less on the moon so it would hurt less. Lesson

3 NOTE The distinction between mass and weight is tricky, so do not expect students to grasp it right away. Return to questions such as these throughout this unit as the occasion arises. Can you think of an activity where your weight changes but your mass stays the same? Sample answers: skydiving; jumping off a diving platform; riding on an elevator that is either starting to move or coming to a stop Would an astronaut be able to move a large satellite easily since it is weightless in outer space? No, because the satellite is still massive and resists being moved. Review ounces by asking students to name objects that weigh about 1, 4, 8, 16, and 32 ounces. Have students use the scale or balance to weigh some of the objects they suggest. For example: 1 ounce chalk/white board eraser 4 ounces calculator 8 ounces pad of paper; 50 sheets 16 ounces Student Math Journal 32 ounces Student Reference Book Review the relationship between ounces and pounds (16 ounces = 1 pound) and pounds and tons (2,000 pounds = 1 ton). Ask: What might be measured in ounces? Sample answer: letters In pounds? Sample answer: body weight In tons? Sample answer: trucks Adjusting the Activity Display a poster in the classroom to remind students of weight equivalencies and approximate comparisons. Consider adding pictures of items for the weights listed to provide a reference for students. For example: Metric Units 1 gram (g) = 1,000 milligrams (mg) 1 kilogram (kg) = 1,000 grams 1 metric ton (t) = 1,000 kilograms ELL NOTE Use a variety of measuring tools for the Gram and Ounce Museum (for example, a bathroom scale, a diet scale, and a spring scale) so students can measure a range of weights. The minimum equipment is a rocker balance or pan balance and a set of standard masses. Use commercial standard masses, or for metric standard masses, use nickels (about 5 grams each) and pennies dated 1983 or later (about 2.5 grams each). for customary standard masses, use quarters (about 0.2 ounce each). To make larger standard masses for weighing heavier objects, coins, washers, or other objects can be taped together or placed in resealable plastic bags. U.S. Customary Units 1 pound (lb) = 16 ounces (oz) 1 ton (T) = 2,000 pounds Rules of Thumb 1 kilogram equals about 2.2 pounds. 1 ounce equals about 30 grams. 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 Setting up a Gram and Ounce Museum WHOLE-CLASS DISCUSSION Introduce a project to create a museum of objects of different weights measured in grams and ounces. Use index cards to label objects in the museum and record their weights. The measuring tools available determine the range of weights you can display. For example, if you are limited to one balance and coins as standard 850 Unit 11 3-D Shapes, Weight, Volume, and Capacity

4 masses, then aim for a modest weight range (possibly up to 500 grams or 16 ounces). If you also have a scale or a balance that can accommodate larger weights, then expand the range of weights. Discuss the goals for the collection, the kinds of objects to be collected, and the procedures for adding objects to the museum. For example, if you have a scale that is precise enough to weigh objects to the nearest gram, you might decide to try to find an object for every number of grams from 1 to 100. Because this will be a large collection, you might focus on common items like rocks. The procedure for adding items should probably be managed by students. Ask students to bring in objects for the museum over the next week or two. To ensure accuracy and to assess students skill in weighing different objects, require that every item added to the museum be weighed by two or three students working independently. Date LESSON 11 1 Time Estimating Weights in Grams and Kilograms A nickel weighs about 5 grams (5 g). A liter of water weighs about 1 kilogram (1 kg). In Problems 1 7, circle a possible weight for each object. 1. A dog might weigh about 20 kg 200 kg 2,000 kg 2. A can of soup might weigh about 4 g 40 g 400 g 3. A newborn baby might weigh about 3 kg 30 kg 300 kg 4. An adult ostrich might weigh about 1.5 kg 15 kg 150 kg 5. A basketball might weigh about 0.6 kg 6 kg 60 kg 6. The weight limit in an elevator might be about 100 kg 1,000 kg 10,000 kg 7. A pencil might weigh about 4.5 g 45 g 450 g Student Page 8. Choose one of the problems above. Explain why you chose your answer. Sample answer: Problem 7 I thought a pencil would weigh about the same as a nickel so I chose 4.5 grams. 140 Estimating Weights (Math Journal 2, p. 286) PARTNER PROBLEM SOLVING Math Journal 2, p _EMCS_S_MJ2_G4_U11_ indd 286 2/15/11 6:15 PM Students estimate the weights of different objects. Partners should discuss the possibilities and come to an agreement about which measure is the most reasonable for each object. Adjusting the Activity ELL Have a handful of nickels and a couple of liter bottles of water available so students have an opportunity to hold the different weights, compare them, and use this information to make better estimates. 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 Converting between Metric and Customary Weights (Math Journal 2, p. 287; Math Masters, p. 448) Students use a double-scale number line to convert between grams and ounces. Use a transparency of Math Masters, page 448 to demonstrate how to use the number line. PARTNER PROBLEM SOLVING Date LESSON 11 1 Time Metric and Customary Weight The number line below has ounces on the top and grams on the bottom. It shows, for example, that 7 ounces are about equal to 200 grams. ounces grams Use the number line to give the approximate weight of each object. Sample answers: Student Page ounces 16 ounces About 425 grams About 455 grams Ongoing Assessment: Informing Instruction Watch for students who do not notice that the ounces number line has a different scale than the grams number line. Have students cover the grams portion of the double-scale number line with a sheet of paper while they label the tick marks on the ounces number line. Then have them reverse the procedure. 100 grams 500 grams About 3 1_ 2 ounces About 17 1_ 2 ounces Use the number line to help you determine which object weighs more. Circle the heavier object grams 2.3 ounces 6. 5 ounces 454 grams Math Journal 2, p _EMCS_S_MJ2_G4_U11_ indd 287 2/16/11 1:33 PM Lesson

5 Date LESSON 11 1 Math Boxes 1. a. Explain how you know that the pattern below is an example of a translation. 2. Find the solution of each open sentence. 2 a. 6 7 y 4 7 y b. 1 0 a 1 0 a 10 c. 3 5 r r 10, or d. 3 4 m 7 8 m 8 4. Insert parentheses to make each number sentence true. a b c. 48 / d. 150 / Time Sample answer: The figure is slid to the right. It was not turned or flipped. The size and shape are the same. Student Page b. Draw the figure after it is translated to the right. 3. Circle the numbers that are multiples of 6. Put an X through the numbers that are multiples of , If you use an average of 7 sheets of paper per day, about how many sheets would you use in ,548 5,096, or 5, a. 1 week? sheets b. 4 weeks? sheets c. 52 weeks? sheets d. 2 years? sheets Ongoing Learning & Practice Updating the World Tour INDEPENDENT (Math Journal 2, pp , 340, and 341; Student Reference Book, pp. 276, 277, 281, 292, 293, 297, and ; Math Masters, pp ) Social Studies Link Students follow the established World Tour routine: They update the Route Map by drawing a line segment connecting Beijing, China, and Mexico City, Mexico. They use the World Tour section of the Student Reference Book to locate facts about Mexico and Mexico City, and fill in the Country Notes pages for this country and capital. If they are keeping a Route Log, they update it. Math Journal 2, p. 288 Math Boxes 11 1 (Math Journal 2, p. 288) INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson The skill in Problem 5 previews Unit 12 content. Study Link Master Name Date Time STUDY LINK 11 1 The World s Largest Foods Food Weight Date Location 140 Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 1a Use Math Boxes, Problem 1a to assess students ability to describe a translation. Students are making adequate progress if they state that the pattern is an example of a translation because the original figure moved or slid to the right, without being turned or flipped, and that the size and shape of the figure remained the same. Some students might be able to sketch an example of a translation in Problem 1b. [Geometry Goal 3] Apple 3 pounds 11 ounces October 1997 Linton, England Bagel 714 pounds July 1998 Mattoon, Illinois Bowl of pasta 7,355 pounds February 2004 Hartford, New York Chocolate bar 5,026 pounds March 2000 Turin, Italy Garlic 2 pounds 10 ounces 1985 Eureka, California Gingerbread man pounds November 2003 Vancouver, Canada Hamburger 6,040 pounds September 1999 Sac, Montana Ice cream sundae tons July 1988 Alberta, Canada Pumpkin 1,337 pounds October 2002 Topsfield, Massachusetts Taco 1,654 pounds March 2003 Mexicali, Mexico Source: Use the information in the table to solve the following problems The largest apple weighed ounces. Study Link 11 1 (Math Masters, p. 327) INDEPENDENT Home Connection Students convert among ounces, pounds, and tons as they solve problems involving some of the world s largest foods. 2. A typical hamburger weighs about 4 ounces. The largest hamburger weighed 96,640 ounces. 3. Which 2 foods together weigh about a ton? and pumpkin bagel Or, gingerbread man and taco 4. A kilogram is a little more than 2 pounds. Which 4 foods each weigh more than 1,000 kilograms? Pasta, chocolate bar, hamburger, ice cream sundae 5. On the back of this page, use data from the table to write and solve your own problem. Answers vary. Practice $75 $50 $0 $55 ($25) 8. $60 $60 9. $30 6. $75 $25 7. $45 ($30) Math Masters, p Unit 11 3-D Shapes, Weight, Volume, and Capacity

6 3 Differentiation Options READINESS Ordering Weights (Math Masters, p. 389) SMALL-GROUP Min To explore estimating and ordering weights, have students hold and compare the weights of five objects and then place them in order from lightest to heaviest. Ask students to record the estimated order on an Exit Slip. Then have the group use a balance or scale to check their estimates and record the actual order and weights on the Exit Slip. Discuss how this activity uses the force of gravity as a guide to ordering objects by weight. In the Space Shuttle, the objects would be weightless, but their masses would be the same as they are on Earth. Ask students how they might order a set of objects by mass in the Space Shuttle. Sample answer: One method would be to give each object a push to set it in motion. The more an object resists being set in motion, the more massive it is. So the harder an object is to push, the more mass it has. SMALL-GROUP EXTRA PRACTICE Estimating Weights Min To practice estimating weights of objects with and without tools, have students estimate the weights of objects by holding them and by comparing the weights to benchmarks. Then have students use a scale to determine the actual weight. Consider having students do this activity in teams. Have students devise a scoring system to determine the winning team. SMALL-GROUP EXTRA PRACTICE 5-Minute Math 5 15 Min To offer students more experience with units of weight, see 5-Minute Math, page 134. Planning Ahead Have models of the following geometric solids available for Lesson 11-2: rectangular prism, triangular prism, square pyramid, cylinder, cone, and sphere. Gather examples from everyday objects or make them from Math Masters, pages Lesson