This month in Geometry...

After finishing the mailbox system for Rachel's Level 1 classroom, which looks and works quite well, we've focused on surface area and volume.  This has involved: a mini design  project that combines creativity, precise calculations, thinking three-dimensionally, and some silliness to create drawings and calculate surface area and volume of such multi-shaped structures as the 'enormous dog-shaped hamster cage', the 'space table', and the 'futuristic space ferret cage'.

We also looked at the significance of the surface area to volume ratio of an object, from igloos to airports, ants to seals, and donuts to water droplets.

And students from both high school math classes worked together to design and build planter boxes to go in front of our high school classroom building.  They are at various stages of completion, one that is ready for soil, another quite close, and a third still in the design and layout stages.  More to come on this in the upcoming weeks...

Geometry Mini-Design Project...Objectives, Explanation, and Time line

Objectives: -Learn/review concepts of volume and surface area and of applying volume and surface area formulas to solve problems.

-Practice thinking in 3 dimensional space and representing that space in 2 dimensional diagrams.

Each student is to design a 3 dimensional figure that includes at least one of each of the following shapes:

-prism

-cylinder

-sphere

-cone

-pyramid

There should be at least three areas of intersection. (I encourage you to have objects intersect on flat planes and not curved surfaces.) You may use portions of shapes instead of the full object (like a hemisphere instead of a sphere, for example.)

Possible suggestions for the design are: a super-duper hamster house, space station, underwater home, etc. Also, you are asked to come up with a reason that your figure's surface area and volume might need to be measured (a special space-proof wax that needs to coat the whole exterior surface, for instance.)

Your drawing(s) should be clear enough, with dimensions labeled, to accurately determine the surface area and volume of your figure. You will need to determine these measurements, and then you will eventually exchange drawings. Your new task is will be determine the surface area and volume of the figure given to you by another student. Finally, you will check the work of the person who received your original design.

For all calculations, you should include clearly the separate parts that you calculate, so that if there is a discrepancy between your work and the other person that works on your design, it will be easy to go back and see where possible mistakes were made.

The time line:

Due Tuesday March 17: Bring to class drawings with dimensions that you can find the volume and surface area of. You will have some time in class to do the actual calculations and ask questions. (I recognize that this may not be entirely clear as we haven't yet worked with volume, but my hope is to give you time to ask questions as you go, and that you'll learn by doing. I am of course available for whatever help you need.)

In class on March 17 you should be able to complete a clear and detailed drawing to give to someone else.

Thursday March 19: Turn in the calculations for the design given to you (total volume and surface area.) If you are crammed for time or need extra help, you can take the option of working during study hall the following day and turning it in on that Friday, March 20.

After break: Students will check each others' work and determine where there are differences and what happened if students get different calculations for the same design.

Corrections for Geometry Party #3 due Tuesday March 31.

This is optional.  Here are the instructions that are also posted in the classroom...

Math Party/Test Corrections

Tests should be, like the rest of school, part of the learning process.  If you want to improve your test score and improve your understanding of the material, you can do CORRECTIONS for that test.  Here's how: 

1.  Use a separate sheet of paper.  Write your name and "Corrections" at the top.

2.  For each problem that you want to correct, write the problem number and the full problem.

3.  Write out your new solution to the problem, showing every step of your process.

4.  Explain in a sentence what you needed to do that you missed the first time.

5.  Staple it to the original test, and put it in the math assignment box on the teacher's desk.

 You may use any resources for this: look at the text book, ask me, ask a friend for help, etc. You should not, however, simply copy someone else's work. 

 For every problem that you correct, you may get up to half of the points back that you missed the first time around.  The credit you get back depends on how correct and how thorough your explanations are.  As always, let me know if you have any questions.

 

-Brook

 

This month in Geometry…

Our first design-build commission! (If you can call it a commission if we don't get paid, I'm not sure.)  Rachel, an FGCS Level 1 teacher, saw our mailbox cubbies and said to me how much she liked them and how much she'd love something similar for her classroom.  So our next class period we headed as a group over to Rachel's classroom, and she gave us her parameters: the spot in the classroom where the mailbox set will go; it needs to hold papers for all of her students, a place to store work overnight; it should hold papers without needing to fold or bend them too much; it cannot stick out too far from the wall so as not to impede site.  The group went to work that period and came up with a rough idea of a design.  The next period they had refined the design and done most of the layout and the cutting.  This week we hope to paint and install the completed product.  Photos on the way…

As for specific Geometry topics, students practiced multiple ways to create right angles, including the well-known Pythagorean theorem.  We studied properties of circles.  And currently students are honing their skills for solving area problems for two- and three-dimensional objects.  This will be useful with further projects in class this spring, and of course endless applications in life beyond class.

-Brook