Why Part-Part-Whole Comes Before + and −
One picture, four facts
A number bond is not decoration — it is the mental model behind both operations. The diagram of 7 split into 3 and 4 simultaneously says 3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4 and 7 − 4 = 3. Children who internalize this see addition and subtraction as one family instead of two subjects, which is why Singapore-style teaching starts with bonds rather than equations. When you introduce a new target, fill one bond together talking in part-whole language — "the whole is 7, one part is 3, what is the other part?" — before any child writes a plus sign. The blank circle does the asking; the child does the thinking. Keep a finished bond page on the wall for a week and refer back to it: "Remember how 9 splits into 5 and 4? Use that to work out 9 + 4."
Drill the bonds of ten until they snap
Of all targets, the bonds of 10 deserve the most repetitions: they power every crossing-the-ten calculation for years (8 + 5 becomes 8 + 2 + 3). Use the target-10 setting for short daily bursts — eight bonds takes under two minutes — until the answers are automatic. Then move to 20, which is really "bonds of 10 plus a ten" and rewards children who master the first set. Bonds to 100 belong with two-digit work: pairs like 63 + 37 are the exact skill needed for column addition with carrying and for making change with money. The custom field lets you match whatever the class needs this week — 5 for beginners, or 1000 as a stretch.
Missing part first, missing whole as the check
Start every new target in "missing part" mode: the whole is visible at the top, one part given, and the empty circle invites subtraction thinking without ever printing a minus sign. Once fluent, switch to "missing whole" — now the child adds — and use it as your diagnostic: if a child hesitates on 4 + 5 but knew "4 and what makes 9" instantly, the bond knowledge is ahead of the written operation, and that is exactly the right order. Mixed mode on a Friday ties it together. Watch for the child who always writes the target number in the blank regardless of position; that error means they are pattern-matching, not partitioning, so drop back to concrete counters in the circles for a few days.
一张图，四个算式
数与分解图不是装饰——它是加法减法背后共同的心智模型。7 拆成 3 和 4 的那张图，同时说出了 3+4=7、4+3=7、7−3=4、7−4=3 四个算式。把这件事内化了的孩子，会把加减法看成一个家族而不是两门功课——新加坡数学正是从分解图起步，而不是从算式起步。介绍新目标时，先带着孩子一起填一张图，全程用「部分—整体」的语言：「整体是 7，一个部分是 3，另一个部分是几？」在任何加号出现之前就让空圈来提问、让孩子来思考。
把 10 的分解练到「脱口而出」
所有目标里，10 的分解最值得反复练：它支撑着此后多年所有「跨十」的计算（8+5 变成 8+2+3）。用目标 10 做每日短练——八张分解图不到两分钟——直到答案自动化。再进到 20：它本质上就是「10 的分解加一个十」，第一个集合练熟的孩子会在这里得到奖励。100 的分解则和两位数运算配对：63+37 这种凑整，正是竖式进位和找零钱所需要的核心技能。自定义框可以配合本周的教学任意设置——启蒙用 5，拔高可以试试 1000。
先挖部分，再挖整体当检验
每个新目标都从「缺部分」开始：整体亮在顶部，给出一个部分，空圈引导孩子用减法思维——但页面上从头到尾没印过一个减号。熟练之后切到「缺整体」，这时孩子做的是加法，正好当诊断用：如果孩子秒答「4 和几凑成 9」，却在 4+5 上犹豫，说明分解知识跑在了算式前面——这正是正确的顺序。周五用混合模式收个尾。要特别留意那种「不管挖哪里都把目标总数填进空圈」的孩子：这说明他在找规律而不是真的拆分，退回去几天，在圆圈里摆实物小方块。