Klasifikasi Masalah Matematika

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Masalah Penemuan dan Masalah PembuktianPusat Kurikulum

Penemuan (Problem to find), yaitu mencari, menentukan, atau mendapatkan nilai atau objek tertentu yang tidak diketahui dari soal serta memenuhi kondisi atau syarat yang sesuai dengan soal.

Pembuktian (Problem to prove), yaitu prosedur untuk menentukan apakah suatu pernyataan benar atau tidak benar. Soal membuktikan terdiri atas bagian hipotesis dan kesimpulan. Untuk membuktikan kita harus membuat atau memproses pernyataan yang logis dari hipotesis menuju kesimpulan, sedangkan untuk membuktikan bahwa suatu pernyataan tidak benar kita harus memberikan contoh penyangkalnya sehingga pernyataan tersebut menjadi tidak benar.

Apa langkah pertama yang harus dilakukan dalam mengerjakan $ 3\frac{1}{2}:5\frac{1}{4} $ ?

Tentukan hasilnya bila $ 3\frac{1}{4} \times 6:2\frac{1}{2} $ ?

Manakah yang lebih luas, kebun yang berbentuk persegipanjang dengan panjang 314 m dan lebar 12 m atau kolam renang yang berbentuk lingkaran dengan jari-jari lingkaran 12 m?

Ani lebih tua dari Budi, Budi lebih tua daripada Chandra, Chandra lebih muda daripada Deni. Siapakah yang paling muda di antara mereka?

Diketahui sejumlah bangun geometri datar, yaitu persegi, persegipanjang, segitiga, lingkaran, belahketupat, jajargenjang, laying-layang, dan trapesium. Buatlah hubungan di antara mereka dalam bentuk diagram peta konsep!

Dengan cara bagaimana kita menunjukkan 6 dibagi 3 adalah 2?

Jelaskan mengapa $ 2\sqrt{5} \times 3\sqrt{5}-5=25 $

Mengapa bilangan-bilangan ganjil dikalikan dengan bilangan genap selalu menghasilkan bilangan genap?

Mengapa setiap persegi adalah pesegi panjang?

Mengapa sebuah relasi belum tentu merupakan fungsi?

Pada soal no 1 siswa akan menentukan langkah pertama untuk mendapatkan nilai dari $ 3\frac{1}{2}:5\frac{1}{4}$(masalah penemuan).

Pada soal no 2 siswa akan mencari nilai dari $ 3\frac{1}{4} \times 6:2\frac{1}{2} $ (masalah penemuan).

Pada soal no 3 siswa akan menentukan mana yang lebih luas dengan mencari luas kebun dan kolam renang dengan ukuran masing-masing yang sudah di tentukan (masalah penemuan).

Pada soal no 4 siswa akan menentukan kondisi yang sesuai soal dengan yang diberikan (masalah penemuan).

Pada soal no 5 siswa akan mencari, menentukan, dan mendapatkan hubungan bangun geometri datar yang diberikan dalam diagram peta konsep (masalah penemuan).

Pada soal no 6 siswa akan menunjukkan bahwa 6 dibagi 3 adalah 2 merupakan pernyataan yang bernilai benar (masalah pembuktian).

Pada soal no 7 siswa akan menunjukkan bahwa image002.gif adalah benar (masalah pembuktian).

Pada soal no 8, 9, 10 merupakan masalah pembuktian diserahkan kepada Anda sebagai latihan.

Jawaban

Masalah penemuan berhubungan erat dengan proses mencari, menentukan, atau mendapatkan nilai atau objek tertentu yang tidak diketahui dari soal.

Masalah pembuktian berhubungan erat dengan prosedur untuk menentukan apakah suatu pernyataan benar atau tidak benar.

Pada soal no 8, 9, 10 di atas siswa membuktikan bahwa bilangan-bilangan ganjil dikalikan dengan bilangan genap selalu menghasilkan bilangan genap, setiap persegi adalah pesegi panjang, dan sebuah relasi belum tentu merupakan fungsi.

Masalah penemuan terkait proses mencarian nilai tertentu yang tidak diketahui dari soal, masalah pembuktian terkait proses membuktikan kebenaran dari soal yang diberikan.

Tipe soal sebagai masalah penemuan dalam matematika menuntut siswa mencari suatu nilai tertentu misalnya mencari hasil dari beberapa operasi pada bilangan, sedangkan tipe soal sebagai masalah pembuktian menuntut siswa untuk mencari kebenaran dari soal misalnya $x$ yang memenuhi persamaan $2 + x = 5$ adalah $3$, dsb.

Rangkuman

Penemuan (Problem to find), yaitu mencari, menentukan, atau mendapatkan nilai atau objek tertentu yang tidak diketahui dari soal serta memenuhi kondisi atau syarat yang sesuai dengan soal. Contoh: Tentukan hasilnya bila $ 3\frac{1}{4} \times 6:2\frac{1}{2} $?

ita dapat mengklasifikasikan masalah dalam kehidupan kita Klasifikasi Masalah Matematika

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Tags Matematika Realistik Pembelajaran

Brahma Prasetya Diposting : Kamis, 06 Desember 2012, Desember 06, 2012

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e=i.slides.first(),t=i.vars.itemMargin,a=i.vars.minItems,n=i.vars.maxItems;i.w=void 0===i.viewport?i.width():i.viewport.width(),i.h=e.height(),i.boxPadding=e.outerWidth()-e.width(),p?(i.itemT=i.vars.itemWidth+t,i.itemM=t,i.minW=a?a*i.itemT:i.w,i.maxW=n?n*i.itemT-t:i.w,i.itemW=i.minW>i.w?(i.w-t*(a-1))/a:i.maxW<i.w?(i.w-t*(n-1))/n:i.vars.itemWidth>i.w?i.w:i.vars.itemWidth,i.visible=Math.floor(i.w/i.itemW),i.move=i.vars.move>0&&i.vars.move<i.visible?i.vars.move:i.visible,i.pagingCount=Math.ceil((i.count-i.visible)/i.move+1),i.last=i.pagingCount-1,i.limit=1===i.pagingCount?0:i.vars.itemWidth>i.w?i.itemW*(i.count-1)+t*(i.count-1):(i.itemW+t)*i.count-i.w-t):(i.itemW=i.w,i.itemM=t,i.pagingCount=i.count,i.last=i.count-1),i.computedW=i.itemW-i.boxPadding,i.computedM=i.itemM},i.update=function(e,t){i.doMath(),p||(e<i.currentSlide?i.currentSlide+=1:e<=i.currentSlide&&0!==e&&(i.currentSlide-=1),i.animatingTo=i.currentSlide),i.vars.controlNav&&!i.manualControls&&("add"===t&&!p||i.pagingCount>i.controlNav.length?g.controlNav.update("add"):("remove"===t&&!p||i.pagingCount<i.controlNav.length)&&(p&&i.currentSlide>i.last&&(i.currentSlide-=1,i.animatingTo-=1),g.controlNav.update("remove",i.last))),i.vars.directionNav&&g.directionNav.update()},i.addSlide=function(t,a){var n=e(t);i.count+=1,i.last=i.count-1,u&&v?void 0!==a?i.slides.eq(i.count-a).after(n):i.container.prepend(n):void 0!==a?i.slides.eq(a).before(n):i.container.append(n),i.update(a,"add"),i.slides=e(i.vars.selector+":not(.clone)",i),i.setup(),i.vars.added(i)},i.removeSlide=function(t){var a=isNaN(t)?i.slides.index(e(t)):t;i.count-=1,i.last=i.count-1,isNaN(t)?e(t,i.slides).remove():u&&v?i.slides.eq(i.last).remove():i.slides.eq(t).remove(),i.doMath(),i.update(a,"remove"),i.slides=e(i.vars.selector+":not(.clone)",i),i.setup(),i.vars.removed(i)},g.init()},e(window).blur(function(e){t=!1}).focus(function(e){t=!0}),e.flexslider.defaults={namespace:"flex-",selector:".slides > li",animation:"fade",easing:"swing",direction:"horizontal",reverse:!1,animationLoop:!0,smoothHeight:!1,startAt:0,slideshow:!0,slideshowSpeed:7e3,animationSpeed:600,initDelay:0,randomize:!1,fadeFirstSlide:!0,thumbCaptions:!1,pauseOnAction:!0,pauseOnHover:!1,pauseInvisible:!0,useCSS:!0,touch:!0,video:!1,controlNav:!0,directionNav:!0,prevText:"Previous",nextText:"Next",keyboard:!0,multipleKeyboard:!1,mousewheel:!1,pausePlay:!1,pauseText:"Pause",playText:"Play",controlsContainer:"",manualControls:"",customDirectionNav:"",sync:"",asNavFor:"",itemWidth:0,itemMargin:0,minItems:1,maxItems:0,move:0,allowOneSlide:!0,start:function(){},before:function(){},after:function(){},end:function(){},added:function(){},removed:function(){},init:function(){}},e.fn.flexslider=function(t){if(void 0===t&&(t={}),"object"==typeof t)return this.each(function(){var a=e(this),n=t.selector?t.selector:".slides > li",i=a.find(n);1===i.length&&t.allowOneSlide===!1||0===i.length?(i.fadeIn(400),t.start&&t.start(a)):void 0===a.data("flexslider")&&new e.flexslider(this,t)});var a=e(this).data("flexslider");switch(t){case"play":a.play();break;case"pause":a.pause();break;case"stop":a.stop();break;case"next":a.flexAnimate(a.getTarget("next"),!0);break;case"prev":case"previous":a.flexAnimate(a.getTarget("prev"),!0);break;default:"number"==typeof t&&a.flexAnimate(t,!0)}}}(jQuery); $(window).load(function(){$('#mbt-c').flexslider({animation:"slide",directionNav:false,itemWidth:415,itemMargin:0,touch:true,slideshowSpeed:1500,pauseOnHover:true,animationSpeed:600,})}); function Scroller(t){this.options=t,this.button=null,this.stop=!1}Scroller.prototype.constructor=Scroller,Scroller.prototype.createButton=function(){this.button=document.createElement("button"),this.button.classList.add("scroll-button"),this.button.classList.add("scroll-button--hidden"),this.button.textContent="TOP",document.body.appendChild(this.button)},Scroller.prototype.init=function(){this.createButton(),this.checkPosition(),this.click(),this.stopListener()},Scroller.prototype.scroll=function(){return 0==this.options.animate||"false"==this.options.animate?void this.scrollNoAnimate():"normal"==this.options.animate?void this.scrollAnimate():"linear"==this.options.animate?void this.scrollAnimateLinear():void 0},Scroller.prototype.scrollNoAnimate=function(){document.body.scrollTop=0,document.documentElement.scrollTop=0},Scroller.prototype.scrollAnimate=function(){this.scrollTop()>0&&0==this.stop&&setTimeout(function(){this.scrollAnimate(),window.scrollBy(0,-Math.abs(this.scrollTop())/this.options.normal.steps)}.bind(this),this.options.normal.ms)},Scroller.prototype.scrollAnimateLinear=function(){this.scrollTop()>0&&0==this.stop&&setTimeout(function(){this.scrollAnimateLinear(),window.scrollBy(0,-Math.abs(this.options.linear.px))}.bind(this),this.options.linear.ms)},Scroller.prototype.click=function(){this.button.addEventListener("click",function(t){t.stopPropagation(),this.scroll()}.bind(this),!1),this.button.addEventListener("dblclick",function(t){t.stopPropagation(),this.scrollNoAnimate()}.bind(this),!1)},Scroller.prototype.hide=function(){this.button.classList.add("scroll-button--hidden")},Scroller.prototype.show=function(){this.button.classList.remove("scroll-button--hidden")},Scroller.prototype.checkPosition=function(){window.addEventListener("scroll",function(t){this.scrollTop()>this.options.showButtonAfter?this.show():this.hide()}.bind(this),!1)},Scroller.prototype.stopListener=function(){var t=this.scrollTop();window.addEventListener("scroll",function(o){this.scrollTop()>t&&this.stopTimeout(200),t=this.scrollTop()}.bind(this,t),!1),window.addEventListener("wheel",function(t){t.deltaY>0&&this.stopTimeout(200)}.bind(this),!1)},Scroller.prototype.stopTimeout=function(t){this.stop=!0,setTimeout(function(){this.stop=!1,console.log(this.stop)}.bind(this),t)},Scroller.prototype.scrollTop=function(){var t=document.documentElement.scrollTop||document.body.scrollTop;return t};var options={showButtonAfter:200,animate:"normal",normal:{steps:15,ms:1e3/60},linear:{px:80,ms:1e3/60}},scroll=new Scroller(options);scroll.init(); function resizeThumb(el,from,to){$(el).each(function(){$(this).attr({'src':$(this).attr('src').replace('/s'+from+'-c/','/s'+to+'-c/'),'width':to,'height':to})})} $(function(){resizeThumb('.related-thumb','72','150')}) $(function(){$('#controltab1').click(function(){var divID=$(this).attr('href');$('html,body').animate({scrollTop:$(divID).offset().top},{duration:'slow',easing:'swing'})})});$(function(){$('#controltab2').click(function(){var divID=$(this).attr('href');$('html,body').animate({scrollTop:$(divID).offset().top},{duration:'slow',easing:'swing'})})}); var uri=window.location.toString();if(uri.indexOf("%3D","%3D")>0){var clean_uri=uri.substring(0,uri.indexOf("%3D"));window.history.replaceState({},document.title,clean_uri)} var uri=window.location.toString();if(uri.indexOf("%3D%3D","%3D%3D")>0){var clean_uri=uri.substring(0,uri.indexOf("%3D%3D"));window.history.replaceState({},document.title,clean_uri)} var uri=window.location.toString();if(uri.indexOf("&m=1","&m=1")>0){var clean_uri=uri.substring(0,uri.indexOf("&m=1"));window.history.replaceState({},document.title,clean_uri)} var uri=window.location.toString();if(uri.indexOf("?m=1","?m=1")>0){var clean_uri=uri.substring(0,uri.indexOf("?m=1"));window.history.replaceState({},document.title,clean_uri)} function replaceText(){if(!document.getElementById){return} bodyText=document.getElementById("Blog1");theText=bodyText.innerHTML;theText=theText.replace(/default/gi,"mqdefault");bodyText.innerHTML=theText}replaceText() //]]> $(".entry-content img").parents("a").on("click",function(a){a.preventDefault();a.stopPropagation();return $(this).lighter()}); (function(){var g,h,e,f=function(b,a){return function(){return b.apply(a,arguments)}};g=jQuery;h=(function(){function a(){}a.transitions={webkitTransition:"webkitTransitionEnd",mozTransition:"mozTransitionEnd",oTransition:"oTransitionEnd",transition:"transitionend"};a.transition=function(k){var c,l,d,b;c=k[0];b=this.transitions;for(d in b){l=b[d];if(c.style[d]!=null){return l}}};a.execute=function(d,b){var c;c=this.transition(d);if(c!=null){return d.one(c,b)}else{return b()}};return a})();e=(function(){a.settings={padding:40,dimensions:{width:960,height:540},template:"<div class='lighter fade'>\n <div class='lighter-container'>\n <span class='lighter-content'></span>\n <a class='lighter-close'>×</a>\n <a class='lighter-prev'>‹</a>\n <a class='lighter-next'>›</a>\n </div>\n <div class='lighter-overlay'></div>\n</div>"};a.lighter=function(c,d){var b;if(d==null){d={}}b=c.data("_lighter");if(!b){b=new a(c,d);c.data("_lighter",b)}return b};a.prototype.$=function(b){return this.$lighter.find(b)};function a(c,b){if(b==null){b={}}this.show=f(this.show,this);this.hide=f(this.hide,this);this.toggle=f(this.toggle,this);this.keyup=f(this.keyup,this);this.align=f(this.align,this);this.resize=f(this.resize,this);this.process=f(this.process,this);this.href=f(this.href,this);this.type=f(this.type,this);this.image=f(this.image,this);this.prev=f(this.prev,this);this.next=f(this.next,this);this.close=f(this.close,this);this.$=f(this.$,this);this.$el=c;if((this.$el.data("width")!=null)&&(this.$el.data("height")!=null)){if(b.dimensions==null){b.dimensions={width:this.$el.data("width"),height:this.$el.data("height")}}}this.settings=g.extend({},a.settings,b);this.$lighter=g(this.settings.template);this.$overlay=this.$(".lighter-overlay");this.$content=this.$(".lighter-content");this.$container=this.$(".lighter-container");this.$close=this.$(".lighter-close");this.$prev=this.$(".lighter-prev");this.$next=this.$(".lighter-next");this.$body=this.$(".lighter-body");this.width=this.settings.dimensions.width;this.height=this.settings.dimensions.height;this.align();this.process()}a.prototype.close=function(b){if(b!=null){b.preventDefault()}if(b!=null){b.stopPropagation()}return this.hide()};a.prototype.next=function(b){if(b!=null){b.preventDefault()}return b!=null?b.stopPropagation():void 0};a.prototype.prev=function(){if(typeof event!=="undefined"&&event!==null){event.preventDefault()}return typeof event!=="undefined"&&event!==null?event.stopPropagation():void 0};a.prototype.image=function(b){return b.match(/\.(jpeg|jpg|jpe|gif|png|bmp)$/i)};a.prototype.type=function(b){if(b==null){b=this.href()}return this.settings.type||(this.image(b)?"image":void 0)};a.prototype.href=function(){return this.$el.attr("href")};a.prototype.process=function(){var j,c,d,b=this;d=this.type(j=this.href());this.$content.html((function(){switch(d){case"image":return g("<img/>").attr({src:j});default:return g(j)}})());switch(d){case"image":c=new Image();c.src=j;return c.onload=function(){return b.resize(c.width,c.height)}}};a.prototype.resize=function(b,c){this.width=b;this.height=c;return this.align()};a.prototype.align=function(){var d,b,c;b=Math.max((d=this.height)/(g(window).height()-this.settings.padding),(c=this.width)/(g(window).width()-this.settings.padding));if(b>1){d=Math.round(d/b)}if(b>1){c=Math.round(c/b)}return this.$container.css({height:d,width:c,margin:"-"+(d/2)+"px -"+(c/2)+"px"})};a.prototype.keyup=function(b){if(b.target.form!=null){return}if(b.which===27){this.close()}if(b.which===37){this.prev()}if(b.which===39){return this.next()}};a.prototype.toggle=function(b){if(b==null){b="on"}g(window)[b]("resize",this.align);g(document)[b]("keyup",this.keyup);this.$overlay[b]("click",this.close);this.$close[b]("click",this.close);this.$next[b]("click",this.next);return this.$prev[b]("click",this.prev)};a.prototype.hide=function(){var d,b,c=this;d=function(){return c.toggle("off")};b=function(){return c.$lighter.remove()};d();this.$lighter.removeClass("fade");this.$lighter.position();this.$lighter.addClass("fade");return h.execute(this.$container,b)};a.prototype.show=function(){var d,b,c=this;b=function(){return c.toggle("on")};d=function(){return g(document.body).append(c.$lighter)};d();this.$lighter.addClass("fade");this.$lighter.position();this.$lighter.removeClass("fade");return h.execute(this.$container,b)};return a})();g.fn.extend({lighter:function(a){if(a==null){a={}}return this.each(function(){var b,c,d;b=g(this);d=g.extend({},g.fn.lighter.defaults,typeof a==="object"&&a);c=typeof a==="string"?a:a.action;if(c==null){c="show"}return e.lighter(b,d)[c]()})}})}).call(this);

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