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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

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
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
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
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
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
Problem 1 to Explore
  • Find the area of the entire tangram:
problem 2 to explore scaling up
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
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 explore12
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
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 discussion15
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 discussion16
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 discussion17
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 …..
  • Allow students to voice confusion instead of moving ahead
  • 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
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
slide19

We want to thank the National Science

  • Foundation for funding this work
  • We want to thank you for coming!
  • Please take a few minutes to fill out our evaluation.
  • For more information starting you can go to: http://www.msu.edu/~stemproj
  • If you have any questions please e-mail us at: stemproj@msu.edu