The Importance of Non-Standard Units in Area Measurement

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The Importance of Non-Standard Units in Area Measurement. Funda Gonulates and Ashley Taglauer Michigan State University Math in Action 2012. Strengthening tomorrow’s education in measurement (stem). Research

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The Importance of Non-Standard Units in Area Measurement

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The Importance of Non-Standard Units in Area Measurement

Funda Gonulates and Ashley Taglauer

Michigan State University

Math in Action 2012

Strengthening tomorrow’s education in measurement (stem)
• Research
• analyzing the capacity of three written elementary curricula to support robust learning of spatial measurement (length, area, volume)

Professional Development

• work with pre-service teachers on measurement lesson study
• working with facilitators throughout Michigan who are in turn working with teachers in their areas
Unit and Unitizing a region
• What does a unit do?
• What is the distinction between standard units and non-standard units?
• Why working with non-standard units might help understanding area better?
CCSSM: Area and Area Units

Recognize area as an attribute of plane figures and understand concepts of area measurement.

a) A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

b) A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Problems to explore worksheet
• 5 problems into explore
• While exploring problems consider:
• What is my unit of measure?
• What does unit do in this problem?
• How does this problem support conceptualization of area?
Problem 1 to Explore
• Find the area of the entire tangram:
Problem 2 to Explore Scaling Up
• Use Rectangle, Trapezoid build similar figures with scale factors of 2 and 3. Then calculate the area of each enlargement in terms of the original polygon, and record your results in the table provided.
Problem 4 to explore
• How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide and 100 inches long? (NAEP, 2009, Grade 8)
Problem 4 to explore
• How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide and 100 inches long? (NAEP, 2009, Grade 8)
Reflective discussion
• In Problems we explored:
• Comparing /creating areas by using a practical unit or an available unit (P1,P2,CC)
• Area is quantification of a region enclosed in a boundary (as an alternative to seeing area just as count of unit squares)
• Dynamic view of area in addition to static view (P2)
• Area changes as the region change – area increases as we enlarge the boundary
• Changes in boundary-scaling up by k – change in area k2
• There might be variety in unit selection (or in provided units) depending on purpose (P1, P2,P3, P4, P5)
• Any objects that provide a 2D measure –beans, cut out foot, …
• Any 2D shape –triangles, rectangles, trapezoid, …
• Squares and Unit squares
Reflective discussion
• In Problems we explored:
• Measuring area by actually covering or structuring the actual or a representative region in contrast to counting number of squares provided in already structured regions (P4)
Reflective discussion
• In Problems we explored:
• Communication of our measurement (P1, P3)
• Stating our unit of measure at the end of our measurement
• Describing our unit of measure as best as we can
Reflective discussion
• Encourage use of proper names of units in stating area measurement
• Area is …. smallest triangle/blue rectangles/(5 by 5) squares/ in. squares
• Area is …..
• Why we had different numbers for the same area
• What is the most appropriate unit of measure
• Why we do prefer square units over other units
• Why area goes by k2 when you increase each side by k
• What is the difference between practical and standard
• Provide visuals to allow others to see
• Units move us from seeing area as quality of 2D regions to measurable quantities
Suggestion
• Improve lesson we already have
• EM Grade 2 : Lesson Find the area of each shape by using pattern blocks.
• Compare and contrast area measurement by using different units
• Bring what is missing as problems to explore
• Allow violations

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