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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). Research

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The Importance of Non-Standard Units in Area Measurement

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  1. The Importance of Non-Standard Units in Area Measurement Funda Gonulates and Ashley Taglauer Michigan State University Math in Action 2012

  2. 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

  3. Crazy CAKES

  4. Sample Student solutions

  5. 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?

  6. 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.

  7. 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?

  8. Problem 1 to Explore • Find the area of the entire tangram:

  9. 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.

  10. Problem 3 to explore

  11. 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)

  12. 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)

  13. Problem 5 to explore

  14. 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

  15. 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)

  16. 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

  17. 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

  18. 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

  19. 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

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