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Mystery Blocks Connecting Geometry, Algebra and Science Lenny VerMaas ESU #6 Residence th 210 5 Street P.O. Box 748 205 South Washington Ave Milford, NE 68405 Cortland, NE 68331 402-761-3341 402-798-7453 lvermaas@esu6.org http://manila.esu6.org/lvermaas Grade level 6-10 Students calculate the surface area and volume of various sized blocks of wood. They measure the mass, water displaced when floating, and water displaced when submerged of the blocks. Several important concepts are discovered as well as a “surprise” about the blocks. Agenda Overview of the mystery blocks activity. Relate to Nebraska State Standards Learning Strategies Complete part of the activity. o Estimation is important o Measure a block and fill in the chart o Plot point on graph paper Processing and analyzing the data Alternative assessment idea o The Nebraska Hot Tub Lenny VerMaas page -1- lvermaas@esu6.org http://manila.esu6.org/lvermaas Mystery Blocks Materials needed: 6 pieces of wood block cut to fit inside graduated cylinder 6 pieces of wood blocks cut from another type of wood 1 piece of wood could be fixed with a plug to change the density of the block (add lead) Cedar and oak block work well. The shape of the blocks is dependent on the level of students. Rectangular and triangular blocks work well to start with. The blocks can be number and painted to help disguise the type of wood and plugs. Graduated cylinders Gram scales Paper towels Scissors of some other tool to get blocks from cylinders Calculators and rulers Chart paper for graphing points with the volume on the horizontal and mass on the vertical. Guided practice (depth depending on level and experience of teachers) Review how to find the volume of a rectangular prism (triangular, pyramid, or others) Measure in cm but use accuracy of mm Volume is measured in cm cubed Find the mass of the objects using the scales Work in groups o Blocks may be rotated to confirm measurements and check for accuracy Plot the mass and the volume of each block and place the number of block by the point. Sample graph X X X X Mass X X X Volume As students plot points look for blocks with the same number being placed at different points. Drawing a line between numbers that are the same will highlight these points. Most of these lines will be horizontal because the masses will be similar and volumes will vary. Volumes will differ due to rounding or calculation mistakes. Have students reconcile differences. Lenny VerMaas page -2- lvermaas@esu6.org http://manila.esu6.org/lvermaas After data is collected and plotted. Ask for observations from the data collected and graphed. Depending on the group some will quickly observe the following while others will need some guidance. Help them to discover the following: There are different types of wood. Why? Same volume different weight. Float in water differently. Discuss how water displacement can be used to confirm the volume o Block must be completely under the water o Accuracy will vary depending on graduated cylinders used The density of a block can be determined by o Mass/volume o The percent of the block that floats under water o The slope of the line that goes through points from the same type of wood. Have students estimate the density and compare with calculated density. Show how the points of the graph are related be a line. (could use best fit) o (0,0) is a point on both lines o slope of the line will be the average density of the wood. Using the gram stackers the smallest cube is 1 cm cubed, has a weight of 1 gram and a density of 1 so it will just float in water. (actually it should remain suspended in the water at any level) If using the wood with the plug its point will be off of the line What is the difference between mass and weight? Mass remains the same weight changes due to gravity. Estimate the density of blocks by observing the percent of the block under water while floating. Have students calculate the density of their blocks. Use a yard stick to draw a line through the points that come from the same type of wood. Pick two points from different places on the line and find the slope of the line. Compare this slope with the density of the blocks. Checking the density of an object is a way to check for purity. If an object is hollow or not pure the point would be above or below the line. Other explorations What changes would occur if the liquid was not water or salt water? What is the density of objects that float or sink? How can something that weights a lot not sink? Literature connections “Mr. Archimedes’ Bath by Pamela Allen. Assessments The California Hot Tub Lenny VerMaas page -3- lvermaas@esu6.org http://manila.esu6.org/lvermaas Mystery Blocks 1. Pick a block and complete the information requested in the table. 2. Measure the length to the nearest millimeter but write as centimeters. 3. Measure mass to the nearest gram. 4. When the measurements are completed, plot and label the points on the graph with the mass on the vertical axis and volume on the horizontal axis. Put the block number and group ID by the point. 5. If another group has measured the same block compare your measurements. If your measurements are significantly different from another group check with that group to see how they arrived at their numbers. Block # Estimated Estimated Measured volume Measured ml of water ml of water volume in mass in in cubic cm (show mass in displaced displaced when cubic cm. grams work) grams when floating submerged Lenny VerMaas page -4- lvermaas@esu6.org http://manila.esu6.org/lvermaas Mystery Block Worksheet Make a graph of the following information. Block # Volume Mass Density 1 45ml 9.5 grams 2 18 ml 4.2 grams 3 33 ml 6.6 grams 4 88 ml 19.2 grams 5 55 ml 11.6 grams Find the equation of the best fit line through the above points. What does the slope of the line represent? Explain why. If a block of wood was made of the same material with a volume of 160 cubic centimeters, how much would the block weigh? If a block of wood was made of the same material with a weight of 45 grams what would be the volume of the block? Another piece of wood weighs 60 grams and has a volume of 195 ml. Is this block made out of the same type of wood? Explain. Measure the trapezoid below. Find the area of the trapezoid in as many ways as possible. Give the answer in square cm. Lenny VerMaas page -5- lvermaas@esu6.org http://manila.esu6.org/lvermaas Mystery Block Quiz Name ___________________ Score __________ 1. Find one of the rectangular blocks. Find the volume and weight. Sketch a picture of the block and show measurements. Show your work. Block # ______ Volume ______ Weight _______ Density _______ 2. Find one of the triangular blocks. Find the volume and weight. Sketch a picture of the block and show measurements. Show your work. Block # ______ Volume ______ Weight _______ Density _______ 3. Find the area of the trapezoid shown below. Show your measurements and work. Give your answer in square cm. Lenny VerMaas page -6- lvermaas@esu6.org http://manila.esu6.org/lvermaas Mystery Block Quiz Name ___________________ Score __________ 1. The mass of an object can be found by weighing the object or by observing what with water? Explain 2. The volume of an object can be calculated by measuring with a ruler or by observing what with water? Explain 3. The density of a piece of wood can be calculated or it can be found by observing what in water? Explain and draw a diagram. 4. On the back of this sheet make a graph of the information Block # Volume Mass Density 1 40 ml 28 grams 2 15 ml 10 grams 3 33 ml 24 grams 4 82 ml 59 grams 5 51 ml 35 grams 5. Find the equation of the best fit line through the above points. 6. What does the slope of the line represent? Explain why. 7. If a block of wood was made of the same material with a weight of 88 grams what would be the volume of the block? 8. If a block of wood was made of the same material with a volume of 185 cubic centimeters, how much would the block weigh? 9. Another piece of wood weighs 126 grams and has a volume of 210 ml. Is this block made out of the same type of wood? Explain. Lenny VerMaas page -7- lvermaas@esu6.org http://manila.esu6.org/lvermaas The Nebraska Hot Tub Depth of water Time What’s the story??? Write a story that will fully explain the graph above. Lenny VerMaas page -8- lvermaas@esu6.org http://manila.esu6.org/lvermaas