Division with Decimals

For ages 10–11: divide decimals to hundredths by whole numbers using written division, continuing past the decimal point. The central insight is that the quotient's decimal point sits directly above the dividend's point (structural, not guessed), and that continuing past the point is the SAME regrouping used in whole-number division — each leftover is exchanged into ten of the next-smaller place. Worked anchor: 14.76 ÷ 4 = 3.69; and annexing zeros (13 → 13.00 ÷ 4 = 3.25) lets division continue when a remainder is left after the dividend's last digit (a place where the divisor doesn't fit instead gets a 0 in the quotient). Context problems (sharing £18.60 among 5 = £3.72) motivate decimal quotients and connect to money and measures.

• Misplacing or omitting the decimal point in the quotient (getting 369 or 36.9 for 14.76÷4).
• Stopping at a remainder instead of continuing past the point or annexing a zero (13÷4 = 3 r1 left unfinished rather than 3.25).
• Treating the tenths/hundredths digits as separate whole-number divisions without carrying the remainder down.
• Writing the remainder as a whole number when the context calls for a decimal (money answer given as '3 remainder 2').
• Losing place-value alignment so digits drift into the wrong column.

• Short/long division layout (bus stop) with the quotient's decimal point drawn directly above the dividend's point before dividing.
• Place-value regrouping picture: a leftover one 'exchanged' into ten tenths, a leftover tenth into ten hundredths, mirroring the carry.
• Money/measure context model (£18.60 shared into 5 equal parts) that names the tenths and hundredths as 10p and 1p.
• Annexing-zeros illustration: 13 = 13.00 shown as equivalent, enabling the division to continue to 3.25.

• Teach the decimal point in the quotient as ALIGNED with the point in the dividend — place it first, then divide place by place — so the point's position is structural, not an afterthought.
• Show that continuing past the point is the SAME process as whole-number division: the remainder is regrouped into the next-smaller place (tenths, then hundredths), which children already know from long division of whole numbers (mt_WsM4EmdOLe).
• Use annexing zeros deliberately: when there is a remainder at the last given place, adding a zero (13 ÷ 4 → 13.00 ÷ 4 = 3.25) lets division continue — grounded in equivalence, not a trick.
• Anchor in context and estimation: sharing money/measures makes decimal quotients meaningful, and an estimate (14.76÷4 ≈ 15÷4 ≈ 3.7) sanity-checks the point placement.
• Connect to ×÷ by powers of ten and place value (mt_wPgpMJ0-PA): dividing regroups a unit into ten of the next-smaller unit, exactly the place-value structure underpinning the method.