The introduction of any new math concept at the early elementary level should always be in the concrete form. So, when I introduce multiplication concepts to my 3rd grade students, I go straight to my Montessori materials and lessons! It should be noted, that while the Common Core standards list learning, understanding, and memorizing the multiplication tables as a third-grade standard, it is not unusual for kindergarten age children in a Montessori classroom to be working multiplication tables with the same materials I am about to spotlight. This is not because Dr. Montessori pushed difficult math onto young children, but because the younger children in her schools were curious about what the older children were doing, and wanted to do the work themselves. Because the Montessori materials and lessons are concrete, beautiful, and isolate a single concept, she discovered that children this young can indeed do multiplication, and other math usually reserved for children several years older than them! There are Montessori materials and lessons for the other tables (addition, subtraction, and division), but that is another blog post.
In this post, I will show you the three main Montessori materials I use to introduce multiplication tables.
COLORED BEAD BARS + TABLES BOOKLETS
What Are the Colored Bead Bars?
The Montessori colored bead bars (which are used all throughout the curriculum), consist of a divided box, or in some cases, separate boxes. In each divided compartment, there are beads strung together on a wire. The beads are perfectly round (this allows them to be used for amazing geometry lessons). Each quantity has a consistent color: 1=red, 2=green, 3=pink, 4=yellow, 5=light blue, 6=purple, 7=white, 8=brown, 9=dark blue, 10=gold. The beads are used with a small green felt mat so they do not roll away.
Pre-requisite Mini-Lesson:
If a child has never seen the colored bead bars, I will do a quick introductory “bead stair” lesson. I also show them where to get the bead box, how to carry and open it, and where to return it to the shelf when they are done using it. In the bead stair lesson, the child takes out the first bead from the box (one red 1 bead), and places it on the felt mat, then they take one green 2 bead, and place it on the mat directly under the first bead. They continue in this way until they have built a tiny triangle. This familiarizes them with the color and quantity scheme, and indirectly gives an impression of the geometry of a triangle. I use as few words as possible in order to allow the child to concentrate.
Here is a video showing the bead stair lesson (I made this for my class during distance learning. In the classroom, the child would be holding the beads, and I would be doing WAY less talking!
Multiplication Tables Intro Lesson:
Once a child understands which quantities match which color of bead bar, you can present to them the steps in the first multiplication lesson.
1. I have them take out one bead of any color besides one, (lets go with the pink three), count it and place it on the mat.
2. I say, “this is one three”, “one times three”, then I count it, and say, “it equals three”.
3. I show them where to record the answer in a little booklet of tables. CLICK HERE for the printable bookelts I made and use.
4. Next, I have the child take out another of the same bead, and have them place it directly under the first. This will not only start to form an array, but will also reveal the geometry of multiplication! No need to point this out, as it is more exciting for the child to make these discoveries on their own!
5. I next tell the child to count on from the first bead, and show them how to record, 2x3=6 on their paper.
6. I continue on this way, until I see they have caught on. When they finish, they are shown how to check their answers using a control chart containing all of the multiplication tables. This reinforces their math facts, gives them independence, and immediate feedback. CLICK HERE to download a printable of the control chart.
After completing a table or two, a child can usually figure out how to use the bead box to work other tables on their own. I leave the bead box and felt out on the shelf, along with lots of copies of the times tables booklets for them to use whenever they like. The beauty of this lesson in a conventional classroom, is that once my students understand how to use the bead box, they are allowed to use it with their textbook, or online math intervention programs. My struggling students, and students with special needs absolutely LOVE to use the bead box in this way, because it allows them to be successful and independent. In a Montessori class, there are no textbooks, but instead a multitude of differentiated individual and small group mini-lessons.
Here is a video of the above lesson (another distance learning video, so less talking in person)! CLICK HERE for a printable of the little booklet in the video.
MULTIPLICATION BEAD BOARD
What is the Multiplication Bead Board?
The board consists of a square slab of wood with the numbers 1-10 written across the top. Under the numbers are ten columns, and ten rows of little divots where a single bead can rest without rolling away. On the side of the board is a slot where a wooden number card (1-10) can be placed. There is a box of number cards in one compartment, and 100 red beads in another. The multiplication bead board provides another way for children to practice their times tables concretely. Dr Montessori discovered that after 6 years old, children stop enjoying repetition of activities, and instead need novelty in how they practice new concepts. The bead board meets this need. The bead board is designed so the beads are loose, and all one color, requiring a bit more focus on the part of the child. As a secondary purpose, grasping the tiny beads also aids in the development of the fine motor grip needed to properly hold a pencil (something kiddos still struggle with in third grade). It also provides a nice visual of the concept of arrays (rows and columns).
Multiplication Bead Board Intro Lesson:
1. I have the child take a number card out of the box, and place it in the slot (lets go with three).
2. I show them how to place three beads in a column under the number 1.
3. Then I say, “one times three is three”, and they record it in a little book.
4. Next, the child places three more beads in the column under the number 2.
5. I tell them that two times three equals six.
6. When they make three times three (as with the colored bead bar lesson), they will visually see the square of the number formed!
7. When the child catches on, they again can independently complete and check all of their tables.
I find that my students with fine motor difficulties prefer to use this tool when their text book asks them to draw lots of little dots on paper to form arrays. I don’t find that they tend to return to this material like they do the bead bars however because the loose beads take more time to build with. CLICK HERE for a printable version of the bead board I made, that can be used with plastic pony beads.
Here is a video I made for my grade level partner showing how to introduce the Montessori bead board. Again, with students, I would be talking way less, notice a theme here? : )
MULTIPLICAITON FINGER CHART + EQUATION SLIPS
What is the Multiplication Finger Chart?
This is a tool most educators are familiar with. It is made up of a grid with the numbers 1-10 written across the top, representing one factor. Along the left side is a column with the second factor written. The middle of the chart is a grid containing the products (answers). The finger chart serves as a quick, more abstract way to do multiplication, and can be used by children to find answers to problems they have not yet memorized. Because the finger chart is a conventional tool, I will not give a step-by-step lesson here, but will talk a bit more about ways it can be used.
1. Lesson 1: Show children how to place their fingers on two factors, and find the product where they meet.
2. Lesson 2: Give children loose, mixed multiplication equation slips. They can pull them from a container, and use the chart to find the answer. This is another activity that can be left on a shelf for children to use independently.
3. Lesson 3: Give children a blank chart with only factors, and no products on it. They use products written on little chips of paper and place them on the blank square, or they can write in the answers. Giving the second option is nice for students who may enjoy writing, while the first option is great for children who do not enjoy writing.
Here is a...you guessed it - distance learning video with too much talking, ha ha, showing how to introduce the finger chart. CLICK HERE for a printable of the charts and equation slips.
Here is another video showing two ways students can fill out the blank multiplication chart. I made this video for my grade level partner pre-pandemic. With a student, I would let them take over as soon as they caught on to the pattern.
The beauty of these lessons is that they can be introduced quickly, and empower children to develop a deep understanding of multiplication. There are many, many more amazing, mind-blowing Montessori lessons for teaching multiplication concepts, but these three offer a great introduction, and can be easily incorporated into any classroom or homeschool.
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