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Securing the times tables, division with remainder

In grade 3 the times tables have to stick. Division is then just the times tables backwards.

What is happening here?

All the times tables get automated in grade 3, and with them their reverse: a child who knows 7 × 8 = 56 also knows 56 ÷ 8 = 7. For "47 ÷ 8" the question is how often 8 fits in. It fits 5 times (40), and 7 are left over. That is division with remainder.

Problems with tens build on the times tables too: 6 × 40 is 6 × 4 and a zero. So every gap in the times tables resurfaces later in written multiplication.

What helps at home

Practice in short, mixed bursts: five minutes a day, single facts from across all the tables. The child marks the hard ones (usually 6 × 7, 6 × 8, 7 × 8, 7 × 9); those come up more often.

For division with remainder one question helps: "Which fact from the 8s table comes closest without going over?" That is the key fact, and the remainder is the difference. Act it out with marbles or coins: share 23 among 4 children, what is left?

What can go wrong

A remainder as big as the divisor or bigger is a warning sign: in 47 ÷ 8 = 4 R 15 the 8 still fits once more. The remainder must always be smaller than the divisor.

Mistakes also happen when reciting a table, because the child only knows it from the start. Practice the tables backwards and from the middle too. And point out that remainder problems turn up in daily life: with 25 guests at tables for 4, how many seats are left over?

Matching task explanations

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