Multi-Digit Multiplication

Teaching multiplication using the standard algorithm seems so easy…in theory.  In reality, it is a skill that students can take a long time to grasp and be able to execute flawlessly.  There are many common errors that kids can make, and misconceptions that can cause students to struggle with how to complete the problem accurately.

Common Problems

Some of the common problems and misconceptions students run into when learning to multiply using the standard algorithm:

  • Multiplying only in columns as if adding/subtracting
  • Forgetting to place the zeros in the partial products of the tens and hundreds place.
  • Lack of multiplication and addition fact fluency
  • Only multiplying the top number by the ones place below
  • Writing partial products in a sloppy way, causing difficulty figuring out which digits should  be added.

Foundational Skills

Some of these errors can be prevented by ensuring that your students have the foundational skills necessary to complete the steps of the problem and understand the concepts associated with multiplication.  Students need:

Building Blocks

Using area models as seen in the anchor chart here can help students break multiplication problems into easy-to-handle chunks and help the students associate the partial product in the area model to the partial products when solving the standard algorithm.

Originally, I did not love the way the area model seemed “upside-down” when looking at the multiplier on the side, since you put the digit in the ones place in the top row and work your way down from there, but once you are showing students how the partial products relate to the standard algorithm, and can draw arrows simply straight across, it really makes a lot of sense.



I also like to use color to help students keep track of the place value position they are working with as in this anchor chart.  It helps the students see that they do need to multiply by each digit in the multiplier, and helps them keep track of their place when regrouping and going from digit to digit.


Give it Time

Ultimately, teaching multiplication with the standard algorithm is not a one or two day lesson. I know it seems easy to us, but for students, there is a lot involved, and it takes them time to apply all of the concepts needed to be able to execute the skill with fluency.


Happy teaching!


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