Twenty-Two Children Who Subtract the Smaller Digit from the Larger
In a Class IV mathematics class in Rayagada district with 31 children, a two-week unit on subtraction up to four digits with regrouping ended with a four-item exit slip. Only 6 children answered all four items correctly. Twenty-two wrote 365 for 503 − 268, and several of these also wrote 24 for 42 − 18. Nine children worked correctly when given bundled sticks but made the same errors without them, and three left the slip blank. Two children are children of migrant labourers and were absent for 11 of the last 20 days; they attended four lessons. The annual examination is six weeks away and the next unit in the textbook is multiplication.
1. Explain what the 365 error shows that the children do and do not understand about place value, and why the word 'borrowing' may contribute to it.
Read the worked answer
503 − 268 = 365 is not random. The child works column by column: 3 − 8 gives 5, 0 − 6 gives 6, and 5 − 2 gives 3. The child has a rule - take the smaller from the larger - and applies it consistently. The 24 for 42 − 18 confirms that it is systematic rather than a slip.
What is missing is the idea that a numeral is a sum of place values and that one ten can be exchanged for ten ones. Without exchange, a column sometimes has no answer among the counting numbers, and the child resolves the impossibility by reversing the subtraction.
What is present: column layout, single-digit subtraction facts, and the written algorithm. This is partial understanding, not ignorance, so reteaching from zero would waste what they have. The 9 children who succeed with sticks but not on paper have the concept but not the bridge to symbols. The 3 blank slips may be a fluency or confidence issue and should be checked orally.
Why 'borrow' misleads: borrowing implies a loan that must be returned, so children expect to give something back. 'Regrouping' or 'exchange' - one ten traded for ten ones with the total unchanged - matches the action with bundles. Odia classrooms often use ଧାର ନେବା with the same difficulty, so the teacher should demonstrate the exchange rather than rely on the word.
2. Design a five-day reteach sequence using only what the school has, and say what you would do about the two children with irregular attendance.
Read the worked answer
Day 1 - material only. 42 − 18 with bundles. Children physically break a ten and say '3 tens and 12 ones'. No symbols yet.
Day 2 - material to record. The teacher writes each step on the board as the children perform it; children copy the record beside their bundles, one line at a time.
Day 3 - the zero. 503 − 268 on a hundreds-tens-ones mat. The zero forces two exchanges; act the whole thing out. Pair work: one child moves the material, the other records.
Day 4 - mixed set. Six items, three with materials allowed and three without; children choose and must justify the choice.
Day 5 - check. Four items in the exit-slip format, plus one oral item: 'explain why 503 becomes 4 hundreds, 9 tens and 13 ones'. Listen to the explanation, not only the answer, and compare against the original slip.
The two irregular attenders: do not build the plan around them. Prepare a 20-minute catch-up card (bundles plus five items) for the volunteer to use on their return, and keep a one-page record so they re-enter at the concept, not at page one.
Sequencing decision: six weeks is enough. Begin multiplication only after the Day 5 check, or run it in parallel for the 6 secure children with peer-tutoring cards.