L1 · Multiplying by a 2-digit number: strategies

Learning goal

“I can multiply two 2-digit numbers by splitting them into parts on an area model - and I can explain where every part of the answer comes from.”

Factor — a number being multiplied. In 26 x 14, the factors are 26 and 14.

Product — the answer to a multiplication. The product of 26 x 14 is 364.

Partial product — the product of one part of a split factor. 26 x 10 = 260 is a partial product of 26 x 14.

Area model — a rectangle whose side lengths are the factors; splitting the sides splits the rectangle into partial-product sections.

Worked example

Compute 26 x 14. Step 1: Split 14 into 10 + 4. Now there are two easier multiplications. Step 2: 26 x 10 = 260. (Multiplying by 10: every part of 26 shifts one place.) Step 3: 26 x 4 = 104. Step 4: Add the partial products: 260 + 104 = 364. Say it plainly: 26 x 14 means 26 groups of 14 - that is 26 groups of 10 plus 26 groups of 4. Nothing is lost by splitting; we just pay in two smaller bills.

Check yourself — explain it

Why are we allowed to split 14 into 10 + 4?

Paired problem — example still visible

Compute 32 x 13 by splitting 13. -> 32 x 10 = 320; 32 x 3 = 96; 320 + 96 = 416.

Faded completion — last step is yours

"21 x 15: 21 x 10 = 210; 21 x 5 = 105; total = ___" -> 315

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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