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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
| mso-list-type:simple;
| |
| mso-list-template-ids:10;
| |
| mso-list-name:WW8Num9;}
| |
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| |
| {mso-level-number-format:bullet;
| |
| mso-level-text:·;
| |
| mso-level-tab-stop:18.0pt;
| |
| mso-level-number-position:left;
| |
| margin-left:18.0pt;
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
| @list l10:level1
| |
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| |
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| |
| mso-level-tab-stop:36.0pt;
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
| @list l11:level1
| |
| {mso-level-number-format:bullet;
| |
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| |
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| |
| mso-level-number-position:left;
| |
| text-indent:-18.0pt;
| |
| font-family:Symbol;}
| |
| ol
| |
| {margin-bottom:0cm;}
| |
| ul
| |
| {margin-bottom:0cm;}
| |
| -->
| |
| </style>
| |
| <!--[if gte mso 10]>
| |
| <style>
| |
| /* Style Definitions */
| |
| table.MsoNormalTable
| |
| {mso-style-name:"Normal tabell";
| |
| mso-tstyle-rowband-size:0;
| |
| mso-tstyle-colband-size:0;
| |
| mso-style-noshow:yes;
| |
| mso-style-parent:"";
| |
| mso-padding-alt:0cm 5.4pt 0cm 5.4pt;
| |
| mso-para-margin:0cm;
| |
| mso-para-margin-bottom:.0001pt;
| |
| mso-pagination:widow-orphan;
| |
| font-size:10.0pt;
| |
| font-family:"Times New Roman";}
| |
| </style>
| |
| <![endif]--><!--[if gte mso 9]><xml>
| |
| <o:shapedefaults v:ext="edit" spidmax="2050"/>
| |
| </xml><![endif]--><!--[if gte mso 9]><xml>
| |
| <o:shapelayout v:ext="edit">
| |
| <o:idmap v:ext="edit" data="1"/>
| |
| </o:shapelayout></xml><![endif]-->
| |
| </head>
| |
|
| |
| <body lang=SV style='tab-interval:65.2pt'>
| |
|
| |
| <div class=Section1>
| |
|
| |
| <h1 style='margin-left:0cm;text-indent:0cm;tab-stops:0cm'>Tal och räknesätt</h1>
| |
|
| |
| <p class=MsoNormal>Detta är en kursplan för hela området, aritmetik vilket
| |
| vanligen kallas tal och räknesätt<a style='mso-footnote-id:ftn1' href="#_ftn1"
| |
| name="_ftnref1" title=""><span class=MsoFootnoteReference><span
| |
| style='mso-special-character:footnote'><![if !supportFootnotes]><span
| |
| class=MsoFootnoteReference><span style='font-size:12.0pt;font-family:"Times New Roman";
| |
| mso-fareast-font-family:"Times New Roman";mso-ansi-language:SV;mso-fareast-language:
| |
| AR-SA;mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></a>.
| |
| De två nationella målen för aritmetiken har brutits ned i mindre delar dels för
| |
| att bli mer begripliga och dels för att man ofta bara sysslar med en del av
| |
| innehållet i ett mål under ett undervisningsavsnitt (en del av en termin). </p>
| |
|
| |
| <p class=MsoNormal>Denna lokala kursplan/arbetsplan kommer därför i praktiken
| |
| att delas upp så att man arbetar med en del av denna plan under ett
| |
| arbetsavsnitt. I årskurs sex arbetar man förmodligen bara med de grundläggande
| |
| delarna. I årskurs sju tillkommer några delar av de nationella målen samtidigt
| |
| som man bara repeterar några av de tidigare delarna. I åttan kanske man arbetar
| |
| med de sista delmålen och nian kanske man repeterar allt.</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <p class=MsoNormal><span class=GramE><i style='mso-bidi-font-style:normal'>Syfte
| |
| mm.</i></span><i style='mso-bidi-font-style:normal'> <span class=SpellE><span
| |
| class=GramE>Strävansmål</span></span><span class=GramE>.</span> Sälj in ämnet. <span
| |
| class=GramE>Ämnets roll i världen.</span><o:p></o:p></i></p>
| |
|
| |
| <h2 style='margin-left:0cm;text-indent:0cm;tab-stops:0cm'>Innehåll</h2>
| |
|
| |
| <p class=MsoNormal><i style='mso-bidi-font-style:normal'>Diverse filmer,
| |
| labbar, övningar och laborationer kan listas här.<o:p></o:p></i></p>
| |
|
| |
| <h2 style='margin-left:0cm;text-indent:0cm;tab-stops:0cm'>Betygskriterier</h2>
| |
|
| |
| <p class=WW-Normalwebb>De två <span class=SpellE>aritmetikmålen</span>
| |
| fokuserar dels <span class=SpellE>taluppfattningen</span> och dels
| |
| färdigheterna:</p>
| |
|
| |
| <p class=WW-Normalwebb style='margin-left:36.0pt;text-indent:-18.0pt;
| |
| mso-list:l11 level1 lfo2;tab-stops:list 36.0pt'><![if !supportLists]><span
| |
| style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
| |
| Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]>Målet att eleven skall ha utvecklat sin <span
| |
| class=SpellE>taluppfattning</span> till att omfatta hela tal och rationella tal
| |
| i bråk- och decimalform, [Ma U1] bryts med fördel ned i tre delmål vilka blir:</p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l11 level1 lfo2;tab-stops:list 36.0pt'>Målet
| |
| att eleven skall ha goda färdigheter i och kunna använda överslagsräkning
| |
| och räkning med naturliga tal och tal i decimalform samt procent och
| |
| proportionalitet i huvudet, med hjälp av skriftliga räknemetoder och med
| |
| tekniska hjälpmedel, [Ma U2]</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal><span style='mso-spacerun:yes'> </span></p>
| |
|
| |
| <p class=MsoNormal>Av tradition organiseras undervisningen i tre stora områden
| |
| som återkommer under flera (alla) år. Dessa områden är tal och räkning, bråk
| |
| och procent samt eventuellt proportionalitet. Målen kan brytas ner i mindre
| |
| komponenter för varje område.</p>
| |
|
| |
| <h3 style='margin-left:0cm;text-indent:0cm'>Tal och räkning</h3>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'>Förstå
| |
| hur tiosystemet fungerar.<span style='mso-tab-count:2'> </span></li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis: </p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:29.2pt'>Skapa ett så
| |
| stort tal som möjligt med siffrorna 3567.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Hur
| |
| förändras talet 12 345 om trean ersätts med en åtta?<span
| |
| style='mso-tab-count:1'> </span></p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'><span
| |
| class=GramE>Kunna</span> räkna med decimaltal.</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Skriv
| |
| fem hundradelar som ett decimaltal.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Gör
| |
| om 13 mm till m.</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'><span
| |
| class=GramE>Kunna</span> avrunda heltal och decimaltal</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Avrunda
| |
| 795 till tiotal.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Avrunda
| |
| 658,3235 till tusendelar.</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'>Veta
| |
| vad ett primtal är och hur man undersöker om ett tal är ett primtal. <span
| |
| class=GramE>Kunna</span> <span class=SpellE>faktorisera</span> tvåsiffriga
| |
| tal.</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Visa
| |
| att 34 inte är ett primtal. </p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Är
| |
| 37 ett primtal?</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Vilka
| |
| tal är 60 delbart med?</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span><span
| |
| class=SpellE>Faktorisera</span> talet 36.</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'><span
| |
| class=GramE>Kunna</span> använda några vanliga algoritmer vid huvudräkning</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Vid
| |
| talet 123,4+9,2 adderar du heltal och decimaler var för sig.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>Vid
| |
| talet 12.3-8.8 gör du om det till addition av 1,2+2,3.</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'>Multiplikation
| |
| och division med 10, 100, 1000</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>45.6*100</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>0,73/10</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'>Multiplikation
| |
| och division med 0,1, 0,01, 0,001</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>63,5*0,001</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>0,6/0,01</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'>Multiplikation
| |
| med uppställning</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>82,5*24</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'><span
| |
| class=GramE>Kunna</span> räkna med kort division</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-tab-count:1'> </span>20,8/6,5</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <ul style='margin-top:0cm' type=disc>
| |
| <li class=MsoNormal style='mso-list:l10 level1 lfo12;tab-stops:list 36.0pt'>Överslagsräkning</li>
| |
| </ul>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:65.2pt;text-indent:.05pt'>Räcker två
| |
| hundra kronor om du handlar dessa varor: ost 67,50, pasta 12,30, 6 l mjölk
| |
| á`8,65, <span class=SpellE>cornbiffar</span> 57,90?</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:-18.0pt;mso-list:l4 level1 lfo5;
| |
| tab-stops:36.0pt 177.2pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> omvandla stora
| |
| tal till tiopotensform och grundpotensform och tvärtom.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:63.8pt 177.2pt'><span style='mso-tab-count:
| |
| 1'> </span>Skriv 75 000 i grundpotensform.</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:63.8pt 177.2pt'><span style='mso-tab-count:
| |
| 1'> </span>Skriv 10<sup>9</sup> som vanligt tal.</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:177.2pt'><o:p> </o:p></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:-18.0pt;mso-list:l2 level1 lfo3;
| |
| tab-stops:36.0pt 177.2pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]>Förstå vad som menas med potensform.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:29.2pt'>Skriv på
| |
| vanligt sätt 3<sup>4</sup>.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:29.2pt;tab-stops:190.5pt'>Beräkna
| |
| 2<sup>4</sup> + 3<sup>2<span style='mso-tab-count:1'> </span></sup><o:p></o:p></p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:-18.0pt;mso-list:l2 level1 lfo3;
| |
| tab-stops:36.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> utföra addition,
| |
| subtraktion med negativa tal.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:18.0pt'><span style='mso-tab-count:1'> </span>Beräkna
| |
| a) 4+ (-3)<span style='mso-spacerun:yes'> </span>b) 6 – <span
| |
| class=GramE>8<span style='mso-spacerun:yes'> </span>c</span>) –7 +1</p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <h4>Mer än G</h4>
| |
|
| |
| <p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l3 level1 lfo4;
| |
| tab-stops:18.0pt 148.85pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> utföra, addition,
| |
| subtraktion, division och multiplikation med negativa tal.</p>
| |
|
| |
| <p class=MsoNormal style='text-indent:18.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='text-indent:18.0pt'><span style='mso-tab-count:1'> </span><span
| |
| class=GramE>-</span>3+-5, 3- - 5, -15/-3, -3*-5</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:148.85pt'><o:p> </o:p></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l1 level1 lfo10;
| |
| tab-stops:18.0pt 148.85pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> utföra
| |
| multiplikation och division av tal i potensform.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:63.8pt 148.85pt'><span style='mso-tab-count:
| |
| 1'> </span><span class=GramE>Beräkna<span
| |
| style='mso-spacerun:yes'> </span>a</span>) 4<sup>6</sup> / 4<sup>3</sup><span
| |
| style='mso-spacerun:yes'> </span>b) 10<sup>5</sup> / 10<sup>-2</sup><span
| |
| style='mso-spacerun:yes'> </span>c) 3<sup>2</sup> <span style='font-family:
| |
| "MS Mincho";mso-hansi-font-family:"MS Mincho"'>·</span> 3<sup>6</sup><span
| |
| style='mso-spacerun:yes'> </span>d) 10<sup>-5</sup> <span style='font-family:
| |
| "MS Mincho";mso-hansi-font-family:"MS Mincho"'>·</span> 10<sup>-2<o:p></o:p></sup></p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:63.8pt 148.85pt'><sup><span
| |
| style='mso-tab-count:1'> </span></sup><span
| |
| class=GramE>Beräkna<span style='mso-spacerun:yes'> </span>a</span>) 1,3 <span
| |
| style='font-family:"MS Mincho";mso-hansi-font-family:"MS Mincho"'>·</span>10<sup>6</sup><span
| |
| style='mso-spacerun:yes'> </span><span style='font-family:"MS Mincho";
| |
| mso-hansi-font-family:"MS Mincho"'>·</span><span style='mso-spacerun:yes'>
| |
| </span>2 <span style='font-family:"MS Mincho";mso-hansi-font-family:"MS Mincho"'>·</span>
| |
| 10<sup>4</sup><span style='mso-spacerun:yes'> </span>b) 3 <span
| |
| style='font-family:"MS Mincho";mso-hansi-font-family:"MS Mincho"'>·</span> 10<sup>6</sup>
| |
| / 2 <span style='font-family:"MS Mincho";mso-hansi-font-family:"MS Mincho"'>·</span>10<sup>4<o:p></o:p></sup></p>
| |
|
| |
| <h3 style='mso-list:none;tab-stops:65.2pt'>Bråk</h3>
| |
|
| |
| <p class=BodyText style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l7 level1 lfo7;
| |
| tab-stops:18.0pt 177.2pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> utföra
| |
| omvandlingar mellan tal i bråkform och tal i decimalform.<span
| |
| style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'>Exempelvis:</p>
| |
|
| |
| <p class=BodyText style='tab-stops:18.0pt 63.8pt 177.2pt'><span
| |
| style='mso-tab-count:2'> </span>Skriv <span class=GramE>¼<span
| |
| style='mso-spacerun:yes'> </span>i</span> decimalform.<br style='mso-special-character:
| |
| line-break'>
| |
| <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
| |
| <![endif]><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l3 level1 lfo4;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE><span style='mso-bidi-font-family:
| |
| Tahoma'>Kunna</span></span><span style='mso-bidi-font-family:Tahoma'>
| |
| storleksordna naturliga tal och enkla tal i bråk- och decimalform.</span><span
| |
| style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt'><span style='mso-bidi-font-family:
| |
| Tahoma'><span style='mso-spacerun:yes'> </span></span>Exempelvis:</p>
| |
|
| |
| <p class=Normal1><span style='mso-tab-count:1'> </span><span
| |
| style='mso-bidi-font-family:Tahoma'>Skriv talen i storleksordning. Börja med
| |
| det minsta.</span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='tab-stops:42.55pt 49.65pt'><span style='mso-bidi-font-family:
| |
| Tahoma'><span style='mso-spacerun:yes'> </span>3/<span
| |
| class=GramE>2<span style='mso-spacerun:yes'> </span>0</span>,5<span
| |
| style='mso-spacerun:yes'> </span>4/5<span
| |
| style='mso-spacerun:yes'> </span>1,2<span
| |
| style='mso-spacerun:yes'> </span>1/3<span style='mso-spacerun:yes'>
| |
| </span>1<br style='mso-special-character:line-break'>
| |
| <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
| |
| <![endif]></span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l8 level1 lfo8;
| |
| tab-stops:18.0pt 42.55pt 49.65pt'><![if !supportLists]><span style='font-family:
| |
| Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE><span style='mso-bidi-font-family:
| |
| Tahoma'>Kunna</span></span><span style='mso-bidi-font-family:Tahoma'> utifrån
| |
| enkla exempel ange delen av något i bråkform.</span><span style='mso-bidi-font-family:
| |
| Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='tab-stops:42.55pt 49.65pt'><span style='mso-bidi-font-family:
| |
| Tahoma'><span style='mso-spacerun:yes'> </span><span class=GramE>Tex.</span>
| |
| Hur stor del av en timme är 10 minuter? (svara i bråkform).</span><span
| |
| style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='tab-stops:42.55pt 49.65pt'><span style='mso-bidi-font-family:
| |
| Tahoma'><o:p> </o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l9 level1 lfo9;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE><span style='mso-bidi-font-family:
| |
| Tahoma'>Kunna</span></span><span style='mso-bidi-font-family:Tahoma'> förkorta
| |
| och förlänga bråk.</span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><span
| |
| style='mso-spacerun:yes'> </span><span class=GramE>Tex.</span>
| |
| Förläng bråket 3/5 med 4.</span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><span
| |
| style='mso-spacerun:yes'> </span>Skriv bråket 18/30 med
| |
| så liten nämnare som möjligt.</span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><span
| |
| style='mso-spacerun:yes'> </span></span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l2 level1 lfo3;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE><span style='mso-bidi-font-family:
| |
| Tahoma'>Kunna</span></span><span style='mso-bidi-font-family:Tahoma'> beräkna
| |
| storleken utifrån given bråkdel.</span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-spacerun:yes'> </span><span
| |
| class=GramE>Tex.</span> Räkna ut 5/8 av 1650 kg<o:p></o:p></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><o:p> </o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l4 level1 lfo5;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE><span style='mso-bidi-font-family:
| |
| Tahoma'>Kunna</span></span><span style='mso-bidi-font-family:Tahoma'> utföra
| |
| omvandlingar mellan tal i bråkform och tal i blandad form.</span><span
| |
| style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><span
| |
| style='mso-spacerun:yes'> </span><span class=GramE>Tex.</span> <span
| |
| style='mso-tab-count:1'> </span>Skriv 17 / 4 i blandad form.</span><span
| |
| style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><span
| |
| style='mso-spacerun:yes'> </span><span style='mso-tab-count:
| |
| 1'> </span><span class=GramE>Skriv<span style='mso-spacerun:yes'> </span>3</span>
| |
| 1/3<span style='mso-spacerun:yes'> </span>i bråkform.</span><span
| |
| style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1><span style='mso-bidi-font-family:Tahoma'><o:p> </o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l5 level1 lfo6;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE><span style='mso-bidi-font-family:
| |
| Tahoma'>Kunna</span></span><span style='mso-bidi-font-family:Tahoma'> utföra
| |
| addition, subtraktion av bråk med samma nämnare samt multiplikation av bråk med
| |
| ett heltal.</span><span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <p class=Normal1 style='margin-left:63.8pt;text-indent:1.45pt;tab-stops:63.8pt'><span
| |
| class=GramE>Tex.</span> <span style='mso-tab-count:1'> </span>beräkna<span
| |
| style='mso-spacerun:yes'> </span>a) 3/6 + 1/6<span
| |
| style='mso-spacerun:yes'> </span>b) 5/8 – 3/8<span
| |
| style='mso-spacerun:yes'> </span><br>
| |
| <span style='mso-tab-count:1'> </span>c) I ett recept på äppelkräm står det att
| |
| man skall ha ¾ kg äpplen till 4 portioner kräm. Hur mycket äpplen skall du ta
| |
| om du tänker göra 12 portioner?<span style='mso-bidi-font-family:Tahoma'><o:p></o:p></span></p>
| |
|
| |
| <h3 style='margin-left:0cm;text-indent:0cm'>Procent </h3>
| |
|
| |
| <p class=MsoNormal style='margin-left:36.0pt;text-indent:-18.0pt;mso-pagination:
| |
| none;mso-list:l1 level1 lfo10;tab-stops:36.0pt 70.5pt'><![if !supportLists]><span
| |
| style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
| |
| Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]>Förstå procentbegreppet.</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:70.5pt'><span style='mso-spacerun:yes'>
| |
| </span><span style='mso-tab-count:1'> </span><span
| |
| class=GramE><i>Tex.</i></span><i> Hur stor del av figurerna är skuggat. Svara i
| |
| procent.<o:p></o:p></i></p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:70.5pt'><!--[if gte vml 1]><v:rect id="_x0000_s1026"
| |
| style='position:absolute;margin-left:73.15pt;margin-top:2.45pt;width:14.4pt;
| |
| height:36pt;z-index:1;v-text-anchor:middle' fillcolor="#333" strokeweight=".26mm">
| |
| <v:fill color2="#ccc"/>
| |
| </v:rect><v:rect id="_x0000_s1027" style='position:absolute;margin-left:101.95pt;
| |
| margin-top:2.45pt;width:14.4pt;height:36pt;z-index:2;v-text-anchor:middle'
| |
| strokeweight=".26mm">
| |
| <v:fill color2="black"/>
| |
| </v:rect><v:rect id="_x0000_s1028" style='position:absolute;margin-left:87.55pt;
| |
| margin-top:2.45pt;width:14.4pt;height:36pt;z-index:3;v-text-anchor:middle'
| |
| strokeweight=".26mm">
| |
| <v:fill color2="black"/>
| |
| </v:rect><v:rect id="_x0000_s1029" style='position:absolute;margin-left:116.35pt;
| |
| margin-top:2.45pt;width:14.4pt;height:36pt;z-index:4;v-text-anchor:middle'
| |
| strokeweight=".26mm">
| |
| <v:fill color2="black"/>
| |
| </v:rect><v:shape id="_x0000_s1030" style='position:absolute;margin-left:195.55pt;
| |
| margin-top:2.45pt;width:43.25pt;height:36.05pt;z-index:5;
| |
| mso-position-horizontal:absolute;mso-position-horizontal-relative:text;
| |
| mso-position-vertical:absolute;mso-position-vertical-relative:text;
| |
| v-text-anchor:middle' coordsize="866,722" path="m216,l865,,648,721,,721,216,e"
| |
| fillcolor="maroon" strokeweight=".26mm">
| |
| <v:fill color2="#7fffff"/>
| |
| </v:shape><v:shape id="_x0000_s1031" style='position:absolute;margin-left:224.35pt;
| |
| margin-top:2.45pt;width:43.25pt;height:36.05pt;z-index:6;
| |
| mso-position-horizontal:absolute;mso-position-horizontal-relative:text;
| |
| mso-position-vertical:absolute;mso-position-vertical-relative:text;
| |
| v-text-anchor:middle' coordsize="866,722" path="m216,l865,,648,721,,721,216,e"
| |
| strokeweight=".26mm">
| |
| <v:fill color2="black"/>
| |
| </v:shape><![endif]--><![if !vml]><span style='mso-ignore:vglayout'>
| |
|
| |
| <table cellpadding=0 cellspacing=0 align=left>
| |
| <tr>
| |
| <td width=97 height=2></td>
| |
| <td width=78></td>
| |
| <td width=84></td>
| |
| <td width=99></td>
| |
| </tr>
| |
| <tr>
| |
| <td height=50></td>
| |
| <td align=left valign=top><img width=78 height=50
| |
| src="Tal%20och%20räknesätt-filer/image001.gif" v:shapes="_x0000_s1026 _x0000_s1027 _x0000_s1028 _x0000_s1029"></td>
| |
| <td></td>
| |
| <td align=left valign=top><img width=99 height=50
| |
| src="Tal%20och%20räknesätt-filer/image002.gif" v:shapes="_x0000_s1030 _x0000_s1031"></td>
| |
| </tr>
| |
| </table>
| |
|
| |
| </span><![endif]><span style='color:red'><o:p> </o:p></span></p>
| |
|
| |
| <br style='mso-ignore:vglayout' clear=ALL>
| |
|
| |
| <p class=MsoNormal style='tab-stops:70.5pt'><span
| |
| style='mso-spacerun:yes'> </span></p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:70.5pt'><span style='color:red'><o:p> </o:p></span></p>
| |
|
| |
| <p class=MsoBodyText style='margin-left:18.0pt;text-indent:-18.0pt;mso-pagination:
| |
| none;mso-list:l3 level1 lfo4;tab-stops:18.0pt 70.5pt'><![if !supportLists]><span
| |
| style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
| |
| Symbol;mso-bidi-font-style:italic'><span style='mso-list:Ignore'>·<span
| |
| style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> utföra
| |
| omvandlingar mellan tal i bråkform och tal i decimalform till procentform.<i><o:p></o:p></i></p>
| |
|
| |
| <p class=MsoBodyText style='mso-pagination:none;tab-stops:35.45pt 70.5pt'><span
| |
| style='mso-tab-count:1'> </span><span class=GramE><i>Tex.</i></span><i>
| |
| Skriv ¼<span style='mso-spacerun:yes'> </span>i decimalform och procentform.<o:p></o:p></i></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-pagination:
| |
| none;mso-list:l2 level1 lfo3;tab-stops:18.0pt 70.5pt'><![if !supportLists]><span
| |
| style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
| |
| Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]><span class=GramE>Kunna</span> göra beräkningar
| |
| med procent.</p>
| |
|
| |
| <p class=MsoNormal style='margin-left:35.45pt;text-indent:-35.45pt;tab-stops:
| |
| 70.5pt'><span style='mso-spacerun:yes'> </span><i>Hur mycket <span
| |
| class=GramE>är<span style='mso-spacerun:yes'> </span>a</span>)10 % av 500
| |
| kr<span style='mso-spacerun:yes'> </span>b) 4% av 150 kr.<o:p></o:p></i></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:35.45pt;text-indent:-35.45pt;tab-stops:
| |
| 70.5pt 93.0pt'><i><span style='mso-spacerun:yes'> </span><span
| |
| style='mso-tab-count:1'> </span>En lön på 12000 kr höjs med <span
| |
| class=GramE>3%</span>. Vilken blir den nya lönen?<o:p></o:p></i></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:35.45pt;text-indent:-35.45pt;tab-stops:
| |
| 70.5pt 93.0pt'><i><span style='mso-tab-count:1'> </span>Priset på en
| |
| vara steg från 80 kr till 100 kr. Med hur många procent steg priset?<o:p></o:p></i></p>
| |
|
| |
| <p class=MsoNormal style='margin-left:35.45pt;text-indent:-35.45pt;tab-stops:
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| 70.5pt 93.0pt'><i><span style='mso-tab-count:1'> </span>Priset på en
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| vara sjönk med 2 kr till 18 kr. Med hur många procent sänktes priset?<span
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| style='mso-spacerun:yes'> </span><o:p></o:p></i></p>
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|
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| <h4>Mer än godkänt</h4>
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|
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| <p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-pagination:
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| none;mso-list:l4 level1 lfo5;tab-stops:18.0pt 36.0pt'><![if !supportLists]><span
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| style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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| Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
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| </span></span></span><![endif]><span class=GramE>Kunna</span> räkna med
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| upprepad förändring.</p>
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|
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| <p class=MsoNormal style='tab-stops:18.0pt 1.0cm 35.45pt 71.25pt 92.25pt'><span
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| style='mso-spacerun:yes'> </span><span style='mso-tab-count:3'> </span><i>En
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| vara som kostar 35 kr höjs med fem procent fyra gånger.<o:p></o:p></i></p>
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|
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| <p class=MsoNormal style='tab-stops:18.0pt 35.45pt 71.25pt 92.25pt'><i><span
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| style='mso-tab-count:2'> </span>Hur många procent dyrare är den
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| efter alla höjningar?<o:p></o:p></i></p>
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|
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| <p class=MsoNormal style='tab-stops:18.0pt'><o:p> </o:p></p>
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|
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| <p class=MsoNormal style='margin-left:21.0pt;text-indent:-18.0pt;mso-pagination:
| |
| none;mso-list:l5 level1 lfo6;tab-stops:list 18.0pt left 21.0pt 39.0pt'><![if !supportLists]><span
| |
| style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
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| Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
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| </span></span></span><![endif]><span class=GramE>Kunna</span> beräkna hela
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| mängden med hjälp av procentsats och delmängd.</p>
| |
|
| |
| <p class=MsoNormal style='tab-stops:35.45pt 71.25pt'><span style='mso-tab-count:
| |
| 1'> </span><i>18 % av något är 4140 kg. Vad fanns från början?<o:p></o:p></i></p>
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|
| |
| <p class=Normal1 style='margin-left:18.0pt'><o:p> </o:p></p>
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|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l6 level1 lfo11;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]>Visa säkerhet i sina beräkningar och sitt
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| problemlösningsarbete samt välja och anpassa räknemetoder till den aktuella
| |
| problemsituationen.<span style='mso-spacerun:yes'> </span></p>
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|
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| <p class=Normal1><o:p> </o:p></p>
| |
|
| |
| <p class=Normal1 style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l6 level1 lfo11;
| |
| tab-stops:18.0pt'><![if !supportLists]><span style='font-family:Symbol;
| |
| mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
| |
| style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
| |
| </span></span></span><![endif]>Använda sin kunskap i nya sammanhang för att t
| |
| ex lösa ett problem</p>
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|
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| <p class=MsoNormal><o:p> </o:p></p>
| |
|
| |
| <h3 style='margin-left:0cm;text-indent:0cm'>Proportionalitet</h3>
| |
|
| |
| <p class=MsoNormal><i style='mso-bidi-font-style:normal'>Var ingår normalt
| |
| proportionalitet<span class=GramE>.</span> Vad menas med begreppet?<o:p></o:p></i></p>
| |
|
| |
| <p class=MsoNormal><o:p> </o:p></p>
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|
| |
| </div>
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|
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| <div style='mso-element:footnote-list'><![if !supportFootnotes]><br clear=all>
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|
| |
| <hr align=left size=1 width="33%">
| |
|
| |
| <![endif]>
| |
|
| |
| <div style='mso-element:footnote' id=ftn1>
| |
|
| |
| <p class=MsoFootnoteText><a style='mso-footnote-id:ftn1' href="#_ftnref1"
| |
| name="_ftn1" title=""><span class=MsoFootnoteReference><span style='mso-special-character:
| |
| footnote'><![if !supportFootnotes]><span class=MsoFootnoteReference><span
| |
| style='font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family:
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| "Times New Roman";mso-ansi-language:SV;mso-fareast-language:AR-SA;mso-bidi-language:
| |
| AR-SA'>[1]</span></span><![endif]></span></span></a> Det finns en övergripande <span
| |
| class=SpellE>kurspplan</span> för vardera av de fem områdena aritmetik,
| |
| geometri, algebra, statistik och <span class=SpellE>sannolikhetslära</span>.</p>
| |
|
| |
| </div>
| |
|
| |
| </div>
| |
|
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| </body>
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|
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| </html>
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