Double Digit Multiplication Strategies

After students have mastered their single digit multiplication it is time for them to move on to double digit by single digit then to double digit by double digit which is what we are going to be exploring today. If students do not have their 1-9 tables memorized or are able to read a multiplication chart to help them. Then more time needs to be spent on that before moving on. However, if they are ready then there are plenty of double digit multiplication strategies that will help them pick it up faster.

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Double digit Multiplication Strategies #1 Break the Number Up

The number one strategy that will probably help students the most is to break up the number. There are several ways to do this, but all of them will help students in different ways. Overall, it is important to have a lot of double digit multiplication strategies because one student may understand one better whereas another will understand it better another way. Two versions of splitting up the number are the distributive property and area models.

Distributive Property

One of the major double digit multiplication strategies is using the distributive property. This is an act of breaking a number into smaller parts to multiply it. For instance, if we have 12 times 15. We could break it up as 15(10+2)=150+30=180. We could also set up a double distributive property which would be (10+5)(10+2)= 10×10+10×2+ 5×10+ 5×2= 100+20+50+10=180. Either of these ways of breaking it up are helpful, and they are also teaching students algebraic concepts, which are important for math later down the line.

Area Models

Another method of breaking up the number is to create area models. These are a more visual way of looking at the distributive property. Look at the pictures below to see the process of breaking it down.

Step One create your model

Step Two: Multiply the first number on the top by the 1st number on the side.

Step Three: Multiply the 2nd number on the top by the 1st number on the side

Step Four: Multiply the 1st number on the top by the 2nd number on the side

Step five: Multiply the 2nd number on the top by the 2nd number on the side

Step six: Add all the numbers in the boxes up.

Double-Digit Multiplication Strategies #2 Lattice Multiplication

Another double digit multiplication strategy is lattice multiplication. This method is not seen very Often but is a bit of a variation of the area models. One reason that I love this method is it employs only single digit addition, which can be easily done in students’ heads. Also, students do not have to worry about placeholders which can often be a problem for students when they are using the standard algorithm. To see a step by step version of this please go to my blog post How to do Lattice Multiplication Step by Step

I have a couple different products that I use to teach this method. Plus some of them are digital items that work great for Google classroom. I have found that teachers that are either just introducing this concept to students or who have students that struggle with placeholders love this method. Plus, the digital lattice multiplication is easily assigned to their students through google classroom. This makes it an easy homework assignment or an assignment for math centers in class with ipads or chromebooks.

You can get a sample of my printed version by signing up for my email list. The sample is included in The Ultimate Multiplication Toolkit. To do this click on the picture below.

Double Digit Multiplication Strategies #3 The Japanese Method

So the Japanese method of double digit multiplication follows the same concept of lattice multiplication, but is a more visual double digit multiplication strategy. Instead of writing numbers students draw lines and then they count and add up the number of intersections between the lines. Look at the pictures below for a step by step process.

Step one: Draw the same number of lines vertically that are in the tens place of the first number.

Step two Draw the same number of lines vertically that are in the ones place of the first number

Step three: Draw the same number of lines horizontally crossing the first lines as the number in the tens place of the second number.

Step four: Draw the same number of lines horizontally as the number in the ones place of the second number

Step Five Circle the bottom set of dots. The two middle sets of dots and the top set of dots.

Step 6: Add up the dots in a section. If over ten carry the remaining to the next section.

Want to Read More?!?!

How to do Lattice Multiplication Step by Step

How to Incorporate Multiplication Lesson Plans into your Classroom

5 Math Games to Make Learning Fun

Double Digit Multiplication Strategy #4 The Standard Algorithm

Lastly, the standard algorithm. Which is how we all remember to do double digit multiplication. This used to be the only double digit multiplication strategy there was. With all the new math you might wonder why we still do the standard algorithm. I, however, have found that for many of my students, usually the more advanced ones, this is the method that clicks best with them. Look at the steps below to see exactly how to do this method.

Step One: Multiply the number in the ones place on the bottom by the number in the ones place on top.

Step Two: Multiply the number in the ones place on bottom by the number in the tens place on top

Step three: Put a place holder.

Step four: Multiply the number in the tens place on the bottom by the number in the ones place on the top.

Step five: Multiply the number in the tens place on the bottom with the number in the tens place on the top.

Step six: Add the Numbers.

There are many double digit multiplication strategies, but it is important to teach all of them. One strategy is going to click with some students better than others. By teaching all of them you can help students find a method that works best for them, which is ultimately what we want.

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