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應用資訊科技於小學數學科教學

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是次與深水埔街坊福利會小學的協作在四年級開展。學校在四年級有兩班，非華語學生集中於其中一班，而其他學生平均分配在兩班之中。有非華語學生的一班整體學習表現較弱。學生主要來自區內家庭，部份是新移民及少數族裔學生，亦有學生有特別學習需要，學生之間的學習差異頗大。對小四學生來說，因數 （factors）是一個較困難的學習課題，因涉及除法和整除性，令基礎稍遜的學生較難理解，亦對抽象的找因數方法（因式分解法）感到較難掌握。

QSIP支援人員與教師透過是次協作，期望能發展更有效的校本適異教學設計，並將成功經驗擴散至其他年級及科目。

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「拓展選擇」範疇　科本經驗分享 數學科 - 深水埔街坊福利會小學 | 賽馬會「校本多元計劃」

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是次與深水埔街坊福利會小學的協作在四年級開展。學校在四年級有兩班，非華語學生集中於其中一班，而其他學生平均分配在兩班之中。有非華語學生的一班整體學習表現較弱。學生主要來自區內家庭，部份是新移民及少數族裔學生，亦有學生有特別學習需要，學生之間的學習差異頗大。對小四學生來說，因數 ...

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GeoGebra Infographic 2014 (Chinese Traditional)

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對二年級學生來說，從活動的開始時間和結束時間求時間間隔是頗為困難的。坊間的教科書未能清晰地介紹可行的方法處理這類問題。過往老師嘗試引入時間的直式減法來教授如何找出時間間隔（圖一），但在需要退位的情況下，學生往往未能掌握「借1小時等於借60分鐘」，而錯用10進制進行退位減法（圖二）。而且由於二年級學生尚未學習24小時報時制，所以運用直式亦未能處理如圖三般的情況，更不排除有學生會以「大減細」策略得出錯誤的答案（圖三）。

[1] 舊課程稱為「活動時間」

1.資訊科技輔助教學： 運用電子學習課件讓學生在學習的過程中有額外的選擇，以照顧學生不同學習風格及多元智能

事實上，求時間間隔是屬於課程中「度量」範疇的課題。學生可運用時鐘作為量度工具，透過把時針和分針由開始時間撥到結束時間，得出時間間隔。可是學校通常都沒有足夠的教學時鐘，讓每位學生個別操作。有見及此，QSIP支援人員運用免費數學軟件GeoGebra，製作〈量度時間間隔〉電子學習課件（圖四），為學生在學習的過程中提供額外選擇。運用課件的目的是讓學生通過平板電腦，體驗拖拉時鐘的「小時」和「分鐘」滑杆，將時針和分針由開始時間撥至結束時間，由此得出活動的時間。此學習經驗能幫助學生建立基本概念，從而過渡到在沒有電子學習課件的情況下，亦能找出時間間隔的方法。電子學習課件只需用電腦或任何流動裝置的瀏覽器即可在網上開啓，而無需安裝任何電腦軟件或應用程式（apps）。

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「拓展選擇」範疇　科本經驗分享 數學科 - 循道衞理聯合教會亞斯理衛理小學 | 賽馬會「校本多元計劃」

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對二年級學生來說，從活動的開始時間和結束時間求時間間隔是頗為困難的。坊間的教科書未能清晰地介紹可行的方法處理這類問題。過往老師嘗試引入時間的直式減法來教授如何找出時間間隔（圖一），但在需要退位的情況下，學生往往未能掌握「借1小時等於借60分鐘」，而錯用10進制進行退位減法（圖二）。而且由於二年級學生尚未學習24小時報時制，所以運用直式亦未能處理如圖三般的情況，更不排除有學生會以「大減細」策略...

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GeoGebra Institute of Hong Kong (GIHK) is an independent and self-sustaining community of practice formed by a group of teachers, educators and scholars in Hong Kong. It is hosted by the Department of Education Studies, Hong Kong Baptist University. Our goals: To build teachers' capacity for using

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本课程提供起步页面，您可以将其复制并粘贴到课程中。这些页面旨在帮助您为学生创建有关分数的题目。 如果要复制页面，请先打开想要复制的页面，再按 cmd + c（在 Mac 上）或 ctrl + c（在 Chromebook 或 Windows 上）。然后，按 cmd + v（在 Mac 上）或 ctrl + v（在 Chromebook 或 Window s上），将页面粘贴到您的课程中。 由 Desmos 翻译团队制作。

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01 乘數表：測驗 | Quiz on Multiplication Table 02 四則計算：測驗 | Quiz on Four Basic Operations 03 分數和百分數 | Fractions & Percentages 04 所佔百分數 | Percentage (Part-Whole) 05 四邊形的分類 | Types of Quadrilaterals 06 繪畫四邊形：測驗 | Quiz on Drawing Quadrilaterals 07 平行四邊形的面積 | Area of Parallelograms 08 三角形的面積 | Area of

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gMath - 小學數學老師學習社群

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目的： 在專家導師支援下，進行跨校老師的專業發展活動，凝聚專業學習社群，並提升教師運用GeoGebra製作互動數學科課件的能力及藉此提升學生的學習成效。 目標： 1 學生方面 1.1 提升學生對數學的興趣 1.2 加深學生對數學概念的理解 2 教師方面 2.1 提升教師對以GeoGebra製作互動課件的能力 2.2 提升教師在數學課堂運用電子學習的能力 2.3 建立一個屯門區小學數學老師專業學習社群 2.4 建立存放GeoGebra課件的教學資源庫

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Unleash your creativity with the world's best virtual manipulatives!

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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https://cn.mathigon.org/about#principles

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What's New on Polypad

August

Support for 3D geometry: add some built-in solids to the canvas, or create custom nets using polygon tiles. Polyhedra can be rotated

Many different chart tiles (row, column, line, area, pie, donut or box plot): you can data from any table to a chart, modify individual series by double-clicking, and choose from many different display options (e.g. stacked or grouped).

New Clock components

Improved graphic precision, and support for implicit multiplication in equation editor.

High contrast mode for projecting Polypad in the classroom (enable in settings popup).

July

Significantly updated "File" menu: organise saved Polypads into folders, more granular sharing settings (public, students/teachers, private), examples and assignments appear as a special folder, and we moved the share and changelog panels.

Re-organised "Tiles" sidebar with improved grouping of tile types.

Buttons to change the denominator of fraction bars (expand and reduce), including support for denominators up to 1/24.

New "Number Dot Arrangement" component.

New number tables (addition, multiplication and integers) and number frame components.

Remember the weight of balance scale tiles when you save a Polypad. Fix support for algebra tiles on the balance scale: you can now change the value of "x" and even solve quadratic equations.

New algebra tiles for y, y² and xy, including support on balance scales.

New advanced options to lock the position of a tile (but allow selecting/copying/etc) and to make a tile invisible.

Improved change handling with the colour picker (create a single "undo" state when moving a slider or typing in the RGB fields).

Updated number card colours, and action to "negate" their value.

June

Polyhedral Dice.

Stack, shuffle and draw playing cards, standard deck template in sidebar.

New "join" action to merge multiple polygons. Improved "cut" algorithm for polygons.

Double-click dice, coins and spinners to randomise, and playing cards to draw a card.

Tutorial Pages for every tile type.

Improved numberline resizing and snapping, and flip actions for ruler and protractor.

Significant performance improvements.

Improved graph plotting with implicit functions.

Hide Exploding Dots labels when the "hide number labels" option is selected.

Pride Month background.

May

Transparency support in colour picker.

Drag to select ranges of cells in tables, and copy/delete them.

New Domino tiles under Probability.

Irregular pentagons under Geometry.

Handle to partially highlight fraction bars.

Function plotting: create a coordinate system and an equation editor component. Next, drag the blue triangle on the right side of the equation editor onto the coordinate system. You can plot any expression with one variable, an equation of the form y = f(x), an implicit function containing x and y, as well as polar functions of the form r = f(θ).

Buttons to quickly change the axes scales of coordinate systems.

Decimal and percentage labels for fraction bars and fraction circles. You can switch between the different display modes in the settings panel on the right.

Direct number inputs for the RGB values in the colour picker.

New table component in the Tools section of the sidebar.

Layering and locking for tiles: enable Advanced Options in the settings panel on the right. Then you can use the new options in the toolbar to force tiles to stay in the foreground or background, or lock tiles. To revert locking, click Unlock All Tiles in the settings panel.

Increased limit of saved Polypad canvases per account from 100 to 250.

Equation editor improvements.

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ARROWS: move the currently selected tiles up, down, left or right (hold SHIFT to reduce the shift size, for more precise moving)

R: rotate the currently selected tile by 15° (hold SHIFT to rotate by -15°)

S, D, F: move the focus to the sidebar on the left, toolbar at the bottom or canvas area respectively

ESC: clear the current selection and close any open popups and modals

TAB: cycle through all buttons on the page and tiles on the canvas (hold SHIFT to reverse direction)

SHIFT + S: save the current canvas (if you are signed into a Mathigon account)

Use CTRL/CMD + X/C/V to cut, copy or paste tiles. You can even copy and paste tiles from one canvas onto another!

Points and tiles will automatically snap to nearby shapes or gridlines as you move them. You can disable this behaviour by pressing the SHIFT key while moving an item with your mouse or trackpad.

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You can embed a Polypad canvas on other websites like Wordpress: just select the features required below, and then copy the code block into the HTML of your website. We provide this service only for non-commercial, educational purposes. If you want to use Polypad commercially, please contact us.

What's New on Polypad

August

Support for 3D geometry: add some built-in solids to the canvas, or create custom nets using polygon tiles. Polyhedra can be rotated

Many different chart tiles (row, column, line, area, pie, donut or box plot): you can data from any table to a chart, modify individual series by double-clicking, and choose from many different display options (e.g. stacked or grouped).

New Clock components

Improved graphic precision, and support for implicit multiplication in equation editor.

High contrast mode for projecting Polypad in the classroom (enable in settings popup).

July

Significantly updated "File" menu: organise saved Polypads into folders, more granular sharing settings (public, students/teachers, private), examples and assignments appear as a special folder, and we moved the share and changelog panels.

Re-organised "Tiles" sidebar with improved grouping of tile types.

Buttons to change the denominator of fraction bars (expand and reduce), including support for denominators up to 1/24.

New "Number Dot Arrangement" component.

New number tables (addition, multiplication and integers) and number frame components.

Remember the weight of balance scale tiles when you save a Polypad. Fix support for algebra tiles on the balance scale: you can now change the value of "x" and even solve quadratic equations.

New algebra tiles for y, y² and xy, including support on balance scales.

New advanced options to lock the position of a tile (but allow selecting/copying/etc) and to make a tile invisible.

Improved change handling with the colour picker (create a single "undo" state when moving a slider or typing in the RGB fields).

Updated number card colours, and action to "negate" their value.

June

Polyhedral Dice.

Stack, shuffle and draw playing cards, standard deck template in sidebar.

New "join" action to merge multiple polygons. Improved "cut" algorithm for polygons.

Double-click dice, coins and spinners to randomise, and playing cards to draw a card.

Tutorial Pages for every tile type.

Improved numberline resizing and snapping, and flip actions for ruler and protractor.

Significant performance improvements.

Improved graph plotting with implicit functions.

Hide Exploding Dots labels when the "hide number labels" option is selected.

Pride Month background.

May

Transparency support in colour picker.

Drag to select ranges of cells in tables, and copy/delete them.

New Domino tiles under Probability.

Irregular pentagons under Geometry.

Handle to partially highlight fraction bars.

Function plotting: create a coordinate system and an equation editor component. Next, drag the blue triangle on the right side of the equation editor onto the coordinate system. You can plot any expression with one variable, an equation of the form y = f(x), an implicit function containing x and y, as well as polar functions of the form r = f(θ).

Buttons to quickly change the axes scales of coordinate systems.

Decimal and percentage labels for fraction bars and fraction circles. You can switch between the different display modes in the settings panel on the right.

Direct number inputs for the RGB values in the colour picker.

New table component in the Tools section of the sidebar.

Layering and locking for tiles: enable Advanced Options in the settings panel on the right. Then you can use the new options in the toolbar to force tiles to stay in the foreground or background, or lock tiles. To revert locking, click Unlock All Tiles in the settings panel.

Increased limit of saved Polypad canvases per account from 100 to 250.

Equation editor improvements.

Keyboard Shortcuts and Accessibility

These are the keyboard shortcuts supported by Polypad for accessibility:

SHIFT: hold while you click on multiple tiles to select all of them at once

ALT: hold before clicking and dragging on a tile to move a copy

BACKSPACE: delete your current selection

C: duplicate your current selection

CTRL/CMD + X/Y: undo or redo your last change

ARROWS: move the currently selected tiles up, down, left or right (hold SHIFT to reduce the shift size, for more precise moving)

R: rotate the currently selected tile by 15° (hold SHIFT to rotate by -15°)

S, D, F: move the focus to the sidebar on the left, toolbar at the bottom or canvas area respectively

ESC: clear the current selection and close any open popups and modals

TAB: cycle through all buttons on the page and tiles on the canvas (hold SHIFT to reverse direction)

SHIFT + S: save the current canvas (if you are signed into a Mathigon account)

Use CTRL/CMD + X/C/V to cut, copy or paste tiles. You can even copy and paste tiles from one canvas onto another!

Points and tiles will automatically snap to nearby shapes or gridlines as you move them. You can disable this behaviour by pressing the SHIFT key while moving an item with your mouse or trackpad.

You can learn more about our commitment to accessibility, as well as a WCAG checklist, at mathigon.org/accessibility
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昨天的課堂上，花了20分鐘用牛頭王的卡牌讓孩子玩淑萍老師分享的「 質數心臟病」，
孩子們玩得超開心，但偶有一些脫序行為惹我生氣（拍不到牌卻故意大力打別人手的）。
是一個簡單易行又有趣有效的活動。

淑萍老師所設計的質數心臟病，

課堂後半段解釋 「花現質因數」的填數方式，
讓孩子熟悉因數的拆解方式。

今天的課程主要是質因數拆解，
未使用短除法，但隱含了短除法的意義。
規定了特定數字的填色，
簡單示範了幾個數字的填色結果後，
就讓各組領取空白百數表及蠟筆，讓孩子們著色。
（因為自己試塗時也花了不少時間，
所以我請孩子不要塗太醜，
但也不要塗得太漂亮，以免整節課花在著色上。）

過程中有些人聽從我的提醒，先取某數的倍數一併著色。
例如先把所有偶數填上「2」的顏色，
把所有個位數字為「0」或「5」的數字填上「5」的顏色。
這樣做的孩子比較能夠有效率的完成著色。
有些人則隨便挑選一個數字，開始做短除法或是「開花（參考 花現質因數）」，
來拆解其數的因數，這方法比較慢，但也讓後段的孩子能夠熟練數字的拆解策略。
而我在個別指導孩子的過程中，
更發現了我填色時的思路居然與我在二年級教導根式化簡時一模一樣，
讓我更加的喜歡這張簡單的學習單。
即使一節課完成不了著色任務
（剩餘未完成的部分則讓孩子回家或利用下課時間完成），
但這一節課的時間我覺得花得很值得。

下一堂課即將連結到「標準分解式」，
並重新強調各數字的組成色塊及其因倍數的關係。

這學習單 用起來 很有引導學生「發散」思考的作用
和我11/25將要參加的研習"SF16"好像有些相同的養分。很有「設計思考」的一份教學資料,讓學生對質數更熟悉,對質因數分解更有感。

我提醒自己不能給太多教導 只要引導
要記得鼓勵學生「任何想法都是好想法」...

(感謝 蔡慶鴻老師的分享)
(也感謝 向陽跑者 分享的PPT檔/圖檔)

活動照片：

運用此網站的其中一個教學範例，18與40的最小公倍數：
https://twitter.com/davidporas/status/1339547428337446915

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[教學活動]質因數填色（搭配單元：一上 因倍數）

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昨天的課堂上，花了20分鐘用牛頭王的卡牌讓孩子玩淑萍老師分享的「 質數心臟病」， 孩子們玩得超開心，但偶有一些脫序行為惹我生氣（拍不到牌卻故意大力打別人手的）。 是一個簡單易行又有趣有效的活動。 淑萍老師所設計的質數心臟病， 課堂後半段解釋 「花現質因數」的填數方式， 讓孩子熟悉因數的拆解方式。 今天的課程主要是質因數拆解， 未使用短除法，但隱含了短除法的意義。 規定了特定數字的填色， 簡單示範了幾個數字的填色結果後， 就讓各組領取空白百數表及蠟筆，讓孩子們著色。 （因為自己試塗時也花了不少時間， 所以我請孩子不要塗太醜， 但也不要塗得太漂亮，以免整節課花在著色上。） 過程中有些人聽從我的提醒，先取某數的倍數一併著色。 例如先把所有偶數填上「2」的顏色， 把所有個位數字為「0」或「5」的數字填上「5」的顏色。 這樣做的孩子比較能夠有效率的完成著色。 有些人則隨便挑選一個數字，開始做短除法或是「開花（參考 花現質因數）」， 來拆解其數的因數，這方法比較慢，但也讓後段的孩子能夠熟練數字的拆解策略。 而我在個別指導孩子的過程中， 更發現了我填色時的思路居然與我在二年級教導根式化簡時一模一樣， 讓我更加的喜歡這張簡單的學習單。 即使一節課完成不了著色任務 （剩餘未完成的部分則讓孩子回家或利用下課時間完成）， 但這一節課的時間我覺得花得很值得。 下一堂課即將連結到「標準分解式」， 並重新強調各數字的組成色塊及其因倍數的關係。 這學習單 用起來 很有引導學生「發散」思考的作用 和我11/25將要參加的研習"SF16"好像有些相同的養分。很有「設計思考」的一份教學資料,讓學生對質數更熟悉,對質因數分解更有感。 我提醒自己不能給太多教導 只要引導 要記得鼓勵學生「任何想法都是好想法」... (感謝 蔡慶鴻老師的分享) (也感謝 向陽跑者 分享的PPT檔/圖檔) 活動照片： 運用此網站的其中一個教學範例，18與40的最小公倍數：https://twitter.com/davidporas/status/1339547428337446915

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Stretch virtual bands around pegs to form line segments and polygons.

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Solve problems and explain your thinking in a digital math workspace.

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Explore time, fractions, and more on virtual clocks with geared or free-moving hands.

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Explore over 300 resources through which elementary school students can learn math concepts in a fun and interactive way!

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五上_分數乘法(教師版)

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五上_分數乘法(教師版)

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五下_分數除法( 教師版)

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五下_分數除法( 教師版)

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Arthur LeeEdited with love by HKU MathsMobileTabletLaptop

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https://www.gmath.hk/primary