L2 · Multiplying 3-Digit by 1-Digit: Personal Strategies

Learning goal

“I can multiply a 3-digit number by a 1-digit number with my own strategy - breaking the 3-digit number into hundreds, tens and ones, multiplying each part (partial products), and adding the parts. I can show my strategy with an area model.”

Break apart — to split a number into its place-value parts: 214 splits into 200 + 10 + 4.

Partial product — the product of one part: for 214 x 3, the partial products are 600, 30 and 12.

Area model — a rectangle split into parts; each part's area is a partial product, and the whole area is the answer.

Worked example

214 x 3. Step 1 (break apart): 214 = 200 + 10 + 4. Step 2 (multiply each part by 3): 200 x 3 = 600; 10 x 3 = 30; 4 x 3 = 12. These three answers are the partial products. Step 3 (add the parts): 600 + 30 + 12 = 642. So 214 x 3 = 642. Picture it as an area model: a rectangle 214 long and 3 wide, cut into three strips of length 200, 10 and 4. The strips have areas 600, 30 and 12 - and the whole rectangle's area is their sum. The strategy works because multiplying is allowed to happen part by part: the 3 has to meet EVERY part of 214, not just the front digit.

Check yourself — explain it

Why must the 3 multiply all three parts of 214?

Paired problem — example still visible

132 x 4 -> 100 x 4 = 400; 30 x 4 = 120; 2 x 4 = 8; 400 + 120 + 8 = 528.

Faded completion — last step is yours

"253 x 2: 200 x 2 = 400; 50 x 2 = ___; 3 x 2 = 6; total = ___." -> 100; 506

Ready to practise?

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

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