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# Introducing Multiplication and The Two Words You Should Always Use

There are two words you should always include when you first introduce multiplication.

Those words are: groups of (or rows of).

When students first learn the concept of multiplication, it’s really important for them to understand what it means to multiply, and how this is similar to, but different from adding.

Using visuals, and the words groups of (and also rows of) will help your students understand the topic.

This concept should be taught and instilled in your students before you introduce the properties of multiplication (specifically the commutative property, identity property, and zero property).

Teaching these students the concept of multiplication before the properties will allow them to develop a foundation of understanding what it truly means to multiply.

When they are later faced with equations they don’t have memorized, they will know how to solve for the answer.

Don’t get me wrong–the properties of multiplication are important and need to be taught! Just not yet!

### How to Teach “Groups of” With Hands-On Practice

You can use any manipulatives as you teach groups. I recommend giving your students twelve buttons (cubes, paperclips, erasers, etc…) to use as their manipulatives. The reason I like to use twelve is that it can be used to make several equations.

Using the manipulatives on their desk, you can ask your students to make:

• One group of twelve
• Two groups of six
• Three groups of four
• Six groups of two
• Twelve groups of one

With each equation, I would have my students write the equation to represent the groups of.

You can also teach your students repeated addition using this hands-on activity.

As you do this activity, your students might begin to naturally notice the commutative property in action! (But remember–you haven’t taught this property explicitly yet.)

Add or take away more manipulatives to do other equations. Once your students have enough practice, you can have them draw pictures to represent groups of.

You can show real-world pictures to your students and have them write equations as well.

### How to Teach “Rows of” With Hands-On Practice

Just like the groups of activities, you can use manipulatives to practice building arrays and creating equal rows.

You can also use a carton of eggs as an example when you are teaching arrays.

Once students have learned the concepts of groups of and rows of, we say this whenever we write out a multiplication equation.

For example, if I wrote the equation 3×5 on the board, my students would say:

• Three groups of five
• Three rows of five
• Three times five

By saying it this way, when students come to an equation they don’t have memorized, they will instinctively be telling themselves what to draw.

Want these and other real-world multiplication photos? Subscribe to my email list and I’ll send them right over!

For when you are first introducing multiplication in third grade:

For going deeper with third grade multiplication skills: