表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版

2025-10-04
| 21页
| 98人阅读
| 2人下载
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资源信息

学段 小学
学科 数学
教材版本 小学数学苏教版(2012)六年级上册
年级 六年级
章节 表面涂色的正方体
类型 课件
知识点 -
使用场景 同步教学-新授课
学年 2025-2026
地区(省份) 全国
地区(市) -
地区(区县) -
文件格式 PPTX
文件大小 12.77 MB
发布时间 2025-10-04
更新时间 2025-10-10
作者 匿名
品牌系列 -
审核时间 2025-10-04
下载链接 https://m.zxxk.com/soft/54213708.html
价格 2.00储值(1储值=1元)
来源 学科网

摘要:

该小学数学课件聚焦正方体分割后小正方体涂色问题,通过“每条棱平均分成n份”的重复呈现结合“我能挑战”中棱长10厘米正方体实例,从具体到抽象搭建学习支架,帮助学生理解3面、2面、1面、0面涂色小正方体数量规律。 其亮点是“我会思考”环节通过2面涂色数量反推棱的份数,培养空间观念与推理意识,体现数学思维。课堂小结引导反思,拓展延伸提升应用意识,助力学生形成抽象能力,方便教师实施分层教学。

内容正文:

表面涂色的正方体 探究新知 探究新知 活动要求: 1.借助学具,分工合作; 2.完成学习单中表1,交流以上问题; 3.推选小组代表全班汇报。 研究问题: 1.一共切成多少个小正方体? 2.不同涂色情况的小正方体在什么位置?各有多少个? 探究活动一 3面涂色 2面涂色 1面涂色 顶点 棱的中间 面的中间 8个 12个 6个 没有涂色 正方体内部 1个 活动要求: 1.借助直观图自主探究; 2.可以看一看、圈一圈、想一想、算一算; 3.完成表2,再小组交流。 探究活动二 3面涂色的小正方体 2面涂色的小正方体 1面涂色的小正方体 没有涂色的小正方体 每条棱被平均分成n份 每条棱被平均分成n份 每条棱被平均分成n份 每条棱被平均分成n份 把一个棱长10厘米的正方体每个面都涂上红色,再把它切成棱长1厘米的小正方体。小正方体的总个数,3面涂色、2面涂色、1面涂色的各有多少个? 我能挑战 通过这节课的学习,你有什么收获? 课堂小结 拓展延伸 一个涂色的正方体,把每条棱都平均分成若干份,得到若干个小正方体,其中2面涂色的有48块,大正方体每条棱被平均分成( )份,3面涂色的有( )个,1面涂色有( )个,0面涂色有( )个。 我会思考 huohua_res/JZ058Mfq6/css/app.b5b3908b.css 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i.attach(e.children[0]),i.addEventListener("change",(function(e){e.target.object&&((e.target.object.position.x>=40||e.target.object.position.x<=-40)&&(e.target.object.position.x=e.target.object.position.x>0?40:-40),(e.target.object.position.y>=40||e.target.object.position.y<=-40)&&(e.target.object.position.y=e.target.object.position.y>0?40:-40),(e.target.object.position.z>=40||e.target.object.position.z<=-40)&&(e.target.object.position.z=e.target.object.position.z>0?40:-40))})),i.addEventListener("dragging-changed",(function(e){t.orbitControl.enabled=!e.value,i.children[0].gizmo.translate.position.set(0,0,0)})),i.size=1.5,i.children[0].helper.rotate.children=[],i.children[0].helper.translate.children=[],i.children[0].gizmo.rotate.children=[],i.children[0].gizmo.translate.children=[],i}}]),e}(),C=i("f257"),S=i("673a"),T=i("9adc"),I=i("1767"),E=i("dd69"),O=i("6ce6"),L=i("1a51"),j=i("510e"),B=i("1837"),M=i("5e56"),D=i("7d05"),A=i("5270"),z=i("e11e"),_=i("523a"),F=i("dca6"),H=i("6dd8"),W=i("45e6"),R=i("1130"),U=i("db43"),G=i("1568"),V=i("e845"),$=i("43a1"),Y=i("0557"),N=i("2156"),X=i("7d35"),q=i("4157"),Q=function(){function e(){Object(s["a"])(this,e)}return Object(u["a"])(e,null,[{key:"initSingleMaterial",value:function(){for(var e=[],t=[C,S,T,I,E,O],i=0;i<t.length;i++)e.push((new g["TextureLoader"]).load(t[i]));return e}},{key:"initTwoFaceMaterial",value:function(){for(var e=[],t=[L,j,B,M,D,A,z,_,F,H,W,R],i=0;i<t.length;i++)e.push((new g["TextureLoader"]).load(t[i]));return e}},{key:"initThreeFaceMaterial",value:function(){for(var e=[],t=[U,G,V,$,Y,N,X,q],i=0;i<t.length;i++)e.push((new g["TextureLoader"]).load(t[i]));return e}}]),e}();Q.oneFacePosArr=[{x:0,y:0,z:10,rx:0,ry:0,rz:0},{x:0,y:0,z:-10,rx:0,ry:0,rz:0},{x:-10,y:0,z:0,rx:0,ry:0,rz:0},{x:10,y:0,z:0,rx:0,ry:0,rz:0},{x:0,y:10,z:0,rx:0,ry:0,rz:0},{x:0,y:-10,z:0,rx:0,ry:0,rz:0}],Q.twoFacePosArr=[{x:-10,y:0,z:10,rx:0,ry:0,rz:0},{x:10,y:0,z:10,rx:0,ry:0,rz:0},{x:10,y:0,z:-10,rx:0,ry:0,rz:0},{x:-10,y:0,z:-10,rx:0,ry:0,rz:0},{x:0,y:10,z:10,rx:0,ry:0,rz:0},{x:0,y:10,z:-10,rx:0,ry:0,rz:0},{x:-10,y:10,z:0,rx:0,ry:0,rz:0},{x:10,y:10,z:0,rx:0,ry:0,rz:0},{x:0,y:-10,z:10,rx:0,ry:0,rz:0},{x:0,y:-10,z:-10,rx:0,ry:0,rz:0},{x:-10,y:-10,z:0,rx:0,ry:0,rz:0},{x:10,y:-10,z:0,rx:0,ry:0,rz:0}],Q.threeFacePosArr=[{x:10,y:10,z:10,rx:0,ry:0,rz:0},{x:10,y:10,z:-10,rx:0,ry:0,rz:0},{x:-10,y:10,z:10,rx:0,ry:0,rz:0},{x:-10,y:10,z:-10,rx:0,ry:0,rz:0},{x:-10,y:-10,z:-10,rx:0,ry:0,rz:0},{x:-10,y:-10,z:10,rx:0,ry:0,rz:0},{x:10,y:-10,z:10,rx:0,ry:0,rz:0},{x:10,y:-10,z:-10,rx:0,ry:0,rz:0}];var J=i("e153"),Z=i("6397");J(g);var K=function(e){Object(r["a"])(i,e);var 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e=Object(f["a"])(regeneratorRuntime.mark((function e(){var t,i,n,o,a,s,r,l;return regeneratorRuntime.wrap((function(e){while(1)switch(e.prev=e.next){case 0:return this.singleMaterialGroup=Q.initSingleMaterial(),this.twoFaceMaterialGroup=Q.initTwoFaceMaterial(),this.threeFaceMaterialGroup=Q.initThreeFaceMaterial(),e.next=5,this.fbxLoader(b);case 5:return t=e.sent,i=(new g["TextureLoader"]).load(k),t.children[0].material=new g["MeshPhongMaterial"]({map:i}),e.next=10,this.fbxLoader(b);case 10:return n=e.sent,e.next=13,this.fbxLoader(b);case 13:return o=e.sent,e.next=16,this.fbxLoader(b);case 16:for(a=e.sent,this.scene.add(t),s=0;s<Q.oneFacePosArr.length;s++)this.singleModelGroup[s]=n.clone(),this.singleModelGroup[s].children[0].material=new g["MeshPhongMaterial"]({map:this.singleMaterialGroup[s]}),this.singleModelGroup[s].position.set(Q.oneFacePosArr[s].x,Q.oneFacePosArr[s].y,Q.oneFacePosArr[s].z),Q.oneFacePosArr[s].rx=this.singleModelGroup[s].children[0].rotation.x,Q.oneFacePosArr[s].ry=this.singleModelGroup[s].children[0].rotation.y,Q.oneFacePosArr[s].rz=this.singleModelGroup[s].children[0].rotation.z,this.objects.push(this.singleModelGroup[s].children[0]),this.scene.add(this.singleModelGroup[s]);for(r=0;r<Q.twoFacePosArr.length;r++)this.twoFaceModelGroup[r]=o.clone(),this.twoFaceModelGroup[r].children[0].material=new g["MeshPhongMaterial"]({map:this.twoFaceMaterialGroup[r]}),this.twoFaceModelGroup[r].position.set(Q.twoFacePosArr[r].x,Q.twoFacePosArr[r].y,Q.twoFacePosArr[r].z),Q.twoFacePosArr[r].rx=this.twoFaceModelGroup[r].children[0].rotation.x,Q.twoFacePosArr[r].ry=this.twoFaceModelGroup[r].children[0].rotation.y,Q.twoFacePosArr[r].rz=this.twoFaceModelGroup[r].children[0].rotation.z,this.objects.push(this.twoFaceModelGroup[r].children[0]),this.scene.add(this.twoFaceModelGroup[r]);for(l=0;l<Q.threeFacePosArr.length;l++)this.threeFaceModelGroup[l]=a.clone(),this.threeFaceModelGroup[l].children[0].material=new g["MeshPhongMaterial"]({map:this.threeFaceMaterialGroup[l]}),this.threeFaceModelGroup[l].position.set(Q.threeFacePosArr[l].x,Q.threeFacePosArr[l].y,Q.threeFacePosArr[l].z),Q.threeFacePosArr[l].rx=this.threeFaceModelGroup[l].children[0].rotation.x,Q.threeFacePosArr[l].ry=this.threeFaceModelGroup[l].children[0].rotation.y,Q.threeFacePosArr[l].rz=this.threeFaceModelGroup[l].children[0].rotation.z,this.objects.push(this.threeFaceModelGroup[l].children[0]),this.scene.add(this.threeFaceModelGroup[l]);this.dragEvent(),this.targetModel=this.singleModelGroup[0],this.boxDragControl=this.transformControl.initModelDragEvent(this.targetModel),this.scene.add(this.boxDragControl);case 25:case"end":return e.stop()}}),e,this)})));function t(){return e.apply(this,arguments)}return t}()},{key:"dragEvent",value:function(){var e=this;document.body.addEventListener("mousemove",(function(t){t.preventDefault(),e.mouseMoveEvent(t)}),!0),document.body.addEventListener("mousedown",(function(t){e.mouseDownEvent(t)}),!0),document.body.addEventListener("touchstart",(function(t){e.mouseDownEvent(t.touches[0])}),!0),document.body.addEventListener("mouseup",(function(t){e.orbit.enabled=!0}),!0),document.body.addEventListener("touchend",(function(t){e.orbit.enabled=!0}),!0)}},{key:"mouseMoveEvent",value:function(e){this.mouse.set(e.clientX/window.innerWidth*2-1,-e.clientY/window.innerHeight*2+1),this.raycaster.setFromCamera(this.mouse,this.camera);var t=this.raycaster.intersectObjects(this.objects);t.length>0?document.body.style.cursor="pointer":document.body.style.cursor="default"}},{key:"mouseDownEvent",value:function(e){this.mouse.set(e.clientX/window.innerWidth*2-1,-e.clientY/window.innerHeight*2+1),this.raycaster.setFromCamera(this.mouse,this.camera);var t=this.raycaster.intersectObjects(this.objects);if(t.length>0){this.orbit.enabled=!1;var i=t[0],n=this.objects.indexOf(i.object);this.targetModel=n<6?this.singleModelGroup[n]:n<18?this.twoFaceModelGroup[n-6]:this.threeFaceModelGroup[n-18],this.boxDragControl.detach(),this.boxDragControl.attach(i.object),this.boxDragControl.update(),this.boxDragControl.updateMatrixWorld()}}},{key:"changeControlMode",value:function(e){e?this.boxDragControl.setMode("rotate"):this.boxDragControl.setMode("translate"),this.boxDragControl.update(),this.boxDragControl.updateMatrixWorld()}},{key:"resize",value:function(){this.renderer.setSize(window.innerWidth,window.innerHeight);var e=window.innerWidth/window.innerHeight>16/9?window.innerHeight/675:window.innerWidth/1200,t=14*e;this.camera.left=-window.innerWidth/t,this.camera.right=window.innerWidth/t,this.camera.top=window.innerHeight/t,this.camera.bottom=-window.innerHeight/t,this.camera.updateProjectionMatrix()}},{key:"resetCamera",value:function(){this.orbit.object.lookAt(new g["Vector3"](0,0,0)),this.camera.position.set(94,77,197),this.orbit.reset()}},{key:"resetModel",value:function(){for(var e=0;e<Q.oneFacePosArr.length;e++)this.singleModelGroup[e].position.set(Q.oneFacePosArr[e].x,Q.oneFacePosArr[e].y,Q.oneFacePosArr[e].z),this.singleModelGroup[e].children[0].position.set(0,0,0),this.singleModelGroup[e].children[0].rotation.set(Q.oneFacePosArr[e].rx,Q.oneFacePosArr[e].ry,Q.oneFacePosArr[e].rz);for(var t=0;t<Q.twoFacePosArr.length;t++)this.twoFaceModelGroup[t].position.set(Q.twoFacePosArr[t].x,Q.twoFacePosArr[t].y,Q.twoFacePosArr[t].z),this.twoFaceModelGroup[t].children[0].position.set(0,0,0),this.twoFaceModelGroup[t].children[0].rotation.set(Q.twoFacePosArr[t].rx,Q.twoFacePosArr[t].ry,Q.twoFacePosArr[t].rz);for(var i=0;i<Q.threeFacePosArr.length;i++)this.threeFaceModelGroup[i].position.set(Q.threeFacePosArr[i].x,Q.threeFacePosArr[i].y,Q.threeFacePosArr[i].z),this.threeFaceModelGroup[i].children[0].position.set(0,0,0),this.threeFaceModelGroup[i].children[0].rotation.set(Q.threeFacePosArr[i].rx,Q.threeFacePosArr[i].ry,Q.threeFacePosArr[i].rz)}},{key:"modelMerge",value:function(){this.resetModel(),this.targetModel=this.singleModelGroup[0],this.boxDragControl.detach(),this.boxDragControl.attach(this.targetModel),this.boxDragControl.update(),this.boxDragControl.updateMatrixWorld()}},{key:"resetDragControl",value:function(){this.targetModel=this.singleModelGroup[0],this.boxDragControl.setMode("translate"),this.boxDragControl.detach(),this.boxDragControl.attach(this.targetModel),this.boxDragControl.update(),this.boxDragControl.updateMatrixWorld()}},{key:"reset",value:function(){this.resetCamera(),this.orbit.enabled=!0,this.resetModel(),this.resetDragControl(),this.orbit.update()}}],[{key:"preload",value:function(){var e=[b,k];console.log(e.length)}}]),i}(w),ee=function(e){Object(r["a"])(i,e);var t=Object(l["a"])(i);function i(){return Object(s["a"])(this,i),t.call(this)}return Object(u["a"])(i,[{key:"domReady",value:function(){Object(d["a"])(Object(p["a"])(i.prototype),"domReady",this).call(this);var e=document.getElementById("3dContainer").clientWidth,t=document.getElementById("3dContainer").clientHeight;this.model=new K(document.getElementById("3dContainer"),null,e,t)}},{key:"resize",value:function(){Object(d["a"])(Object(p["a"])(i.prototype),"resize",this).call(this),this.model.resize()}},{key:"reset",value:function(){Object(d["a"])(Object(p["a"])(i.prototype),"reset",this).call(this),this.model.reset()}}]),i}(v),te=(i("99af"),i("53ca")),ie=function(e){var t=document.createElement("div");t.classList.add("tooltip-wrapper"),t.setAttribute("ref","tooltipDiv");var i='<div name="pointPanel" ref="pointPanel" tabindex="1" :style="pointStyle" class="tooltip-panel-div" > <div name="ctrlPanelDiv" v-show="showPanel" ref="ctrlPanelDiv" class="tooltip-panel" > \x3c!-- 弹出拖拽条 --\x3e <div name="moveBar" class="move_bar" > <div name="moveBarIcon" :style="moveBarStyle" class="move_ico"></div> </div> <div name="closeToolboxIcon" class="close_ico" ></div> \x3c!-- 控件区域放入下面 --\x3e <slot></slot> </div> </div>';return t.innerHTML=i,t},ne=function e(){Object(s["a"])(this,e)},oe=function(e){Object(r["a"])(i,e);var t=Object(l["a"])(i);function i(){var e;return Object(s["a"])(this,i),e=t.apply(this,arguments),e.panelColor="#FFFFFF",e.barColor="rgba(0,0,0,0.08)",e}return i}(ne),ae=function(e){Object(r["a"])(i,e);var t=Object(l["a"])(i);function i(){var e;return Object(s["a"])(this,i),e=t.apply(this,arguments),e.panelColor="#424157",e.barColor="#6F6E7F",e}return i}(ne),se=function(){function e(t,i){Object(s["a"])(this,e),this.option=new oe,this.hasCloseBtn=!1,this.toolBoxStyle={left:"0px",top:"0px",right:"0px",transitionDuration:"400ms"},this.moveBarStyle={},this.ctrlPanelWidth=0,this.ctrlPanelHeight=0,this.showPanel=!1,this.focustimes=0,this.mousePosition={startX:0,startY:0},this.tooltipPosition={x:0,y:0},this.moveFlag=!1,this.isFouchsPanel=!1,this.zoom=1,this.margin=32,this.offset={x:0,y:0},this.collapse=!1,"string"===typeof i&&(this.theme=i,"dark"===this.theme&&(this.option=new ae)),"object"===Object(te["a"])(i)&&(i.hasCloseBtn&&(this.hasCloseBtn=i.hasCloseBtn),this.option=Object.assign(this.option,i));var n=document.getElementById(t);if(this.appendHtml(n),this.hasCloseBtn?this.$refs.closePanelIcon.style.display="":this.$refs.closePanelIcon.style.display="none",this.changePointBgColor(),this.$refs.ctrlPanelDiv.style.cssText="visibility:hidden",this.option.width&&this.option.height)this.ctrlPanelHeight=this.option.height,this.ctrlPanelWidth=this.option.width;else{var o=this.$refs.ctrlPanelDiv.getBoundingClientRect();this.ctrlPanelHeight=o.height,this.ctrlPanelWidth=o.width}this.setZoom(),this.calcTopLeft(),this.changePosition(),this.$refs.ctrlPanelDiv.style.cssText="display:none",this.openPanel(),this.registerListener()}return Object(u["a"])(e,[{key:"setOffset",value:function(e,t){e&&(this.offset.x=e),t&&(this.offset.y=t)}},{key:"calcTopLeft",value:function(){this.option.left?this.toolBoxStyle.left=this.ctrlPanelWidth*(this.zoom-1)/2+this.option.left+"px":this.toolBoxStyle.right=this.ctrlPanelWidth*(this.zoom-1)/2+this.margin+"px",this.option.top?this.toolBoxStyle.top=this.option.top+this.ctrlPanelHeight*(this.zoom-1)/2+"px":this.toolBoxStyle.top=(document.body.clientHeight-this.ctrlPanelHeight)/2+"px"}},{key:"resetPostion",value:function(){this.setZoom(),this.toolBoxStyle.left="",this.toolBoxStyle.right="",this.toolBoxStyle.top="",this.calcTopLeft(),this.changePosition()}},{key:"changeToolBoxPosition",value:function(e,t){this.toolBoxStyle.left="".concat(e,"px"),this.toolBoxStyle.top="".concat(t,"px"),this.changePosition()}},{key:"changeToolBoxTop",value:function(e){this.toolBoxStyle.top=e+this.ctrlPanelHeight*(this.zoom-1)/2+"px",this.toolBoxStyle.right=this.ctrlPanelWidth*(this.zoom-1)/2+this.margin+"px",this.changePosition()}},{key:"changeToolBoxSize",value:function(e,t){this.ctrlPanelHeight=t,this.ctrlPanelWidth=e,!0!==this.collapse&&this.setPointPanelSize()}},{key:"closePanelWithPoint",value:function(){var e=this;setTimeout((function(){if(e.collapse=!0,e.changePointBgColor(),e.showPanel=!1,e.toggleCtrlPanel(),e.$refs.pointPanel.style.width="20px",e.$refs.pointPanel.style.height="20px",e.binding){var t=e.binding.getToolBoxPostion(),i=e.binding.getTipPostion(),n=e.getOffset(),o=i.left-t.left-n,a=i.top-t.top-n;e.binding.zoom&&(o=(i.left-t.left)/1.3,a=(i.top-t.top)/1.3),e.$refs.pointPanel.style.transition="transition: transform 1s linear 0.1s",e.$refs.pointPanel.style.transform="translate(".concat(o,"px, ").concat(a,"px)")}}),100)}},{key:"hideImmediately",value:function(){this.hide(0)}},{key:"hide",value:function(e){var t=this,i=e;e||(i=1e3),setTimeout((function(){if(t.collapse=!0,t.showPanel=!1,t.changePointBgColor(),t.toggleCtrlPanel(),t.$refs.pointPanel.style.width="0px",t.$refs.pointPanel.style.height="0px",t.$refs.pointPanel.style.minWidth="0px",t.$refs.pointPanel.style.minHeight="0px",t.$refs.pointPanel.style.border="0px",t.binding){var e=t.binding.getToolBoxPostion(),i=t.binding.getTipPostion(),n=t.getOffset(),o=i.left-e.left-n,a=i.top-e.top-n;""===t.$refs.pointPanel.style.transform&&(t.$refs.pointPanel.style.transition="transition: transform 0s linear",t.$refs.pointPanel.style.transform="translate(".concat(o,"px, ").concat(a,"px)"))}}),i)}},{key:"closePanel",value:function(){var e=(new Date).getTime()-this.focustimes;e<301||(this.changePointBgColor(),this.showPanel=!1,this.toggleCtrlPanel())}},{key:"openPanel",value:function(){var e=this;this.$refs.pointPanel.style.display="",this.isFouchsPanel=!0,this.focustimes=(new Date).getTime(),this.showPanel||(this.changePointBgColor(),this.updateMoveIconStyle(),this.hasCloseBtn&&this.setPointPanelSize(),this.$refs.pointPanel.style.transform="",this.$ref$

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表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版
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表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版
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表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版
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表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版
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表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版
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表面涂色的正方体(课件)-2025-2026学年六年级上册数学苏教版
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