Feat(Clg_Mouthe): Notes sur les fractions et pythagore
This commit is contained in:
parent
2709aaa1f5
commit
84ace0cd85
Binary file not shown.
Binary file not shown.
Binary file not shown.
|
After Width: | Height: | Size: 227 KiB |
|
|
@ -0,0 +1,324 @@
|
|||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
|
||||
<svg
|
||||
xmlns:dc="http://purl.org/dc/elements/1.1/"
|
||||
xmlns:cc="http://creativecommons.org/ns#"
|
||||
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
|
||||
xmlns:svg="http://www.w3.org/2000/svg"
|
||||
xmlns="http://www.w3.org/2000/svg"
|
||||
xmlns:xlink="http://www.w3.org/1999/xlink"
|
||||
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
|
||||
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
|
||||
version="1.1"
|
||||
width="297mm"
|
||||
height="210mm"
|
||||
id="svg179"
|
||||
sodipodi:docname="Puzzle Pythagore.svg"
|
||||
inkscape:version="0.92.2 2405546, 2018-03-11">
|
||||
<metadata
|
||||
id="metadata183">
|
||||
<rdf:RDF>
|
||||
<cc:Work
|
||||
rdf:about="">
|
||||
<dc:format>image/svg+xml</dc:format>
|
||||
<dc:type
|
||||
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
|
||||
<dc:title></dc:title>
|
||||
</cc:Work>
|
||||
</rdf:RDF>
|
||||
</metadata>
|
||||
<sodipodi:namedview
|
||||
pagecolor="#ffffff"
|
||||
bordercolor="#666666"
|
||||
borderopacity="1"
|
||||
objecttolerance="10"
|
||||
gridtolerance="10"
|
||||
guidetolerance="10"
|
||||
inkscape:pageopacity="0"
|
||||
inkscape:pageshadow="2"
|
||||
inkscape:window-width="1920"
|
||||
inkscape:window-height="1048"
|
||||
id="namedview181"
|
||||
showgrid="false"
|
||||
units="mm"
|
||||
inkscape:zoom="0.49219627"
|
||||
inkscape:cx="735.72156"
|
||||
inkscape:cy="546.14999"
|
||||
inkscape:window-x="1080"
|
||||
inkscape:window-y="387"
|
||||
inkscape:window-maximized="1"
|
||||
inkscape:current-layer="g1276" />
|
||||
<defs
|
||||
id="defs5">
|
||||
<clipPath
|
||||
id="IRovnBPtOcru">
|
||||
<path
|
||||
d="M 0,0 H 1375 V 952 H 0 Z"
|
||||
id="path2"
|
||||
inkscape:connector-curvature="0"
|
||||
style="fill:none;stroke:none" />
|
||||
</clipPath>
|
||||
</defs>
|
||||
<g
|
||||
transform="matrix(0.43921778,0,0,0.43921778,-121.65674,382.56135)"
|
||||
id="g1276">
|
||||
<g
|
||||
id="g1441">
|
||||
<g
|
||||
inkscape:tile-y0="30.913991"
|
||||
inkscape:tile-x0="64.810145"
|
||||
inkscape:tile-h="348.03149"
|
||||
inkscape:tile-w="291.40156"
|
||||
inkscape:tile-cy="204.92956"
|
||||
inkscape:tile-cx="210.51093"
|
||||
transform="matrix(0.93482232,0,0,0.93482232,79.561741,-839.31872)"
|
||||
id="g1355">
|
||||
<g
|
||||
id="g1314">
|
||||
<path
|
||||
style="fill:#00ff00;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1204"
|
||||
d="m 830.04143,341.06718 -230.20489,124.14543 -0.0456,-193.06097 193.06097,-0.0456 z" />
|
||||
<path
|
||||
style="fill:#ff0000;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1206"
|
||||
d="m 668.70647,41.901149 -68.96114,37.189529 0.0456,193.060962 193.06097,-0.0456 z" />
|
||||
<path
|
||||
style="fill:#0000ff;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1208"
|
||||
d="M 406.72997,272.19725 369.54044,203.2361 599.74533,79.090678 l 0.0456,193.060962 z" />
|
||||
<path
|
||||
style="fill:#999999;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1210"
|
||||
d="m 830.04143,341.06718 86.95589,161.24374 161.24378,-86.9559 -86.95594,-161.24373 z" />
|
||||
<path
|
||||
style="fill:#0000ff;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1212"
|
||||
d="m 724.02758,888.47846 -37.18953,-68.96115 230.20488,-124.14543 0.0456,193.06097 z" />
|
||||
<path
|
||||
style="fill:#ff0000;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1214"
|
||||
d="m 599.88215,658.27357 -68.96115,37.18953 0.0456,193.06096 193.06097,-0.0456 z" />
|
||||
<path
|
||||
style="fill:#ffff00;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1216"
|
||||
d="m 916.99732,502.31092 -193.06096,0.0456 124.14542,230.20489 68.96115,-37.18953 z" />
|
||||
<path
|
||||
style="fill:#00ff00;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1218"
|
||||
d="M 761.12589,571.31768 530.921,695.4631 l -0.0456,-193.06096 193.06096,-0.0456 z" />
|
||||
<path
|
||||
style="fill:#ffff00;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1220"
|
||||
d="m 599.79093,272.15165 -193.06096,0.0456 124.14543,230.20489 68.96114,-37.18953 z" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1222"
|
||||
stroke-miterlimit="10"
|
||||
d="M 530.8754,502.40214 830.04143,341.06718 668.70647,41.901149 369.54044,203.2361 Z" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1224"
|
||||
stroke-miterlimit="10"
|
||||
d="m 916.99732,502.31092 -386.12192,0.0912 0.0912,386.12192 386.12193,-0.0912 z" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1226"
|
||||
stroke-miterlimit="10"
|
||||
d="m 530.8754,502.40214 386.12192,-0.0912" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1228"
|
||||
stroke-miterlimit="10"
|
||||
d="M 916.99732,502.31092 830.04143,341.06718" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1230"
|
||||
stroke-miterlimit="10"
|
||||
d="M 830.04143,341.06718 530.8754,502.40214" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1232"
|
||||
stroke-miterlimit="10"
|
||||
d="m 916.99732,502.31092 161.24378,-86.9559" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1234"
|
||||
stroke-miterlimit="10"
|
||||
d="M 1078.2411,415.35502 991.28516,254.11129" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1236"
|
||||
stroke-miterlimit="10"
|
||||
d="M 991.28516,254.11129 830.04143,341.06718" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1238"
|
||||
stroke-miterlimit="10"
|
||||
d="M 830.04143,341.06718 668.70647,41.901149" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1240"
|
||||
stroke-miterlimit="10"
|
||||
d="M 668.70647,41.901149 369.54044,203.2361" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1242"
|
||||
stroke-miterlimit="10"
|
||||
d="M 369.54044,203.2361 530.8754,502.40214" />
|
||||
<g
|
||||
style="stroke-width:3;stroke-miterlimit:10;stroke-dasharray:none"
|
||||
id="g1250">
|
||||
<path
|
||||
d="m 830.04143,341.06718 86.95589,161.24374"
|
||||
stroke-miterlimit="10"
|
||||
id="path1244"
|
||||
inkscape:connector-curvature="0"
|
||||
style="fill:none;stroke:#000000;stroke-width:3;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none;stroke-opacity:1;paint-order:fill stroke markers" />
|
||||
<path
|
||||
d="M 530.8754,502.40214 830.04143,341.06718"
|
||||
stroke-miterlimit="10"
|
||||
id="path1246"
|
||||
inkscape:connector-curvature="0"
|
||||
style="fill:none;stroke:#000000;stroke-width:3;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none;stroke-opacity:1;paint-order:fill stroke markers" />
|
||||
<path
|
||||
d="m 916.99732,502.31092 -386.12192,0.0912"
|
||||
stroke-miterlimit="10"
|
||||
id="path1248"
|
||||
inkscape:connector-curvature="0"
|
||||
style="fill:none;stroke:#000000;stroke-width:3;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none;stroke-opacity:1;paint-order:fill stroke markers" />
|
||||
</g>
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1252"
|
||||
stroke-miterlimit="10"
|
||||
d="m 530.8754,502.40214 0.0912,386.12192" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1254"
|
||||
stroke-miterlimit="10"
|
||||
d="m 530.96661,888.52406 386.12193,-0.0912" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1256"
|
||||
stroke-miterlimit="10"
|
||||
d="m 917.08854,888.43285 -0.0912,-386.12193" />
|
||||
<path
|
||||
style="fill:none;stroke:#0000ff;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1258"
|
||||
stroke-miterlimit="10"
|
||||
d="M 406.72997,272.19725 369.54044,203.2361" />
|
||||
<path
|
||||
style="fill:none;stroke:#00ff00;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1260"
|
||||
stroke-miterlimit="10"
|
||||
d="M 761.12589,571.31768 530.921,695.4631" />
|
||||
<path
|
||||
style="fill:none;stroke:#ff0000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1262"
|
||||
stroke-miterlimit="10"
|
||||
d="M 599.88215,658.27357 530.921,695.4631" />
|
||||
<path
|
||||
style="fill:#999999;fill-opacity:1;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1264"
|
||||
d="m 599.88215,658.27357 86.9559,161.24374 161.24373,-86.9559 -86.95589,-161.24373 z" />
|
||||
<path
|
||||
style="fill:none;stroke:#999999;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1266"
|
||||
stroke-miterlimit="10"
|
||||
d="m 599.88215,658.27357 86.9559,161.24374 161.24373,-86.9559 -86.95589,-161.24373 z" />
|
||||
<path
|
||||
style="fill:#000000;fill-opacity:0.09803922;fill-rule:evenodd;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1268"
|
||||
d="m 830.04143,341.06718 -18.67121,10.06906 10.06905,18.67121 18.67121,-10.06906 -10.06905,-18.67121" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1270"
|
||||
stroke-miterlimit="10"
|
||||
d="m 830.04143,341.06718 -18.67121,10.06906 10.06905,18.67121 18.67121,-10.06906 -10.06905,-18.67121" />
|
||||
<path
|
||||
style="fill:#000000;fill-opacity:1;stroke:none;paint-order:stroke fill markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1272"
|
||||
d="m 833.04143,341.06718 c 0,1.65686 -1.34315,3 -3,3 -1.65686,0 -3,-1.34314 -3,-3 0,-1.65685 1.34314,-3 3,-3 1.65685,0 3,1.34315 3,3 z" />
|
||||
<path
|
||||
style="fill:none;stroke:#000000;stroke-linecap:round;stroke-linejoin:round;stroke-miterlimit:10;stroke-opacity:1;paint-order:fill stroke markers"
|
||||
inkscape:connector-curvature="0"
|
||||
id="path1274"
|
||||
stroke-miterlimit="10"
|
||||
d="m 833.04143,341.06718 c 0,1.65686 -1.34315,3 -3,3 -1.65686,0 -3,-1.34314 -3,-3 0,-1.65685 1.34314,-3 3,-3 1.65685,0 3,1.34315 3,3 z" />
|
||||
</g>
|
||||
</g>
|
||||
<use
|
||||
id="use1385"
|
||||
xlink:href="#g1355"
|
||||
inkscape:tiled-clone-of="#g1355"
|
||||
y="0"
|
||||
x="0" />
|
||||
<use
|
||||
id="use1387"
|
||||
transform="translate(0,871.62827)"
|
||||
xlink:href="#g1355"
|
||||
inkscape:tiled-clone-of="#g1355"
|
||||
y="0"
|
||||
x="0" />
|
||||
<use
|
||||
id="use1389"
|
||||
transform="translate(796.1469)"
|
||||
xlink:href="#g1355"
|
||||
inkscape:tiled-clone-of="#g1355"
|
||||
y="0"
|
||||
x="0" />
|
||||
<use
|
||||
id="use1391"
|
||||
transform="translate(796.1469,871.62827)"
|
||||
xlink:href="#g1355"
|
||||
inkscape:tiled-clone-of="#g1355"
|
||||
y="0"
|
||||
x="0" />
|
||||
<use
|
||||
id="use1393"
|
||||
transform="translate(1592.2938)"
|
||||
xlink:href="#g1355"
|
||||
inkscape:tiled-clone-of="#g1355"
|
||||
y="0"
|
||||
x="0" />
|
||||
<use
|
||||
id="use1395"
|
||||
transform="translate(1592.2938,871.62827)"
|
||||
xlink:href="#g1355"
|
||||
inkscape:tiled-clone-of="#g1355"
|
||||
y="0"
|
||||
x="0" />
|
||||
</g>
|
||||
</g>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 15 KiB |
|
|
@ -45,17 +45,21 @@ On présente l'animation `puzzle <./puzzle.ggb>`_ (ou sous `la version mepc <./p
|
|||
|
||||
On leur demande d'exploiter cette découverte pour calculer la longueur pour le triangle 5-12. Après un travail de groupe, si l'idée n'a pas émergée, on peut faire un croquis pour y calculer l'aire des carrés.
|
||||
|
||||
Cahier de bord: une note sur l'écriture axa qui peut être réécrite avec un carré.
|
||||
Cahier de bord: une note sur l'écriture a*a qui peut être réécrite avec un carré.
|
||||
|
||||
Étape 3: Pratique du proto-théorème
|
||||
===================================
|
||||
|
||||
Réutilisation de ce qui a été fait l'étape 2 sur 3 exemples (sans utilisation de la racine carré). Chaque groupe produit un début de rédaction afin de garder une trace pour le cahier de bord.
|
||||
|
||||
Étape 4: Technique et intro de la racine carré
|
||||
==============================================
|
||||
Cahier de bord: On colle de `puzzle deplié <./B1_Puzzle_Pythagore.pdf>`_, on écrit l'égalité des aires.
|
||||
|
||||
On donne un triangle qui a besoin de la racine carré pour être calculé. Par tâtonnement les élèves essaient d'approcher une valeur. On introduit ensuite la racine carré.
|
||||
Étape 4: cette égalité des aires est-elle vraie pour tous les triangles?
|
||||
========================================================================
|
||||
|
||||
On pose cette question aux élèves. Ils doivent y répondre en illustrant. Cette étape va permettre de continuer à habituer les élèves à ces calculs d'aires.
|
||||
|
||||
Cahier de bord: On écrit que ce n'est le cas que pour les triangles rectangles.
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -33,9 +33,14 @@ Sur la durée on cherchera à travailler les fractions avec un axe.
|
|||
Étape 3: Addition de fractions
|
||||
==============================
|
||||
|
||||
Additions entre fractions avec l'illustration soit en tablette de chocolat soit avec un axe.
|
||||
On donne 4 additions de fractions. Les élèves doivent faire les calculs et les illustrer avec des dessins à chaque fois.
|
||||
|
||||
Cahier de bord: On écrit quelques exemples de calculs bien rédigés.
|
||||
$$ \frac{1}{4} + \frac{2}{4} = ...$$
|
||||
$$ \frac{2}{10} + \frac{7}{10} = ...$$
|
||||
$$ \frac{1}{5} + \frac{5}{10} = ...$$
|
||||
$$ 1 - \frac{3}{4} = ...$$
|
||||
|
||||
Cahier de bord: On écrit des bonnes réponses illustrées et des mauvaises réponses en expliquant ce qui ne marche pas.
|
||||
|
||||
Sur la durée, on fera des exercices du même type.
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue