Posted by: degarcia | December 11, 2008

Customary and Metric Systems

The original “foot” was the length of the foot of King Henry I.

Metric System-A system of weights and measures that uses the gram, meter and liter as its primary units of weight, distance and capacity. The metric system is used all over the world except in the U.S., Liberia and Myanmar (formerly Burma). http://www.pcmag.com/encyclopedia_term/0,2542,t=metric+system&i=46873,00.asp

Customary System-the system of weights and measures based on the foot and pound and second and pint that dates back to colonial America but differs in some respects from the British Imperial System; today in the United States this system exists side by side with the SI system. http://www.thefreedictionary.com/United+States+Customary+System

Teaching Strategies:

Metric System:

Strategy 1:

In Elementary Mathematics is Anything but Elementary, Bahr and Garcia suggest a great teaching strategy in which the teacher uses base 10 blocks to teach about the metric system. The cube represents the millimeter, 10 cubes (1long) represents a centimeter, 100 cubes (1 flat) represents a decimeter, while 1,000 cubes (block) represents 1 meter. This gives students a visual representation of the metric bases.

Bahr and Garcia go on to say that “older students who are learning about the metric system can complete a partially filled out conversion chart by analyzing the relatiohsips between each unit. “

Strategy 2:
King Henry Skit

King Henry was a jolly old English King most of the time. Even though metrics had been used in England for a long time, King Henry had difficulty converting between the different metric units. He had really become frustrated and confuse.  He felt, as a king, that he should be able to do about anything. He asked for help from all of the smart people in his kingdom. They tried hard, but with out a lot of luck, until one of the great math mathematicians, (Substitute students name), in his kingdom, came forward.
________ explained to King Henry, that everything in metrics was done by either multiplying by ten or dividing by 10, which is easy to do by just moving the decimal point. He explained how they convert between the units so well, that King Henry was so excited, he made up a chart to help others. They understood just as well, so he got even more excited. He was so excited that:     King Henry Danced Merrily Down Center Main.

Strategy 3:
 
 
 
Metric Chant
A milli’s one-thousandth,
of the unit you’ve got,
Centi’s one hundredth,
right on the dot,
Deci’s one-tenth,
coming ’round’ the bend,
Theyn you’re back to just,
the unit again.
What about deka?
Means you’ve got 10!
And like hecto?
That’s my 100 friend!
You’re up to a Kilo
before too long.
It’s exactly 1,000
and thats the end of my song.

Customary System:

Strategy 1:

When teaching about cups, pints, quarts and gallons use items from the home that students can relate to. Begin by using a lunch milk carton (1 cup) full of water to see how many cups will fit into a Ben and Jerry’s ice cream container (a pint). Next, find out how many pints will fit into a Powerade bottle (1 quart). Lastly, use the quart to find out how many quarts are in a gallon of milk. This activity will give students a good visual of the different parts found in the customary system. It will also give them something to refer back to when they are making measurement conversions. Any types of cups, pints, quart and gallons can be used for this activity, however it is most effective when students can relate to them.

Strategy 2:

In Elementary Mathematics is Anything but Elementary, Bahr and Garcia suggest that “children’s earliest experiences with customary measurement need to be comparing and developing the language used to describe comparisons.  Younger children need to be able to “take an object and compare it with something else- for example, a pencil, a train of three cubes, or a string the length of their foot. They should be using language such as, ‘the book is longer than the pencil’.”

Centers can be set up around the classroom where students can explore the lengths, and weights of various objects and compare them to one another. (Bahr and Garcia)

Strategy 3:

The Three Phases for Teaching Measurement

from: http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/mcd/measphases.htm

Phase 1 – Identifying the attribute

Purpose

  • Develop the concept of the attribute.
  • Distinguish it from other attributes.
  • Gain intuitive understanding of properties.

Teaching strategies

  • Play and practical activities(trace straight and curvy paths, step out distances, sort pencils by length…)
  • Learning language(how far, how long, tall, short, wide, distance around tree, length…)
  • Comparing objects on basis of attribute(which snake is longer, who is taller, which house is further away, sort pens by length …)
  • Comparing with other attributes(this box is longer, but that box is bigger; he is taller, but I am older)
  • Using informal units(it is 5 giant steps to the window, this table is 12 books long …

Phase 2 – Learning to measure

Purpose

  • Learn to measure the quantity.
  • Use formal units.
  • Estimate measurements.

Teaching strategies

  • Make the transition from informal units to formal units(make ‘ruler’ for informal unit (e.g. popstick length, discuss value of agreed unit, make own ruler measuring in centimetres …)
  • Make and use simplified ‘instruments’ that highlight key features(rulers with only centimetres marked, one-handed clock, mark a jug with ‘cups’…)
  • Measuring objects in various ways, to increasing accuracy, with different equipment(correct use of ruler, tape measure, trundle wheel …)
  • Acquiring a set of personal benchmarks that can be used for estimating (my hand span is about 15 cm; I am about 130cm tall…)

Phase 3 – Learning to calculate

Purpose

  • Convert from one unit to another.
  • Calculate, instead of direct measure.

Teaching strategies

  • Formulas derived from first principles, rather than only memorised (perimeter of rectangle = 2 × length + 2 × width, circumference of circle = 2 πr) Conversions between units draws on principles of proportional reasoning
  • (sketch dual number line to see 3.2 km = 3200 m etc)

(Department of Education and Early Childhood Development http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/mcd/measphases.htm)

Charts

http://www.france-property-and-information.com/table-of-metric-and-imperial-units.htmCharts for the Metric System units and U.S. Customary System units.

Lesson Plans

http://www.eduref.org/Virtual/Lessons/Mathematics/Measurement/MEA0015.html Upper Grades: Students are able to participate in a group game that helps them with their customary measurement and estimation skills.

http://www.education-world.com/a_tsl/archives/03-1/lesson029.shtml Lower Grades: Students estimate and measure.

http://school.discoveryeducation.com/lessonplans/programs/metricworld/ Upper Grades: This lesson plan help students relate the customary system with the metric system so they can grasp how the units of measure compare to each other.

http://www.theteachersguide.com/lesson%20plans/Math/MEA0007.html This is a lesson plan where students convert recipes in customary measurements to their metric equivalents.

http://school.discoveryeducation.com/lessonplans/programs/DM_beginning_measurement/ Lower Grades: Students gain experience with  the customary measurement system by measuring items, weighing objects and reading thermomoters.

pulse.pharmacy.arizona.edu/math/lesson_gifs/how_big/metrics.ppt This is a power point presentation which provides the basic information on the Metric System.

Activities/Games

 
http://www.quia.com/jfc/1421605.html This is a great flash card game for students to play when learning the metric pre-fixes.
 
 
 
 
 
 
 
 
http://www.pps.k12.or.us/instruction-c/math/01_02_lesson_plans/3measurement.pdf Different measurement stations and activities.
 
 
 
 
 
http://oncampus.richmond.edu/academics/education/projects/webunits/measurement/ An introduction to measurements for upper elementary grades. Website explains time, temperature, mass, length, and volume.
 

http://kids.aol.com/homework-help/junior/math/measurement A variety of games and activities to help students practice different measurements.

 
 
 
 
 

Assessments

http://www.teach-nology.com/worksheets/math/measure/compare/small/3/ This is an assessment in which students are given three metric measurements and have to circle the smallest one.
 
http://www.teach-nology.com/worksheets/math/measure/convert/1/ Assessment in which students are required to complete 21 metric conversions.
 
http://www.edhelper.com/metric_math1.htm Assessment in which students converts metric lengths.
 
http://edhelper.com/metric_system.htm This is a website that has various forms of metric assessments. There are word problems, worksheets, crossword puzzles, and stories!
 
http://edujourney.net/Math/Quizzes/measurement.htm Twenty questions. This quiz includes measurement facts on time, metric units and the Imperial/ US standard measurements.

http://edujourney.net/Math/Quizzes/measurement.htm Twenty questions. This quiz includes measurement facts on time, metric units and the Imperial/ US standard measurements.

NCTM Standards

http://standards.nctm.org/document/appendix/meas.htm


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