Math · 數學
Math You Can See 看得見的數學
Why do we count in tens? Why can't you add the bottoms of two fractions? Each lesson takes one “why” and answers it with a model you can play with. No timers, no long pages of drills.
為什麼我們十個一數?分數相加為什麼不能分母加分母?每一課只挑一個「為什麼」,用一個可以動手玩的模型來回答。不計時,也沒有一長串的計算題。
Your textbook already teaches the steps and gives you practice. This series does the one thing a book cannot do: it lets you move the pieces yourself and watch why the steps work. Every lesson has one model, a short English reading with Chinese a tap away, and a small game or two that only counts how many you got right on the first try. Nothing is timed, and there is no leaderboard.
課本和習作已經教了步驟、也給了練習。這個系列只做課本做不到的一件事:讓你自己動手移動那些東西,看見步驟為什麼行得通。每一課有一個模型、一篇英文短文(中文翻譯隨點隨看),再加一兩個小遊戲——只記你第一次就答對幾題,不計時,也沒有排行榜。
Every lesson also has a card called “How do you say it in English?” The hardest part of math in English is often not the vocabulary but the reading aloud: 305 is “three hundred five,” and 10² is “ten squared.” Each line on the card has a speaker button, so teachers can take it straight into a bilingual classroom. The series runs from the middle grades of elementary school to the end of junior high. Facts and readings are checked against the sources listed at the bottom of each lesson, and the numbers in every model are computed and tested.
每一課還有一張「這個用英文怎麼唸」卡。用英文上數學,最難的常常不是單字,而是唸法:305 唸 three hundred five,10² 唸 ten squared。卡片上每一列都有 🔊,老師可以直接帶進雙語教室。整個系列從國小中年級到國中三年級為止。每一課的事實與唸法都依頁尾列出的資料查證過,模型裡的數字都是自己算的,並有自動測試。
4 of 26 lessons are ready so far; more are on the way.
目前完成 4 課(共規劃 26 課),持續增加中。
Unit 1 · 單元一
Numbers 數
How we write numbers, what the four operations really mean, why fractions and negative numbers follow the rules they do, and what makes a number prime.
數是怎麼寫出來的、乘法和除法到底是什麼意思、分數和負數的規則從哪裡來,以及質數是什麼。
Why Do We Count in Tens?
為什麼我們十個一數?Add one cube at a time and watch ten small cubes snap into a rod, ten rods into a flat, and ten flats into a big cube. Then change the rule to five or two, and see that a 0 is there to hold a place.一次加一個小方塊,看十個小方塊「喀」一聲併成一根長條、十根長條併成一片平板、十片平板併成一個大方塊。再把規則改成滿五個、滿二個就換,並看看 0 為什麼是在「佔位子」。Start the lesson · 開始上課 →Why Is 3 × 4 the Same as 4 × 3?
乘法為什麼可以交換?Set cubes on a tray in 3 rows of 4, count across, count down, and then turn the whole tray. Nothing is added and nothing is taken away, so 3 × 4 and 4 × 3 must be the same. Then fold a multiplication table in half and see how much less there is to learn.在盤子上把小方塊排成 3 排、每排 4 個,橫著數、直著數,再把整盤轉九十度。沒有多、也沒有少,所以 3 × 4 和 4 × 3 一定一樣。接著把乘法表對摺,看看要記的少了多少。Start the lesson · 開始上課 →What Does Division Really Mean?
除法到底是什麼意思?Share candies equally among friends, or pack them into bags of the same size. Two different questions, one division sign. Watch what is left over, and see why it is always smaller than the number you divide by.把糖平分給朋友,或是每幾顆裝成一袋。兩種不一樣的問題,用的是同一個除號。看看最後剩下了什麼,以及為什麼剩下的一定比除數小。Start the lesson · 開始上課 →Why Can't You Just Add the Bottoms?
分數相加,為什麼不能分母加分母?One half plus one third is not two fifths, and you can see why: two fifths is smaller than one half. Cut two strips into pieces of the same size, and the answer counts itself.二分之一加三分之一不是五分之二,而且一看就知道為什麼:五分之二比二分之一還小。把兩條切成一樣大的塊,答案自己就數出來了。Start the lesson · 開始上課 →Why Does a Negative Times a Negative Make a Positive?
負負為什麼得正?What Makes a Number Prime?
質數是什麼?Unit 2 · 單元二
Ratios and Measures 比與量
Two amounts that grow and shrink together, what “percent” really says, where pi comes from, and a number whose decimals never end.
兩個量一起放大、一起縮小;百分之幾到底在說什麼;圓周率從哪裡來;還有一個小數永遠寫不完的數。
What Is a Ratio?
比是什麼?What Does “Percent” Really Mean?
百分之幾到底是什麼意思?Where Does Pi Come From?
圓周率是怎麼來的?What Number Times Itself Makes 2?
哪個數自己乘自己等於 2?Unit 3 · 單元三
Shapes and Space 形狀與空間
Tear off the corners of a triangle, cut and move shapes to find their areas, pour water to see the Pythagorean theorem, and fold a box flat.
把三角形的角撕下來拼一拼、把圖形剪開搬一搬來算面積、用倒水看畢氏定理,再把一個盒子攤平。
Why Do a Triangle's Angles Add Up to 180°?
三角形的內角和為什麼是 180 度?Why Is a Triangle's Area Half of Base Times Height?
三角形的面積為什麼要除以二?What Does the Pythagorean Theorem Say?
畢氏定理在說什麼?How Much Does a Shape Hold?
一個立體裝得下多少?Unit 4 · 單元四
Algebra and Graphs 代數與圖形
A number you do not know yet, patterns you can put into a sentence, equations you can draw, and the curve a thrown ball makes.
一個還不知道的數、可以用一個式子說出來的規律、可以畫出來的式子,以及球丟出去畫出的那條曲線。
What Is x?
x 是什麼?What Comes Next?
下一個是什麼?How Do You Draw an Equation?
式子怎麼畫成圖?Why Does a Thrown Ball Make That Curve?
丟出去的球為什麼畫出那條曲線?Unit 5 · 單元五
Data and Chance 資料與機會
Three kinds of average, graphs that mislead, what happens when you flip a coin a thousand times, and how to count every possibility.
三種「平均」、會誤導人的圖表、硬幣丟一千次會怎樣,以及怎麼把所有的可能一個不漏地數出來。
Which Average Tells the Truth?
哪一種「平均」才說實話?How Can a Graph Fool You?
圖表怎麼騙人?What Are the Chances?
機會有多大?How Many Ways Are There?
一共有幾種可能?Unit 6 · 單元六
The Story and Use of Math 數學的故事與用處
Where our numerals came from, how to write numbers that are very big or very small, the math in a honeycomb, and what to do when you are stuck.
我們用的數字從哪裡來、很大和很小的數怎麼寫、蜂巢裡的數學,以及題目不會的時候怎麼辦。