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Tuesday, October 1, 2013

Teaching 2-Digit by 2-Digit Multiplication

Common Core State Standard 4.NBT.B.5 asks fourth graders to "multiply two two-digit numbers, using strategies based on place value and the properties of operations..." How can this be achieved?

Once your students understand the distributive property and can apply it to multiplication of multiple-digit numbers by single-digit numbers, there's no holding them back! (See my September 14th blog post to learn more about the distributive property and multiplication.)

The graphic below illustrates how to break two-digit multiplication into manageable chunks:
  1. Show students how the bottom number in the problem can be decomposed into tens and ones. For example, in the problem below, 43 x 28 = 43 x (20 + 8). Using the distributive property, we also know that this equals (43 x 20) + (43 x 8).
  2. Explain that we reverse the ones and tens because that's how we'll do it in the shortcut (AKA algorithm).
  3. Let the students know that we are using these same steps in the algorithm, but we're simply stacking them to make our lives simpler and easier.
  4. Demonstrate using the same problem. Kids will do much, much better if they're given a small square to cover one digit so they can focus on one part of the problem at a time. (I sometimes use centimeter cubes as well.)
  5. Practice, practice, practice! First, demonstrate; second, do problems together; third, support them while they work the problems independently; fourth, send them on their merry way! It's just like riding a bicycle!

Using graph paper for newbies to long multiplication is essential. You can download graph paper for free at Just click on square then choose the size you want. (I usually choose one centimeter.) Super Teacher Worksheets also offers a cute (free!) doggie themed problem set on graph paper

Long multiplication? It's a breeze! Let's get started!