Trading Post — Ungrouping for Subtraction

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Teacher's Guide: Trading Post

Trading Post is an ungrouping game for vertical subtraction. Every problem is set up the way students write it on paper — digits stacked in place-value columns, a minus sign on the left, a line above the answer — and above each column sit the actual base-ten blocks that digit stands for. When a column does not have enough to subtract, the student drags a block one place to the right and watches it shatter into ten of the next smaller unit, then writes the crossed-out notation themselves. Six levels run from two-digit problems with a single trade, through the hard case of trading across a zero, up to ten-digit problems in the billions using place-value discs. A round is five problems and takes four to six minutes.

What Students Practice

Deciding whether a column has enough to subtract before they start taking away
Trading one unit for ten of the next smaller unit, and seeing that the total never changes
Writing the crossed-out regrouping notation that goes with the trade — one less on the left, ten more on the right
Trading across a zero, where the first trade has to come from two places over
Subtracting inside a single column once the trade is done, then reading the leftover blocks as the answer digit
Carrying the exact same procedure from two digits up to ten, so place value scales instead of restarting

Standards Alignment

CCSS.MATH.1.NBT.C.6 — Subtract multiples of 10, using concrete models and place value
CCSS.MATH.2.NBT.B.7 — Add and subtract within 1000 using concrete models, relating the model to the written method
CCSS.MATH.2.NBT.B.9 — Explain why addition and subtraction strategies work, using place value
CCSS.MATH.3.NBT.A.2 — Fluently subtract within 1000 using strategies based on place value
CCSS.MATH.4.NBT.B.4 — Fluently subtract multi-digit whole numbers using the standard algorithm

Classroom Tips

Run Level 1 on the board with the whole class first — the first problem coaches every step, so it doubles as the mini-lesson
Insist on the language of trading rather than borrowing: nothing is being borrowed and nothing gets paid back, one ten is being exchanged for ten ones
Level 3 (Across the Zeros) is where most students break down — give it its own day, and have them predict where the first trade must come from before they touch anything
Ask "did the number get bigger or smaller when you traded?" after a break animation; students who say bigger have not yet seen that the value is conserved
Once the written notation is automatic, jump a student to Level 5 or 6 — the discs prove the procedure did not change, only the labels did
The fifth problem of every level is a word problem written across the page, so students get practice setting a horizontal sentence up in vertical columns

How long does one session take?

Each level is five problems. Levels 1 through 3 run about four minutes; the ten-digit problems on Level 6 take closer to six because there is more to write. Four correct out of five unlocks the next level. Progress dots along the top show how far a student has gotten, and unlocked levels are saved in the browser.

What grade range is this for?

Levels 1 and 2 target Grade 2, where regrouping in subtraction is first taught. Level 3 suits late Grade 2 and Grade 3. Levels 4 through 6 fit Grade 4 and up, where the standard algorithm is extended to multi-digit numbers. Older students who still miscount trades can start at Level 1 without it feeling babyish, because the blocks give way to place-value discs as the numbers grow.

Do students have to drag, or can they just write the answer?

Both work. A student can drag a block one place right to trade, or click the digit itself and write the new value in the box that opens — the blocks break either way. Taking away is optional: drag the red blocks onto the blue ones to destroy them one pair at a time, or skip straight to typing the answer digit under the line. Every drag also works as tap-then-tap for students who find dragging hard.

Why does the game refuse an answer digit that looks right?

Answers are checked against the true final digit, not against what the column happens to hold at that moment. If a student writes the tens digit of 52 − 27 as 3 before trading, it is rejected, because that column is going to lose a ten. The hint names the reason instead of the answer. This is deliberate — working left to right without accounting for the coming trade is the single most common subtraction error, and the game will not let it pass.