Name:________________________ NUMBER EQUIVALENCE Directions: Decide whether the each number is equivalent to: Is it True? 2
5
Circle yes or no: Explain your thinking A) 2.5 Yes No B) 25% Yes No C) 0.4 Yes No D) 0.25 Yes No FILE: DPEquivalentTwoFifths Adapted from Rose Tobey & Minton (2010). Uncovering Students Thinking. Corwin Press. edc.org/accessmath
1
Name:________________________ NUMBER EQUIVALENCE Directions: Decide whether the each number is equivalent to: 2
5
Circle true or false: Explain your thinking E) 40% Yes No F) 2.5% Yes No G) 0.04 Yes No H) 4% True False FILE: DPEquivalentTwoFifths Adapted from Rose Tobey & Minton (2010). Uncovering Students Thinking. Corwin Press. edc.org/accessmath
2
ResourceforAnalysisofProbe#11:NumberEquivalence
I. Understandings and Successful Approaches
CorrectAnswers:
2
5
A. No,2.5isnotequivalentto 2
5
B. No,25%isnotequivalentto 2
5
C.Yes,0.4isequivalentto 2
5
D.No,0.25isnotequivalentto 2
5
E.Yes,40%isequivalentto 2
5
2
G.No,0.04isnotequivalentto 5
2
H.No,4%isnotequivalentto 5
F.No,2.5%isnotequivalentto Studentswhochoosethesecorrectanswersandhaveexplanationsthatsupporttheirchoicesare
applyingoneormoresuccessfulunderstandingsandstrategiesincluding:
 Makingtheconnectionbetweenafractionandit’sdecimalandpercentequivalents
 Understandingofhowtotranslatefractionsintodecimalsandpercents
 Abilitytojustifytheequivalencebyusingmultipleways,includinguseofvisualmodels
andreasoningaboutthesizeofafractionasabasetendecimalorasapercent.
II.PotentialCommonMisunderstandings/MisconceptionstoLookFor
Amixtureofcorrectandincorrectchoicesmayrevealavarietyofmisunderstandingsrelatedto
findingthedecimalandpercentequivalents.
1.“IncorrectDirectSubstitution”Misconception
AnswerPatternsVary
 Studentswiththismisconceptiondirectlysubstitutethefractionbar(vinculum)witha
decimalpointor%symbolusingthesamenumbers.
Example1:Thestudent
associatesthe%signwiththe
fractionbar.
Example2:Thestudent
associatesthedecimalpoint
withthefractionbar.
Example3:Thestudent
associatesthedecimalpoint
andthe%signwiththe
fractionbar.
The5is 100%andthe2wouldstandfor25%.
©EDC,2012
2.OtherDifficulties:Studentsmayuseavarietyofotherincorrectapproaches,including:
 Associatingequivalencewithhavingfactorsormultiples.Forexample,studentsmaytest
forequivalencebyseeingifavaluecanbedividedevenlybybothfactors,2and5.
Example4:Thestudent
associatesequivalencewith
factorsTheanswerof“yes”
iscorrectbutthestudent’s
explanationdoesnot
provideevidenceof
understandingwhy40%is
equivalentto2/5.
©EDC,2012