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This limits students abilities to comprehend how fractions compare to one another and relate to whole numbers We were interested in exploring how manipulating fractions on the number line can improve students conceptual understanding ~ #   C y$ "$$CC| ` M Z b  ].X  J?Rectangle 93Rh  VThe Developmental Progression of Rational Number Understanding Using the Number Line 8V ( 2VPCPV     J?Text Box 10790W  @Stephanie Hanson, Diana Chang, Michelle Chee, Niki Dowlat Singh, Allison Musson, and Joan Moss Dr. Eric Jackman Institute of Child Study, Ontario Institute for Studies in Education, University of Toronto 0 _(l$$ I }   C  -w-w)?Text Box 3616 ~IFjY  RESULTS/RECOMMENDATIONS \( 2GG+G$C  ]{   3  -w-w)?Rectangle 207$p#  SUPPORTING LITERATURE L( 2GG+G  $]k e=#   # -w-w)?Rectangle 71#$7 $ Placing fractions on a number line is crucial to students understanding because it allows students to: further develop their understanding of fraction size see that the interval between two fractions can be further partitioned see that the same point on the number line represents an infinite number of equivalent fractions (Lewis, p43) In the Japanese Curriculum, the number line model is used to help students recognize fractions as numbers and learn how they are related to whole numbers (Watanabe, 2007)j      i$$  $H: .   w   3 -w-w ?Text Box 2764 %@HJ0  GRADE ONE Participants 4 Grade One students from JICS (2 males, 2 females) Materials A strip of Bristol board for the number line from 0 to 1 Cut-outs of houses (unlabeled) Protocol What if someone wants to build a new house halfway between house 0 and house 1, where would the house be built? If a car is driving from house 0 to house 1 and they break down here (at and then ), where did they end up?    4  Y   C$4$ $Y$ $p$p$ ]d  3 `-w-w ?Text Box 27640%@Hj@  GRADE THREE Participants 4 Grade Three students from JICS (2 males, 2 females) Materials Two strips of Bristol board for the number lines labeled 0 to 1 (one calibrated by tenths, and one uncalibrated) Pointers labeled with fractions Protocol Can you show me where is on the number line? Can you locate on the number line? What about 7/8? Do you think that it is between and or and 1? 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SY<Zy[V˟ĄԯioCxcQd'KbBbJ1ٔӧK"Ą4z 5ݑ5ll _(4uqhY{e*+(<YQC]*mߙWhmJ.jQUW 9"j\Yx ̔i }y D9ܲԄq3Ű=QXIŭOlxYƈ;cZ!VѱAGFE1WDC Ԭ-R[b""&a_$v) f>(qs=O&xAn:ݓ9n6uByu)8+`VUe^ZLՕv15Bm*  }sHH wO,lhChZcXi>/3i3յl"ݾ)հœŌǰ욕+?h*(F\+_ʵ֭ߵ2L-_o/3ʳ#(:o9ܴʂ#094տڠ<0x+ ,+yA>XE[p"y5\GP|ZUxA3M/+OA\`}[#0PjGp_8c6'+}Wj3kpy3/:Av,AJlen/fvWҨo!׆MnmNŌnVn0WT˶J ErF5ؖmO$k/0cg,@T7XK btg{&g*>3$6$ĒEBm25)°گ&1<@bvV,`JO^i[0). ?K @W:ZgºsI= GkRdhDwygLe.9OHQkj,Gڒ.dgrsiueuuuu?2WrˤoAmȘ CC8#>ތ ~'NៜPַNĿ8FxC ݐe!U9d1;gQK |9Eeo29؍ &/aR0;*N|3/D+(5c-ktM'K{3J 1ա]Px%DAQ2ݰ4vT*ELLä{!Uhi=wS`lK) jq40Xw?P`ЕI 4K|?vJr%20Lb3 "}In7w=,;PK!~xdrs/downrev.xmlDN0HHܨ_KB (Zmq^&oYͧ/ۊ)8d ȕ^׮Rxv#:w`$h~+$ T`b )4d'#1:!m+/l*-.-P쾭wVtm7/6WsVJ w " 1UkZ/g9jET(PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!= E*drs/shapexml.xmlPK-!~xx drs/downrev.xmlPK~ i1~IiH aC PRIMARY/JUNIOR Results Students were generally able to identify and compare benchmark fractions on the number line Use of partitioning (concretely with hands) during explanations by some students Generally limited understanding of equivalency Recommendations Build conceptual understanding of part-whole relationships (e.g., using fraction strips) and how they are related to the written representation of fractions Help students develop an understanding that two equivalent fractions can occupy the same point on the number line through layering and fraction wall activities      =  c"$c"$"$"$="$c D]  A:?)?:Screen shot 2011-05-13 at 10Picture 21Screen shot 2011-05-13 at 108t"O 33___PPT10u.A[N+D=' = @B +" r@*>9Oh+'0 `hx  Slide 1PTAllison Black115 Microsoft Macintosh PowerPoint@`MJ@ZN@5t'Gg  pp  pA 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