Find quadrate polynomial each with the given number
and sum and product respectively-1)/2, 1/3 -2)-1/4
1/4
Answers
Step-by-step explanation:
Engaging students: Finding the volume and surface area of prisms and cylinders
In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission again comes from my former student Madison duPont. Her topic, from Geometry: finding the volume and surface area of prisms and cylinders.
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How could you as a teacher create an activity or project that involves your topic?
A couple activities from my lesson plan attached below were activities I found to be helpful and interesting for my students when introducing surface area and deriving the formulas themselves from area and circumference formulas they already knew. The first activity I’d like to highlight, though it’s simple, was successful in introducing the concept of surface area to students. In our engage, students were shown pictures of cat posts, cylinders, prism-shaped presents and so on and asked how they could determine the amount of materials needed to cover the surface. They seemed familiar with the concept, but not necessarily the mathematical term or procedure for doing such. After getting their pre-conception-based suggestions and asking them the difference between that and the space the shape takes up (volume), my partner and I were able to see light bulbs go off in their minds and we were able to provide them the answer by introducing the concept of the lesson, surface area. The remaining lesson was an activity where they found the areas of the shapes connected in a cylinder’s net in order to find the total area. After the explore, we had them build the cylinder and then try to determine the area using other formulas. During class discussion, we had students present answers and solidify the reason behind the concept of the formula they found emphasizing the use of circumference being multiplied by length (like length x width of a rectangle but the circumference is the “width”) and that we needed to multiply the area of the circle by two because there were two bases on top and bottom. The student-lead activity of the lesson can be extended to deriving the formula of a surface area of a prism using a prism net, constructing the 3D shape, and then determining the areas of each with different strategies. Once surface area is completed with the two shapes volume exploration could be performed in a similar matter and after all is said and done, the differences between volume and surface area could be compared and contrasted using a chart or Venn-diagram. The activities used and extended from this lesson plan seemed beneficial and better than simply giving the student formulas to memorize and explain because the students physically create the surfaces and see the transition for 2D to 3D and respective use formulas they know to conceptually understand a method of finding the surface area or volume in addition to seeing the formulas. This will help students remember formulas and extend surface area and volume of prisms and cylinders to future topics.