
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
Learning Goal: Students will investigate and describe how to calculate the volume and density of cones, cylinders, and spheres. Students will carry out and analyze a scientific investigation.
Engineering Goal: Students will develop a method of transport for the shape that they believe will provide the most efficient transport container.

Prior Knowledge: What prior knowledge should students have for this lesson?
Students should recognize the concept of volume and be able to plug numbers into the various formulae.
To prepare students:
 Ask them to complete a circle map on volume. A circle map is a type of thinking map, or tool for learning, that consists of a large circle with a smaller circle in the center. There is a large square or rectangle around the outside of the larger circle.
 Write "volume" in the center of the circle, and then add everything students know about volume into the outer circle.
 In the frame of reference (outermost square or rectangle), have students write how they know this information.

Guiding Questions: What are the guiding questions for this lesson?
 Compare and contrast the volume of a cone and of a cylinder.
 Possible answers include a discussion of the formulae and the different parts of them.
 How does volume or density impact how much material can fit into a certain space?
 Possible answer  Volume is how much room or space is available, so it does impact the amount of material. Density has to do with the amount of material in that space. Adding more material or matter will increase the density of the object.
 Which container would make the most efficient shipping container? Why?
 Possible answer  Cylinders make great shipping containers. They have a flat surface to limit rolling and they are easily stackable. Cones leave large gaps unless you alternate them, which is not easy if they are large and heavy.
 How would you best design a transport method for your container?
 Possible answer  I would prepare my transport to hold cylinders, either having them stand on end or laid flat.
 Explain how density capabilities contribute to your design decisions.
 Possible answers include a discussion of how density factored into their design.
 How did density affect your design?
 Possible answers include a discussion of how increasing the density made it harder to transport the materials.
 How would the density differ if our material changed? What if we used cotton, wood, or steel instead of marshmallows?
 Possible answers should demonstrate understanding that cotton would have the lowest density, wood would have a medium density, and steel would have the highest density.

Teaching Phase: How will the teacher present the concept or skill to students?
 The teacher will review examples of cones, spheres, and cylinders, and how to calculate their volume.
 The teacher will then model how the shapes will be filled with marshmallows to determine their suitability as a shipping container, and then show the students the area across which the containers will need to be shipped.
 Density should be introduced after students have an understanding of volume. Density is a ratio of the mass of an object compared to its volume.
 Using the same examples of objects that were used in practicing volume, calculate density, except this time compare how the density changes when only the material is changed. Students should realize that when an item has more mass, the density increases.
Note: A good way to get a baseline for density is to calculate the density of water. No matter how much water you use, the mass of the water in grams should be equal to the volume of the water in milliliters because the density of water is 1 g/mL. For example, you could use 100 mL and find it has a mass of 100 g; (100 g)/(100 mL) = 1 g/mL. Then if you measure 50 mL of water, you would find the mass to be 50 g; (50 g)/(50 mL) = 1 g/mL. Note that the densities will not come out perfectly. Ask students why the density is not exactly 1 g/mL. Possible answers could include imprecise measurements or even the quality of the water, since tap water is not a pure substance. The temperature of the water can also slightly change the density.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Students will complete an Engineering Design Challenge.
RealWorld Problem:What shape will make the most efficient shipping container? What is the best design for a windpowered vehicle to carry the containers?
Materials:templates for a sphere, cone, and cylinder; aluminum foil, calculator, clay, copy paper, electric fan, marbles, marshmallows, paper plates, pipe cleaners, Popsicle sticks, stopwatch, tape, triple beam balance, and wax paper
Procedure for Part A (Day 1)
 The teacher will demonstrate how to make a sphere and how to determine the number of marshmallows that fit inside the sphere.
 The teacher will demonstrate how to calculate the mass of the sphere and how to calculate the density of the sphere.
 Discuss density of objects as it relates to water (density of 1 g/mL): less than 1 g/mL floats, and more than 1 g/mL will sink.
 Have students give examples of objects that would float or sink when placed in water.
 Using templates such as the "3D Geometric Nets" at MathGeekMama.com, create one cone and one cylinder. Be sure to leave one end open for later use.
 Using your volume formulae, calculate the volume of a cone and of a cylinder. Place the volume of each shape in Data Table 1.
 Place as many marshmallows as you can into the cone without crushing them. Use the triple beam balance to find the mass of the full container. Record the mass on Data Table 1.
 Now dump out the marshmallows and count them. Record the number of marshmallows that fit in the cone on Data Table 1.
 Repeat steps 68 for the cylinder.
 Using the triple beam balance, find the mass (in grams) of each shape.
 Record the data in Data Table 1.
 Calculate the density of each shape using the density formula.
 Record the data in Data Table 1.
 Repeat steps 614 using marbles instead of marshmallows.
 Using your data, decide which shape would make the most efficient shipping container. You need to consider both the amount that can be shipped (volume) and the ease of using the shipping containers as you will have to transport three containers of the shape you choose at one time.
 Give your containers to the teacher for safe keeping.
 Complete IXL lesson on the volume of cones and cylinders and IXL lesson on the volume of spheres, or complete review worksheets found at http://www.mathworksheets4kids.com/volume.php (The answer key can be found as the second page for each worksheet chosen.)
Procedure for Part B (Day 2)
 Brainstorm for 5 minutes about how you would design your transport vehicle knowing that:
 You must transport undamaged marshmallows.
 You must move at least three containers at a time.
 You can only make one trip.
 You must transport the containers at least 50 centimeters along the designated track.
 Decide using the provided budget sheet (see attached) what materials you need to build your transport. Each group will have a budget of $200.
 Draw a picture of your transport vehicle.
 You will have 10 minutes to design your vehicle using the provided materials.
 At the end of the 10 minutes, everyone will stop building and test the designs on the designated track.
 Each group will place their design in front of the fan on a smooth, flat table. A stopwatch will be used to time how long it takes the transport to move 50 cm. If the transport stops for longer than 30 seconds, the transport will be considered lost.
 One student per group will use an iPad to record how well their transport moves.
 Discuss how each group did and record the times on the board. Focus on the positives.
 Each group will be given 10 minutes to review the video of their test and answer the four following probing questions.
 What part of your design worked well?
 What part of your design did not work well?
 How can you alter your design to make it go further? Faster?
 Write a wellconstructed response that summarizes what you learned from the video and what your next step will be.
 Each group will be given 5 minutes for any redesign that needs to occur. Additional materials may be purchased if the budget allows it.
 At the end of 5 minutes, all groups will retest.
Conclusion: Write one paragraph explaining the reasoning behind your design. Be sure to explain which shape you chose and why.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
On Day 1 students will complete a volume worksheet on www.mathworksheets4kids.com. Select the difficulty and topic that meets your students' needs.
If your school has a membership, have students complete an IXL lesson on the volume of cones, cylinders, and spheres.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
At the end of the lesson, discuss how the different designs worked with the class. What was successful? What needed to be redesigned? Which design best met the goal? Compare and contrast the advantages and disadvantages of each shape.

Summative Assessment
See the attached pre/post test for assessment questions and answers.

Formative Assessment
Learning scale:
4  Students will be able to relate the concept of volume and density to real world applications such as shipping containers.
3  Students will be able to calculate the volume of a cone and of a cylinder. Students will be able to calculate the density of a material.
2  With help, students will be able to calculate the volume of a cone and of a cylinder.
1  Students will be able to identify examples of a cone and of a cylinder.
Have students raise their hands and show what level they think they are at using 14 fingers. Then ask the students to explain why they think they are at that level. A level 2 student must be able to complete level 1 and 2, a level 3 student must be able to complete all the levels below it, etc.

Feedback to Students
Walk around the room and ask students guiding questions to determine what they know and any misconceptions that they might have. Use the time to assist and redirect the students as needed and to provide feedback.
Misconceptions may be observed when students relate density mostly to the mass or heaviness of the object. Remind students that it is a ratio between the volume to mass. A 1 kg ball of yarn has the same mass as a 1 kg metal ball, however their size may be quite different. The yarn's volume would have to be much larger while the metal ball would be much smaller.
Mass and weight are different also; while most students know this, they use the terms interchangeably. Correct them when they refer to weight and replace with mass. This helps them understand and use the density formulae.