This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Sugar Cone: | Students are asked to solve a problem that requires calculating the volume of a cone. |
| Platinum Cylinder: | Students are asked to solve a problem that requires calculating the volume of a cylinder. |
| Louvre Pyramid: | Students are asked to find the height of a square pyramid given the length of a base edge and its volume. |
| Cylinder Formula: | Students are asked to write the formula for the volume of a cylinder, explain what each variable represents, and label the variables on a diagram. |
| Cone Formula: | Students are asked to write the formula for the volume of a cone, explain what each variable represents, and label the variables on a diagram. |
| Burning Sphere: | Students are asked to solve a problem that requires calculating the volume of a sphere. |
| Sphere Formula: | Students are asked to write the formula for the volume of a sphere, explain what each variable represents, and label the variables on a diagram. |
| Pyramid Formula: | Students are asked to write the formula for the volume of a pyramid, explain what each variable represents, and label the variables on a diagram. |
| Name |
Description |
| What Floats Your Boat: | Students will solve real-world and mathematical problems involving density. Students will engineer solutions to the given problem using gained scientific content knowledge as application of mathematical skills |
| Slope Intercept - Lesson #1: | This is lesson 1 of 3 in the Slope Intercept unit. This lesson introduces graphing proportional relationships. In this lesson students will perform an experiment to find and relate density of two different materials to the constant of proportionality and unit rate. |
| Knight Shipping, Inc.: | In this design challenge students will take what they have learned about calculating the volumes and densities of cones, cylinders, and spheres, to decide which shape would make the best shipping container. Students will calculate the volumes and densities to help select the best design and then test them to move at least 3 containers of the chosen shape across the classroom. Students will fill the shapes with marshmallows to visually confirm which shape would hold more. |
| How Many Cones Does It Take?: | This lesson is a "hands-on" activity. Students will investigate and compare the volumes of cylinders and cones with matching radii and heights. Students will first discover the relationship between the volume of cones and cylinders and then transition into using a formula to determine the volume. |
| Find your Formula!: | Students will investigate the formula for the volume of a pyramid and/or cone and use those formulas to calculate the volume of other solids. The students will have hands-on discovery working with hollow Geometric Solids that they fill with dry rice, popcorn, or another material. |
| Silly Cylinders: | This is a short activity where students determine the density of the human body by considering each part of the body to be a cylinder. I use this activity during the second week of school, so students have already had some practice with measurement. In addition to providing students with practice in data collection and problem solving, it is a good activity that allows teachers to measure students' previous knowledge in these areas. |
| Area to Volume Exploration: | In this student-centered lesson, the formulas for the volume of a cylinder, cone, and a sphere are examined and practiced. The relationship between the volume of a cone and a cylinder with the same radius and height is explored. Students will also solve real-world problems involving these three-dimensional figures. |
| Pack It Up: | Students use geometry formulas to solve a fruit growing company's dilemma of packing fruit into crates of varying dimensions. Students calculate the volume of the crates and the volume of the given fruit when given certain numerical facts about the fruit and the crates. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom. |
| Victorious with Volume: | In this lesson, the students will explore and use the relationship of volume for cylinders and cones that have equal heights and radii. |
| M&M Soup: | This is the informative part of a two-lesson sequence. Students explore how to find the volume of a cylinder by making connections with circles and various real-world items. |
| Cylinder Volume Lesson Plan: | Using volume in the real world |
| Relating Surface Area and Volume: | Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume. |
| Name |
Description |
| Glasses: | In this resource, students will determine the volumes of three different shaped drinking glasses. They will need prior knowledge with volume formulas for cylinders, cones, and spheres, as well as experience with equation solving, simplifying square roots, and applying the Pythagorean theorem. |
| Comparing Snow Cones: | Students will just be learning about similarity in this grade, so they may not recognize that it is needed in this context. Teachers should be prepared to give support to students who are struggling with this part of the task. To simplify the task, the teacher can just tell the students that based on the slant of the truncated conical cup, the complete cone would be 14 in tall and the part that was sliced off was 10 inches tall. (See solution for an explanation.) There is a worthwhile discussion to be had about parts (c) and (e). The percentage increase is smaller for the snow cones than it was for the juice treats. The snow cones have volume which is equal to those of the juice treats plus the volume of the dome, which is the same in both cases. Adding the same number to two numbers in a ratio will always make their ratio closer to one, which in this case means that the ratio - and thus percentage increase - would be smaller. |
| Flower Vases: | The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers. |
| Shipping Rolled Oats: | Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations. |
| Shamu Stadium Geometry-SeaWorld Classroom Activity: | In this problem solving task, students investigate Shamu Stadium at Sea World. They will use knowledge of geometric shapes to solve problems involving area and volume and examine as well as analyze a diagram making calculations. Students will also be challenged to design an advertising poster using the measurements they mind. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Glasses: | In this resource, students will determine the volumes of three different shaped drinking glasses. They will need prior knowledge with volume formulas for cylinders, cones, and spheres, as well as experience with equation solving, simplifying square roots, and applying the Pythagorean theorem. |
| Comparing Snow Cones: | Students will just be learning about similarity in this grade, so they may not recognize that it is needed in this context. Teachers should be prepared to give support to students who are struggling with this part of the task. To simplify the task, the teacher can just tell the students that based on the slant of the truncated conical cup, the complete cone would be 14 in tall and the part that was sliced off was 10 inches tall. (See solution for an explanation.) There is a worthwhile discussion to be had about parts (c) and (e). The percentage increase is smaller for the snow cones than it was for the juice treats. The snow cones have volume which is equal to those of the juice treats plus the volume of the dome, which is the same in both cases. Adding the same number to two numbers in a ratio will always make their ratio closer to one, which in this case means that the ratio - and thus percentage increase - would be smaller. |
| Flower Vases: | The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers. |
| Shipping Rolled Oats: | Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Glasses: | In this resource, students will determine the volumes of three different shaped drinking glasses. They will need prior knowledge with volume formulas for cylinders, cones, and spheres, as well as experience with equation solving, simplifying square roots, and applying the Pythagorean theorem. |
| Comparing Snow Cones: | Students will just be learning about similarity in this grade, so they may not recognize that it is needed in this context. Teachers should be prepared to give support to students who are struggling with this part of the task. To simplify the task, the teacher can just tell the students that based on the slant of the truncated conical cup, the complete cone would be 14 in tall and the part that was sliced off was 10 inches tall. (See solution for an explanation.) There is a worthwhile discussion to be had about parts (c) and (e). The percentage increase is smaller for the snow cones than it was for the juice treats. The snow cones have volume which is equal to those of the juice treats plus the volume of the dome, which is the same in both cases. Adding the same number to two numbers in a ratio will always make their ratio closer to one, which in this case means that the ratio - and thus percentage increase - would be smaller. |
| Flower Vases: | The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers. |
| Shipping Rolled Oats: | Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations. |
