Calculating Volume of a Cereal Box
1 Introduction and Hook
Introduce the activity by asking the students to define volume and what volume means. Remind students about what they already know about volume. They will be creating a video where they will show and explain their work.
Show them the video on volume on Brainpop. http://www.brainpop.com/math/geometryandmeasurement/volumeofprisms/previ...
If you have not already created a class account, make sure you create course codes for each of your classes for Educreations. Give the course code to your students and have them create their own accounts. Once the students are linked to your course code, their videos will be submitted directly to you so you can view them at any time.
2 Activity Introduction
At this point, you will introduce the problem to the students and review your expectations of how to complete the problem. This is a good time to show and review the rubric.
You and your partner want to find the volume of your cereal box, but you only have ½ inch cubes available. You measured the box and found that it was 7 ½ inches wide, 11 inches tall and 2 ½ inches thick. With your partner, determine how many ½ inch cubes do you need to fill the cereal box?
By the end of the activity, the students will have created a video showing and explaining how they completed the problem with their partner.
3 Partner Work
The first step of this activity involves having the students do the math. Students do the work on paper and then create a storyboard or map on Penultimate or Popplet. I have my students create storyboards or maps so that they are completely sure about what they will be saying and showing on Educreations. Their storyboard acts as a rough draft for their video.
4 Video Creation
After the students are done with their storyboard, they will lay out their work on Educreations. Students will recreate the work they did on their storyboards in Educreations. Each box on the storyboard represents one slide in Educreations. I highly suggest students edit their slides for grammar and spelling as they work. It also looks nicer if some of their text is typed while also adding handwritten work to explain their process. Once they create the slides, they will find a quiet place in the hallway to record their audio.
5 Viewing and Wrap-Up
Students will now get a chance to view a selection of videos created by their classmates. It is more valuable and powerful to view them with the students. Sometimes the students see things I don’t catch. When we view the screencasts, we look for four things:
Technique – How did the creators solve the problem?
Strengths – What did the creators do well?
Improvement – How can the creators improve their work?
Incorrect – If the solution was incorrect, where should the creators go back to correct their work?
As the students critique each others work, I am also assessing the creators by looking at whether or not they understood the content standard and which practices they used to solve the problem.
Key Standards Supported
Expressing Geometric Properties With Equations
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Derive the equation of a parabola given a focus and directrix.
(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Geometric Measurement And Dimension
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
(+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Modeling With Geometry
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).