Perimeter, Area, Volume, and All That: A Study of Measurement

Pre-requisites

Benjamin Banneker once said, “Presumption should never make us neglect that which appears easy to us, nor despair, make us lose courage at the sight of difficulties”.⁷

During a Geometry seminar that I attended, the seminar leader, Roger Howe indicated that “students must have a firm grasp on the use of a ruler as that is a prerequisite for better insight with geometric concepts”.⁸ Students should practice using the ruler and starting at the line marked zero. The zero mark should be lined up with the edge of the object to be measured. The ruler can be used to determine the measurement of the object by determining the distance from the edge of the object where the zero mark is to the other end of the object. The students ability to use exactness when measuring an object from the zero mark matched up to the edge of the object is a necessary step in that many students have the misconception that when using the ruler, it is unimportant as to where you line the ruler up! Students will be unable to use the ruler to count the sides of an object if they aren’t familiar with ruler guidelines. 

Students should be aware of what an array is, as it is an indicator that there is a group of things that have the same size and shape or equal rows and equal columns is another way to put it. I want students to be aware of what they are doing, so as to proceed in an orderly fashion thereby minimizing confusion and/or mishaps.

Figure E. (one, two, and three dimensional arrays)

In addition to the term ‘array’, I will also ensure that students have a solid understanding of other vocabulary that they will be exposed to during the unit study. When students become familiar with the number of sides of the various geometric objects as well as their proper names (Plane figures: square-four sides, rectangle-four sides, hexagon-six sides, octagon-eight sides, Solid figures:  cube- six sides, rectangular prism-six sides) it is very helpful to them as they complete various exercises. There is the chance that fewer mistakes will be made if the students are knowledgeable about the fact that they should be adding eight sides when finding the perimeter for an octagon as opposed to them mistaking the number of sides of the octagon for that of a pentagon-five sides, or a heptagon-seven sides, as this sort of activity will most likely be found on a worksheet that the students must complete or a as a question on an exit ticket. In this way, students will be able to talk in an informed fashion when exploring the various geometric concepts.

Students should, “use appropriate tools strategically and become familiar with a variety of tools, and they should learn to choose which ones are most appropriate for a given situation”.⁹ Taking care of the above mentioned preliminary matters is a firm way to provide for a smooth flowing unit study. Good ruler use, knowledge of geometric terminology, being able to identify the shapes and their number of sides, as well as becoming familiar with pertinent tools ( for example, geoboards )that can be used for this study, are all important initial steps which are vital to the success of the unit study. 

Positivity allows for more positivity and so I believe it is wise to add a geometric exercise to the spiral review portion of my daily lesson plan.

“Research conducted revealed that geometry-related literature that was included in daily activities in an elementary classroom actually improved the achievement and attitudes towards geometry of the students involved in the study”.⁹

Consequently, if you can embody positivity concerning something that you may not be thrilled about, then chances are high that your optimistic viewpoint may prove to be true and things could actually work out for the best! A similar statement of sentiment was once uttered by the late, great, Benjamin Banneker. Mr. Banneker was an African American who was primarily self- taught and he is notably known as an astronomer, mathematician, a publisher of an almanac, creator of the first clock in America, in addition to other significant accomplishments. This section is preceded by the thoughts of Mr. Benjamin Banneker. Much like he alluded to, it is true that, once a child decides to apply himself/herself, then it is at that point that difficulties won’t permanently impede his/her ability.

Many students experience negative thoughts during their elementary school years.  To counteract some of the negative thoughts that my students may go through, it is significantly important that the students are made aware of their roots and lineage in relation to the pyramids, especially since their current unit of study is tied to the pyramids of Africa. Many of them are unaware that their distant relatives, the Egyptians of Africa were very astute with respect to geometry as they are the architects and mathematicians who used the formula for volume in the construction of the pyramids many centuries ago.

“In observation of the astounding architectural accomplishments of the Egyptians, which surely required them to know the quantity of blocks necessary for pyramid construction, it should not come as a surprise to anyone to realize that they were a people with skills and proficiency at calculating volume”.¹⁰

This information alone could possibly encourage and motivate a youngster to take the next step in their geometric study and persevere when facing mathematical challenges.