# Multiplying Large Numbers with a Table: Building Number Sense

I remember the first time that I was introduced to **using tables for multiplying large numbers**, **division and more**. Prior to that, my experience with tables included reading them, interpreting them, and graphing them. Pretty straight forward stuff that most Algebra students experience.

Yet here I was, in a class for math teachers, looking at a table that was clearly written by a 2nd grader. I don’t mean to say that the handwriting was so bad that it looked like a 2nd grader had written it. No, the table was *literally written by a 2nd grader* as proof to the problem they had been working on in class that week.

The problem was something like, If 1 hot dog costs $1.99, how much do 5 hot dogs cost? 10 hot dogs? 20 hot dogs? Looking at the table, I was surprised by the level of understanding this 2nd grader had about numbers and their ability to manipulate them so well.

I decided I might actually pay attention to this class. I’m so glad I did. The strategies I learned in that class have impacted my teaching and my homeschooling in tremendous ways.

Let’s see what you can do with a table to learn multiplication and division.

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*This is a guest post from Danielle at Blessedly Busy.*

**Multiplication and Division Using a Table**

When my students are just *starting* to explore multiplication, I will have them **use manipulatives and build a table** to model the problem. It looks a lot like zooming in on one piece of the traditional multiplication table. We are just starting out, just exploring, so I don’t call it anything.

Here’s how I might approach the problem:

I might take a toy I have in abundance and line them up. Maybe I want them to discover multiples of 5, so, we will line up 5 toys:

π π π π π

I ask, “How many toys are in this row?” and “What if we add another row?”

π π π π π

π π π π π

“Let’s keep track of our findings on a table. I’ll start it for you.”

Rows | Toys |

1 | 5 |

2 | 10 |

3 | ? |

Continue making your table until you are satisfied. I have my students **make many tables** to begin with. It gives them practice **seeing the problem** (1 x 5 =5) and **using a table** in a very *non-threatening* way.

Once they understand how to *use* the table, I will begin to have *already made* tables with the question, **“Can you finish this?”**

At first, they would start with 1 and the focus would be **building multiplication tables**. Once that feels solid, I start stretching them.

Here is an example of a table for students to complete that would stretch them:

Rows | Toys |

1 | |

4 | 20 |

The **multiple they are going to use is not immediately apparent** and it takes some thinking to figure out how to fill in this table.

All of the examples I have been giving might make you think that a table is only really useful for beginning mathematicians. Nothing could be further from the truth, **we are just getting started**.

**Practicing Multiplication with Middle School and Beyond**

If you have an older student you would like to practice using a table with, please introduce the table using *non-threatening math* (stuff they find easy).

While all of the examples I have given use multiples under 10, you can use a table to practice **multiplying large numbers** as well. *Or fractions, or decimals, or integers, etc.*

Some ideas include: multiples of 13, 1/2, or -8.

While it might be useful for students to memorize the multiplication table, that’s not the point of this exercise. **The point is to gain and use a strategy and build number sense**. The more fluid a student’s understanding about numbers, the more successful they will be in math.

The tables I have shown you all increase by one on the left side. As students become more adept, you don’t have to follow that same mold. In fact, this leads nicely into **why and how the table is really so amazing**.

**But Wait, What About Division?**

Ok. I’ll show you the fun mathrobatics in the next section. Let’s take a quick peek at how to use this table to **build division concepts**.

With division, you **start at the end and work your way backwards**. So, if my goal was to practice multiples of 5, I would start with 5×10=50. Again, **start with objects**.

In this case, 50:

π π π π π

π π π π π

π π π π π

π π π π π

π π π π π

π π π π π

π π π π π

π π π π π

π π π π π

π π π π π

Wow! That’s a lot of toys. After our students discover the total, we ask, “What if I take one row *away*?” **And build a table:**

Row | Toys |

10 | 50 |

9 | 45 |

8 | ? |

Then you can continue from there to **find patterns** and solidify an **understanding of division**.

Ready to move on? Here we go.

**Using the Table as a Tool for Multiplying Large Numbers:**

Now we get to the stuff that I was amazed a 2nd grader could do.

Once students are comfortable making tables forwards and backwards it’s time for some fun. It’s time for…**story problems**. Don’t run away! Story problems can be fun! When the emphasis is on discovery and creativity. π

**Here’s our sample problem:**

“If 1 My Little Pony toy costs $5, how much do 10 ponies cost? 20 ponies? 19 ponies?

And if you really want to encourage creativity you ask, *“How many ways can you find the answer?”*

Here’s what a completed table might look like for this problem:

# of Ponies | $ | Method |

1 | 5 | |

10 | 50 | (5×10), (5+5+5+5+5+5+5+5+5+5) |

20 | 100 | (5×20), (2×50), (50+50) |

19 | 95 | (5×19), (100-5) |

As you can see, the 19 comes after the 20. That’s because I **used the 20 to find the answer to 19**. Who wants to do 19×5 when 20×5-5 is so much faster?

The table is being used as a tool to solve problems. Tools sometimes get messy. It’s okay if a table skips around a little, something we typically wouldn’t tolerate.

As your student gains practice **thinking creatively about numbers**, you’ll see not only their **ability to solve problems** easily increase, but also their **ability to think about a problem in multiple ways**.

And like that 2nd grade student, they will amaze people with their **ability to think fluidly about numbers**.

Want some free **multiplication table lessons** to get you started? This set of lessons will stretch your kids and get them thinking, problem solving, and more fluently **multiplying large numbers**!

There are **5 different levels** in this resource pack, including a set of tables to practice **multiplying decimals**.

**{Click HERE to go to my shop and grab the FREE Multiplication with Tables Lesson Pack!}**

And if you’re looking for another tool to aid students in multiplying large numbers, be sure to read this post on multiplication, with a free printable template.

And for more information on **using a table** to solve math problems, check out this post: Problem Solving by Finding Patterns

*Danielle is a homeschooling mamma of 5. Β She is committed to making life with young children easier and sharing her passion for math. Β If you would like to learn more about teaching math to multiple age groups visit Blessedly Busy or follow her on: Β Facebook, Instagram, Pinterest or Twitter.*