These are drawings of three-dimensional objects. Which one doesn’t belong? Explain your reasoning.[img]https://cdn.openupresources.org/uploads/pictures/8/8.9.A1.Image.01.png[/img]
Answers vary. Sample responses:Figure A doesn’t belong because:[list][*]It’s the only object with exactly two surfaces.[/*][*]It’s the only object with exactly one base.[/*][/list]Figure B doesn’t belong because:[list][*]It’s the only object that has no edges or planar faces.[/*][*]It’s the only object that isn’t stable if you set it down (i.e., it would roll around).[/*][/list]Figure C doesn’t belong because:[list][*]It’s the only object in which a side is a rectangle in two dimensions but curved in three dimensions.[/*][*]It’s one object with exactly two bases.[/*][/list]Figure D doesn’t belong because:[list][*]It’s the only object in which all the faces are flat planes.[/*][*]It’s the only object with rectangular faces.[/*][/list]
ACTIVITY: 20 minutes11.2: Height and VolumeCCSS Standards: AddressingCCSS Standards: Building towardsIn this activity, students investigate how the height of water in a graduated cylinder is a function of the volume of water in the graduated cylinder. Students make predictions about how the graph will look and then test their prediction by filling the graduated cylinder with different amounts of water, gathering and graphing the data (MP4).LaunchArrange students in groups of 3–4. Be sure students know how to measure using a graduated cylinder. If needed, display a graduated cylinder filled to a specific measurement for all to see and demonstrate to students how to read the measurement. Give each group access to a graduated cylinder and water.Give groups 8–10 minutes to work on the task, follow with a whole-class discussion.For classrooms with access to the digital materials or those with no access to graduated cylinders, an applet is included here. Physical measurement tools and an active lab experience are preferred.
[list=1][*]The graph shows the height vs. volume function of an unknown container. What shape could this container have? Explain how you know and draw a possible container.[img]https://cdn.openupresources.org/uploads/pictures/8/8.5.D1.Image.01.png[/img][/*][*]The graph shows the height vs. volume function of a different unknown container. What shape could this container have? Explain how you know and draw a possible container.[img]https://cdn.openupresources.org/uploads/pictures/8/8.5.D11.Image.Revision.115.png[/img][/*][*]How are the two containers similar? How are they different?[/*][/list]
[list=1][*]Answers vary. Sample response: A shape in the form of two cylinders stacked on top of each other, with the upper cylinder having a greater radius. The height grows linearly with the volume in each cylinder, but as the water level rises into the second container, the height will begin to grow less quickly (since it takes more volume to achieve the same increase in height). [br][img]https://cdn.openupresources.org/uploads/pictures/8/8.5.D.11.Image01.png[/img][/*][*]Answers vary. Sample response: 3 cylinders stacked on top of each other. The bottom cylinder should be the tallest. The middle cylinder should be shorter and have a smaller radius than the bottom. The top cylinder should be the shortest but have the largest radius.[/*][*]Answers vary. Sample response: Both containers are made up of cylinders stacked on top of each other. The containers are different because the first container is made up of two parts, while the second is made up of three parts.[/*][/list]
Student-Facing Task StatementTwo cylinders, a and b, each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Which cylinder has the larger radius? Explain how you know.[img]https://cdn.openupresources.org/uploads/pictures/8/8.5.D11.Image.Revision.113.png[/img]
Cylinder B. Sample reasoning: a cylinder with a large radius would have a smaller change in height (slope) for the same volume of water added when compared to a cylinder with a smaller radius. Since the line for B has the smaller slope, it must be the cylinder with the larger radius.