Monday, April 11, 2011

Some Small Geometry Lessons For Standardized Test Review

 by vladwtomescu
     Three weeks ago we split up our freshmen engineering classes so that all geometry students went with one teacher and all of the algebra students went with me.  
     The goal:  to focus on math objectives that freshmen traditionally score low on in the state of Texas and in our school district on the upcoming standardized test.  This test comes up during the last week of April and this change allowed our algebra teachers to focus on completing their curriculum with minimum impact from reviewing specific objectives that might not align properly with the curriculum.

     I decided to do a succession of week-long problems that covered geometry objectives such as area, surface area, volume, and changing scale.  The first week we looked at rectangular prisms, the second week we looked at trapezoids and triangles, and this week is a little more open because they are creating a kite and therefore there are many options including a box kite.  

     WEEK ONE:   They were in a company that creates packaging for cosmetics and they were tasked with the following requirements:
  1. Create a wooden box that will hold one of the various chapsticks, lipsticks, and lip balms sold by Balms Away.
  2. Minimize paint waste by only purchasing the amount of paint you anticipate using to color the wooden box.
  3. Create an algorithm to allow our company to manage wooden boxes for other lip product companies with varying sizes and shapes of product.
     Some additional information they were given was that they had to use recycled wooden cubes (left over from a Project Lead the Way activity) to create the box and they had to calculate how much paint they would use based upon a brand that could cover 25 square feet.

    WEEK TWO:   The following scenario was presented to them

1. Create a sail that is a right, isosceles triangle and must cover a cylindrical mast that has a diameter of 6 inches.  The total area of fabric (including the fabric covering the mast) must measure between 100 and 120 square feet.  
2. Create a scale drawing that will fit on a piece of copy paper (8 ½ in x 11 in).   You will then cut out the paper and wrap it around a drinking straw which is representing the mast.
3. Create a company emblem that is a geometric shape which will be located on the sail.  You are to figure out the surface area of this geometric shape and then calculate what percent of the fabric is covered by the emblem.

    This week, as I said, is more opened ended.  They are to research directions to build a kite.  The only material they will be given is one "Oil Absorbing Sheet" (for cleaning faces- measures 5.5 x 8.5 cm), some tooth picks, and some thread (for a tail).  They must scale down their directions so that they will work for their materials and then they are to mount it on a 3 x 5 index card for display.

     They will have to calculate the total area of the material used in the directions and the area of the micro-kite.  Then they are to state the relationship between these two values and show that there is or is not a relationship between the two areas and the scale used to reduce the size of the kite.

     The beauty of being a Project Based teacher is that I never overlook a  chance to get a hands on activity out of a lesson.  And, Project Based teachers always steal ideas and so I expect you to look at these activities and use them as your own.  Any of these could be extended out for a longer project or maybe you could combine a couple of the ideas since they cover the same basic skills.  Either way enjoy these activities and have fun.