Fourth Grade · Math · week 13

Partial products on paper

Record multiplication as a written list of partial products, without drawing the area model.

The same multiplication from the last two weeks can be written as a short list instead of a drawing. Multiply the ones, then the tens, then the hundreds, writing each answer on its own line lined up by place value, then add all the lines.

This is a bridge: some students are ready to drop the picture and just write the list; others still want to sketch it first, and both are perfectly fine for now.

📋 For the teacher
Teach it (10–15 min):
  • Show that this written list is the exact same math as the area model, just recorded without the drawing.
  • Keep every partial product lined up by place value so nothing is missed when they get added together.
  • Let the student choose: draw the boxes first if it helps, or go straight to the list if that already feels solid.
  • This written form is the direct bridge to the compact standard algorithm coming in a couple of weeks.
Talk about it:
  • How is writing partial products the same as the area model?
  • Why do we line up the partial products by place value before adding?
  • Which do you prefer right now, the drawing or the list, and why?

Mastery looks like: They write and add partial products correctly for 1-digit by multi-digit multiplication without needing to draw the area model.

Common stumbles: Writing a partial product in the wrong place-value column; forgetting one of the partial products when adding.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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