MEASURING THE MARIGOLDS

MEASURING THE MARIGOLDS

https://www.youtube.com/watch?v=fXi3bjKowJU

Measurement is a multidimensional topic.  It includes telling time, determining elapsed time, perimeter, area and the degrees of angles.  While some of these topics seem to fall into other categories, each is a measure of something.

TIME IS A MEASUREMENT

Most of us do not consider time to be a measurement.  However, without the separation of the day into hours, hours into minutes and minutes into seconds, we would have no idea where we were at any given point during the day.  This is a measurement of our activities.  We determine the amount of time or more aptly we measure the amount of time it should or does take to complete certain tasks.  Remember that old Algebra problem: “Two trains leave the station at 9:00 a.m., one traveling south at 55 mph and the other traveling north at 65 mph.  How long will it take for the trains to meet?”  This problem measures the elapsed time of each train to a meeting point at an imaginary location.  

In  the Third grade and into the Fourth grade, students are given word problems to solve involving elapsed time.  The problems are not as advanced as the train problem.  There are three possible types of problems that students could be asked to solve.  They could be required to determine how long a flight took, when a flight took off, or when a flight landed.  In the first type of problem, the problem would provide the take off time and landing time.  The second type would contain the landing time and the length of the flight.  Lastly, the third problem type would provide the take off time, along with the length of the flight.    As with earlier word problems, the students would be doing addition and subtraction to solve these problems.

Determining elapsed time is just one of the measurements related to time.  The other is the division of our lives.  This division is the way we measure our days.  The calendar divides our year into months, weeks and days.  Our clocks divide our days into hours, minutes and seconds.  As adults, most of us are constantly looking at our watches or “watching the clock”.  These are the measurements that drive our lives.  The calendar and the clock are our first introduction into measurements.  As we grow older, we begin to apply these divisions to other things.  We begin to look at how long, wide, high, or heavy something is.  These divisions allow us to make sense of our world.

THE INCHWORM AND UNIT BLOCKS

When students begin to look at length, height, and width, they are required to begin with measuring the length of objects based upon a specified unit.  In Kindergarten, a child might be asked to compare a paper circle to the number of pennies it is across.  This is the beginning of measurement.  The students are tasked with measuring objects by the number of a specified “item” it is long/wide/high.  Once this type of measuring is understood, students progress to using rulers and measuring to the nearest inch, which begins in about second grade.  

By third grade, students are again measuring area and perimeters with a unit block or item.  The beginning concept of area is how much of an item is “covered” by a shape.  In other words, if I place a piece of paper on my desk I will have covered an area of 93,5 square inches.  Students would use a unit cube, which is 1" by 1" and count the number of squares contained in that piece of paper.  In the 4th and 5th grades, students are expected to use the formulas for the area of most regular polygons.  (Rectangle–A= l * w. Triangle–A= (b * h)/2, and so on.)  Also, in the 4th and 5th grades, students begin to experiment with volume and learn the formulas for those measurements, as well.  The most important thing for students to remember when calculating these figures is to appropriately label their answers.  93.5 is the correct calculation for the area of a piece of 8.5" x 11" paper.  However, without the appropriate labeling, the area could be square feet, inches or yards.  It is important for students to label their work with the appropriate measurement unit.

MEASURING ANGLES

In the 4th grade, most students begin to measure angles.  I remember buying “pre-filled” school boxes and measuring tools, as a child.  These always had a protractor included.  I never knew what a protractor was for.  Today, students use the protractor in the 4th grade to not only measure angles to the nearest degree, but to also draw these angles as accurately as possible.  I was intrigued, while observing a 4th grade math class this semester, watching the teacher and the students using a protractor to draw and measure angles.  It was great.  I always had to have a protractor in my supplies, but I can never remember using it.  To get the opportunity now was fantastic.  The understanding of the students on how to create the two rays and draw the angles was very impressive.  I learned so much that day.

POSSIBLE “WEEDS” TO PULL

        As with any math topic, there may be some “weeds” to be pulled, during measurement lessons.   The first possible weed is a confusion between area and perimeter.  These topics are introduced in 3rd grade and honed in 4th and 5th grades.  The perimeter is the distance around a shape.  Another way to think of the perimeter is to imagine putting a fence around your yard.  The perimeter is how much fencing you would need to buy to fence in your yard.  It can also be thought of the distance you walk around your residential block.  Explaining perimeter to our students in this manner will give them a real world “picture”.   In explaining area, it is also important to give students a real world frame of reference, so they are able to visualize it.  A teacher could use the yard analogy for area, as well.  However, rather than putting a fence around it, you are concerned with amount of grass needed to cover the inside of the fence.  A better analogy would be the surface of a table.  If I want to cover my desk with a cloth, but have no over hang.  The amount of space on my desk covered by the cloth is the area.  A table top of any kind will give them a frame of reference for area, as fencing the yard does for perimeter.

Each new topic in math has its own little “weeds” to pull.  Being able to provide real world examples to our students can help bridge the gap between our reality and theory we are teaching.