Area model, partial products or lattice: pick the multiplication method

The homework had a grid of four boxes with 20 and 3 along the top and 10 and 4 down the side. I learned to multiply with carrying and had no idea what I was looking at. My daughter explained it to me, which was the moment I realized the box method is not a detour. It is the distributive property, drawn.

What the sheet looks like

The area model generator prints one of four strategies, or mixes the multiplication ones on a page. Area model (box method) splits each factor by expanded form into a grid with an add-up column at the side. Partial products lists each piece under the problem. Lattice draws the diagonal grid. Area model division does partial quotients, with remainders off or allowed. Skills run from 2-, 3- or 4-digit × 1-digit through 2- or 3-digit × 2-digit, and 3- or 4-digit ÷ 1-digit. The scaffold switch either prints the expanded parts (20 and 3) on the grid or leaves the labels blank. Pages have 4, 6 or 8 problems, fewer for big lattices, with an answer key.

Why it works

• The box method makes place value visible. 23 × 14 becomes 20 × 10, 20 × 4, 3 × 10 and 3 × 4, and a child can see why the answer is bigger than 200.
• Parts given versus blank labels is the whole scaffold in one switch. Start with the parts printed, then take them away when the child starts writing them before you ask.
• Mixing three strategies on one page lets a child compare them on the same numbers and pick the one that makes sense to them. That choice is worth more than being told which to use.

Who it suits

Third graders should start with 2-digit × 1-digit, parts given, four problems. Fourth graders are the main audience for 2-digit × 2-digit with blank labels and for lattice. Area model division with remainders allowed is fifth grade work. If a child does not yet see 3 × 4 as a rectangle of dots, the arrays worksheet is where to start, because the box method is an array with the dots removed.

Print the mixed page once the box method is comfortable. Most kids pick lattice as their favorite and then, a month later, drift back to the boxes.