Feat(Clg_Mouthe): Notes sur les fractions et pythagore

This commit is contained in:
Bertrand Benjamin 2018-11-15 09:10:06 +01:00
parent 2709aaa1f5
commit 84ace0cd85
6 changed files with 339 additions and 6 deletions

Binary file not shown.

Binary file not shown.

After

Width:  |  Height:  |  Size: 227 KiB

View File

@ -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

View File

@ -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. 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 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. 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.

View File

@ -33,9 +33,14 @@ Sur la durée on cherchera à travailler les fractions avec un axe.
Étape 3: Addition de fractions 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. Sur la durée, on fera des exercices du même type.