Answer Key Lesson 4: Mass vs. Volume: Proportions and Density

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1 Answer Key Lesson : ass vs. olume: Proportions and Density Student Guide ass vs. olume: Proportions and Density r. oreno s lass is experimentin with thins that sink and float. This piee of lay sinks in water. I will try a smaller piees. That will be lihter, so maybe it will float. I am not sure. A smaller piee would have less mass, but wouldn t it have less volume too? aybe its density would not be different. ass vs. olume: Proportions and Density (SG pp ) Questions 23.* A sample piture: The students do an experiment to find out whether a different amount of the same ass material has a different density,. They measure the mass and volume of olume 3 different amounts of lay, reord their data in a data table, and raph their data. Then they do the same thin for different amounts of steel to see whether they et similar results for different materials. You will do the same in the lab that follows. You will find the mass and volume of 3 steel balls and 3 lumps of lay that are about the same size as the steel balls.. Disuss with your roup how you will do the experiment. Then draw a piture that shows what you will do. Be sure to label the variables and inlude all the equipment you will use. ass vs. olume: Proportions and Density SG Grade 5 Unit Lesson 53 Student Guide - Pae Find and reord the mass and volume of 3 different-sized steel balls to the nearest tenth. To et aurate measurements for the small steel ball, measure the mass and volume of 5 idential small steel balls and divide by 5. aterial : Steel Size of Objet small ( 2 -inh diameter) medium (-inh diameter) lare ( -inh diameter) olume (in ) ass (in ) 3. Find and reord the mass and volume of 3 different-sized lay balls to the nearest tenth. ake your lumps of lay about the same size as eah of the steel balls. Use the same lumps of lay to measure mass and volume. easure the mass first to avoid soy lay. aterial 2: Clay Size of Objet small medium lare olume (in ) ass (in ). Plot the data for eah material on the same raph. Put ass () on the vertial axis and olume () on the horizontal axis. Sale your axes so that oes up to at least 8 and oes up to at least What is the value of when is? Put this point on your raph. 6. Draw a best-fit line or urve to show the pattern of your points. Draw one for steel and a separate one for lay. Label eah line or urve with the name of the material it represents. 5 SG Grade 5 Unit Lesson ass vs. olume: Proportions and Density Student Guide - Pae * Sample data tables: Size of Objet small ( 2 -inh diameter) medium (-inh diameter) lare ( -inh diameter) Size of Objet. See raph below. 5.* 6.* ass in small medium lare aterial : Steel olume (in ) aterial 2: Clay olume (in ) ass vs. olume steel lay olume in ass (in ) ass (in ) 9 5 *Answers and/or disussion are inluded in the lesson. TG Grade 5 Unit Lesson Answer Key

2 Answer Key Lesson : ass vs. olume: Proportions and Density 7. A.* Both raphs are straiht lines that pass throuh the point (, ). B.* The raph for steel is a steeper line than the raph of lay. 8. The answers are based on the sample raph in Question 6. A. About 9 ; interpolate B. About 23 ; extrapolate C. ; interpolate D. About 28 ; extrapolate 9. The answers are based on the sample raph. ass in A. 2 6 B. 2 5 All 3 ratios are equal.. The answers are based on the sample raph in Question A. 2 B. ass vs. olume steel lay olume in Q#9 All 3 ratios are approximately equal.. A. Yes; The density is the ratio and sine this ratio is onstant for different amounts of the same material, they have the same density. B.* No; Sine the smaller piee of the lay has the same density as the larer piee that sinks, the smaller piee will sink also. 2. A. Answers will vary. Usin points from the sample raph as in Questions 9 and, the density of lay is B. Answers will vary. Usin points from the sample raph, the density of steel is *Answers and/or disussion are inluded in the lesson. Q#9 Q#9 Q# Q# Q# A. How is your raph for steel the same as your raph for lay? B. How is your raph for steel different from your raph for lay? 8. Use your raph to find mass or volume. Tell whether you used interpolation or extrapolation. A. What is the mass of a steel ball whose volume is 2? B. What is the volume of a steel ball whose mass is 8? C. What is the mass of a piee of lay whose volume is 5? D. What is the volume of a piee of lay whose mass is 6? 9. A. Choose a point on your line for lay and use it to write the ratio of the mass of lay to the volume of lay. B. Choose two more points on the line for lay and use them to write ratios of mass to volume. Are the three ratios from the line for lay equivalent or approximately equivalent?. A. Choose a point on your line for steel and use it to write the ratio of the mass of steel to the volume of steel. B. Choose two more points on the line for steel and use them to write ratios of mass to volume. Are the three ratios from the line for steel equivalent or approximately equivalent?. Answer Romesh s and Ana s oriinal questions: A. Do different amounts of the same material have the same density? B. Will a smaller piee of lay float? Why or why not? 2. A. Usin your data, ive the density of lay. B. Usin your data, ive the density of steel. ass vs. olume: Proportions and Density SG Grade 5 Unit Lesson 55 Student Guide - Pae 55 TG Grade 5 Unit Lesson Answer Key 2

3 Answer Key Lesson : ass vs. olume: Proportions and Density Chek-In: Questions 3 6 Show or tell how to use the raph and ratios to solve eah problem. 3. Suppose you wanted to find the volume of a lump of lay that was too bi to fit in your raduated ylinder. How an you use your two-pan balane to help find its volume?. aria put a mystery objet in a box. She told the lass it had a mass of 3 and a volume of 6. Was it steel, lay, or a third material? 5. A piee of lay has a volume of. Find its mass. 6. A piee of steel has a mass of 5. Find its volume. Patterns with Graphs: Sink and Float 7. Use your data from the Sink and Float lesson to raph the mass vs. volume line for eah of the objets in that lesson. Be sure to inlude the line for water. The line for eah objet will o throuh the point (, ) and that objet s data point. Romesh s line for a rok is shown at the riht. ake one line for eah objet. Label eah line with the name of the objet. Indiate whether the objet sinks or floats by labelin its line with S or F. 56 SG Grade 5 Unit Lesson Student Guide - Pae 56 ass (in ) rok S ass vs. olume olume (in ) ass vs. olume: Proportions and Density 3. Possible response: We an use the balane toether with our raph of ass vs. olume for lay to find the answer. We an use the two-pan balane to find the mass of the lay. Then, usin the raph, we an interpolate or extrapolate to find the volume. Another method we an use is to represent density as the ratio of and to ompare ratios to find the volume..* It is a third material. The mystery objet has a density of /. This is less than the density of steel and more than that of lay. 5.* 2 or 2 6.* 7.* ass vs. olume ass in steel (s) rok (s) lay (s) olume in orn syrup (s) water plasti (s) veetable oil paraffin (f) wood (f) ork (f) *Answers and/or disussion are inluded in the lesson. 3 TG Grade 5 Unit Lesson Answer Key

4 Answer Key Lesson : ass vs. olume: Proportions and Density 8. The lines of objets that sink lie above the line for water, and the lines of objets that float lie below the line for water. 9. A.* Sine the line for the objet lies below the line for water, the objet will float. 5 B.* Density /. Sine this density is less than /, the objet will float in water. 2. A.* Usin a alulator we an ompute the densities for the mass and volume iven in the data table usin the ratio. B.* Graphially, a steeper line represents more mass per volume than a line that is not as steep. Therefore, a steeper line represents a material that is denser. 2. A.* 32 ; 8 ; 32 B. 25 ; ; ethods may vary. We an represent density as a ratio of and ompare the ratios to solve the problem. 23. We an find the density of eah of the roks, and if they are the same, then we an onlude that the roks are probably made of the same material. Homework (SG pp ) Questions 7. A. Density B. 96 ; 6 ; 96 C. 5 ; 3 6 ; 5 2. These problems an be solved usin the proportion 3. A. 5 B. 27 C. 6 D..5 E. 75 F A. About 5, extrapolate B. About.5, interpolate. Usin the point (3, 5 ): 2 Usin the point (6, 6 ): What pattern do you see in your raph? Explain how to tell from your raph whether an objet will sink or float. 9. On your raph, plot the data point for a mystery objet with a mass of 5 and a volume of 8. Draw the line throuh this point and the point,, representin the mass vs. volume line for this material. (Label it Question 9. ) A. Based on the pattern you observed in your raph, would you expet the objet to sink or float in water? Explain. B. Find the objet s density. Based on its density, would you expet the objet to sink or float in water? Explain. 2. A. Explain how to use the mass and volume data table to ompare densities. B. Explain how to use the raph to ompare densities. 2. An objet has a density of or /. A. If its volume is 8, what is its mass? Show your work. B. If its mass is, what is its volume? Show your work. 22. The final produt from a steel mill should not have air pokets trapped inside. You are iven a piee of steel with a volume of 2. Explain how you would o about determinin whether the piee was solid steel or had air trapped inside. 23. Two roks are thouht to be made of the same material. Explain how you ould investiate whether this is true. ass vs. olume: Proportions and Density SG Grade 5 Unit Lesson 57 Student Guide - Pae 57. An objet has a mass of 8 and a volume of 8. A. Express its density as a ratio of mass to volume. B. An objet made of the same material has a volume of 6. What is its mass? C. An objet made of the same material has a mass of 3. What is its volume? ass 2. A material has a density, olume, of 3. Balls of different sizes are made from this material. The masses of the balls are listed below. Find the volumes. A. 2 B. 36 C. 8 D. 2 E. F Here is the mass vs. volume raph of an unknown material. A. What is the mass of 28 of this Unknown aterial 2 material? Did you interpolate or extrapolate to find your answer? 8 7 B. What is the volume of of this 6 material? Did you interpolate or 5 extrapolate to find your answer? 3 2. A piee of the unknown material represented in the raph has a mass of 2. Find its volume. (Hint: 8 Sine the numbers are too bi to be 7 on the raph, the problem an t be 6 solved by readin the raph diretly.) *Answers and/or disussion are inluded in the lesson. TG Grade 5 Unit Lesson Answer Key (in ) (in ) ass vs. olume: Proportions and Density SG Grade 5 Unit Lesson 59 Student Guide - Pae 59

5 Answer Key Lesson : ass vs. olume: Proportions and Density 5. Find the density of the objets in the table. Whih objet has the reatest density? 6. Here is a raph of the mass vs. volume of several materials. Usin the raph, tell whih of the materials will sink and whih will float in water. Explain why. 5. Objet C has the reatest density. Objet A B C D olume of Objet (in ) 2 9 ass of Objet (in ) Density in / /2 /9 5.5 / 5.5 / 6. The vs. line for water falls between the lines for material F and G. 7. A. Find the densities of the materials in the raph. B. Based on their densities, tell whih materials will sink and whih will float in water. Explain why. E F water G H 55 SG Grade 5 Unit Lesson Student Guide - Pae 55 ass vs. olume: Proportions and Density The lines above the line for water (materials E and F) will sink; materials G and H will float. Alternatively, students an use the raph to find ratios for the four materials. aterials E and F have a ratio that is reater than. The ratio of for materials G and H is less than. Thus, materials E and F sink and materials G and H float. 7. A. Density of aterial E 3 7 Density of aterial F 3 Density of aterial G 3 2 Density of aterial H B. Sine the densities of aterials E and F are reater than, these materials will sink in water. Sine the densities of aterials G and H are less than, these materials will float in water. 5 TG Grade 5 Unit Lesson Answer Key