Geometry Nets

I finally got around to teaching three dimensional shapes in Geometry.  Much of that has to do with between one half and two thirds of my students being off for some school trip.  Its hard to move forward when there is always an excuse for why they couldn't do their homework. 

I love using nets when teaching three dimensional shapes because students can use them to find the formula's for surface area and it allows them to see volume.   Many times I print out the nets and have them cut the patterns out before doing the work but this time I changed it a bit because I had the flu and felt absolutely cruddy.

This time I put a list on the board of a cube, rectangular prism, pyramid, cone, and cylinder with no clues.  I just said draw one shape on a piece of paper.  I refused to tell them how to do it.  I refused to help them in any way except when they wanted help with the rectangular prism.  Then I handed them a tissue box to explore.

I even refused to give them a minimum size the finished shape had to be.  One of the girls asked if one inch was too small for each side in the cube and I said it might be too small to easily use for the next step so I'd make it a bit bigger.  She redid it using a two inch side.

 Most students got the first three figures done easily.  Two students got to the cone and decided a isosceles triangle was perfect and one young man stayed after school working on his cylinder pattern.  One young man kept muttering that I wasn't teaching them because I wouldn't tell them how to do each shape.

Later this week, I will have them cut the nets out and fold them into the appropriate shape to see if they were correct.  I already know the cone patterns are not quite right but I want them to figure that out themselves.  This is the perfect opening for a discussion about what shape is at the top of a cone.  I plan to show a picture so they can see the edge to note its really a circle.

Once the nets are correct, they are going to try to figure out the formula for the surface area of each three dimensional shape.  I've found in the past that it is easier for them to "see" the connection between the shapes and the formulas if they have a net in front of them. 

The volume can be a bit harder to see for shapes such a pyramids and cones but the nets can open a wonderful discussion on why its 1/3rd the volume of a cylinder or a cube.  In addition, its going to be a challenge for them to figure out the height because it will be different than the height of the triangles in the pyramid so I'll introduce the Pythagorean theorem to this part.  I want them to see it applies in other circumstances than the length of a ladder propped against the side of the building.

When a student is able to derive the formulas and make the connections to the "why"s they are more likely to remember the material.  I hope they come out with a better understanding of surface area versus volume and the difference between lateral height versus regular height.

Please let me know what you think, I'd love to hear.  Its possible other entries might be a bit late since I am still having issues with my internet.  The relay that serves this village and a couple others has been covered with snow and ice since March 7th, making both cell and internet service intermittent. It has even gone down at work for days.