If you like this style of learning tools as well and are interested in free, printable versions of the multiplication and division Montessori learning tools, sign up for my newsletter to stay up-to-date (and receive some free educational printables). The more advanced math learning tools are on my near term to-do list.

Recommended Age Range: Preschool, Kindergarten, Early Elementary
Time Required: Less than 1 hour
Difficultly: Easy
Cost: Free printable, less than $2 in used supplies

Materials:

• Printed Subtraction Strip Board document
• Optional: Printed Subtraction Tables and Subtraction Tables – Mixed Up
• Optional: Printed Subtraction Chart document
• 3 laminating pouches
• 1 sheet of poster board (I used a 14″x22″ sheet, though it will be trimmed to roughly 5″x18″)

Supplies & Tools:

• laminator
• scissors
• paper trimmer (optional)
• glue stick

Instructions:

1. Print out the Subtraction Strip Board document.
2. Laminate all 3 sheets.

1. Cut out both halves of the subtraction strip board and the long white strip as well as the 9 numbered pieces.

1. Glue both halves of the Subtraction Strip Board onto the poster board and cut out. Repeat process with the long white strip.

1. Print out the supplemental worksheets to be used with the board: Subtraction Tables, Subtraction Tables-Mixed Up, & Subtraction Chart

To use the subtraction board, use the long, white strip to cover up all the numbers past the first number in the problem (the big number). For example, if the problem is 14 minus something, the child would use the white strip to cover up the number 15 and beyond as shown.

Next the child would find the blue strip corresponding to the number that is being subtracted and place that next to the white strip. For example, if the problem is 11 minus 5, first the child would use the long, white strip to cover up the numbers 12 through 18. Then he would find the blue strip consisting of 5 squares and place this 5-strip next to the white strip which would cover up numbers 7, 8, 9, 10, and 11. The numbers remaining would be 1 through 6. Therefore, the answer to the problem would be 6, as shown.

To use the supplemental worksheets, I recommend starting with Subtraction Table: Ones and progressing through Subtraction Table: Nines if this seems to be at your child’s level. If your child quickly realizes that there is a pattern to the answers and stops thinking about what the problems actually mean, you might want to skip to the Mixed Up Subtraction Tables to give them more practice using the board. Lastly, you can have your child fill out the Subtraction Chart. To use the chart the child picks an empty box and subtracts the number to the right of that box from the number straight above. An answer key is provided. In this case it is completely okay, even desirable, for your child to realize that there is a pattern to the table.

Related Links

Mathematics Activities
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I recently decided to try homeschooling my oldest child for kindergarten rather than continuing to send him to the Montessori school he’s been attending for the past couple years. However, I still want him to have exposure to all the wonderful Montessori tools. Granted, we just started homeschooling a week ago, so he still has a lot of enthusiasm in general, but he loves using this board and the associated strips to add single digit numbers together. We haven’t attempted the full addition chart yet, but he’s done many of the tables, and I’m confident that he understands the concept of addition. He’s even getting better at adding numbers together in his head.

Full instructions for creating and using the board and associated worksheets are below.

Recommended Age Range: Preschool, Kindergarten
Time Required: Less than 1 hour
Difficultly: Easy
Cost: Free printable, less than $2 in used supplies

Materials:

• Printed Addition Strip Board document
• Optional: Printed Addition Tables and Addition Tables – Mixed Up
• Optional: Printed Addition Chart document
• 6 laminating pouches
• 1 sheet of poster board (I used a 14″x22″ sheet, though it will be trimmed to roughly 13″x18″)

Supplies & Tools:

• laminator
• scissors
• glue stick

Instructions:

1. Print out the Addition Strip Board document.
2. Laminate all 6 sheets.

1. Cut out the 18 addition strips (9 red and 9 blue) and set aside in an envelope or Ziploc bag.
2. Cut out the 4 sections of the addition strip board.

1. Glue the 4 sections onto the poster board
2. Trim the extra poster board.
3. Print out the supplemental worksheets to be used with the board: Addition Tables, Addition Tables-Mixed Up, Addition Chart

To use the board, start with Addition Table: Ones. Have your child find the blue “1” square and place it in the upper left corner. Next have them find the red “1” square and place it next to the blue one square. Looking at the top row of numbers, they will see that their 1 blue square and 1 red square has brought them to the number “2”. They then can write the number 2 on the 1+1 line.

Next they leave their red square where it is, but move the blue “1” square down to the next row. Since the next problem on their worksheet is 1+2, they find the red “2” square and place it next to the blue “1” square to see that 1+2=3. They can keep moving down the board until their worksheet is complete.

After doing a few of these tables, they might realize that there is a pattern and that they can “cheat” by just adding 1 to their previous answer. For example, the answer on the Addition Table: Ones worksheet are 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since my son realized this right away, I also made an optional Addition Tables: Mixed-Up version that requires them to actually prove that they understand how to add. This is not an actual Montessori tool, so your child won’t be missing the full experience if they skip it.

My son also does not like using all the rows on his Addition Strip Board, so I let him use whatever row he wants when completing his worksheets. He frequently just uses the top row for every problem.

After a child is good at doing their addition tables, they might want to attempt the full Addition Chart. To use the addition chart, you write the number in each box for the sum of the corresponding row and column. So, for example, when filling out row 4, the first box is 4+1 since it is in row 4, column 1, the second box is 4+2 since it is in row 4, column 2 and so on. A completed chart is included so that the child can compare their answers. A child may or may not need to use the addition strip board to fill out the chart depending on their abilities.

Click here for more Addition and Subtraction activities for kids.

Related Links

Mathematics Activities
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My first child started attending a Montessori preschool just before his 3rd birthday. One of the tools which his teacher said he had trouble understanding was the Montessori pink tower. After I looked up what a “pink tower” was, I just couldn’t believe that my son was unable to stack blocks in order of size. However, I was also unwilling to pay nearly $40 (Affiliate Link) to prove to myself that he could.

After several months, when my son was three and a half, his teacher was still saying he was unable to do the pink tower. Still unable to believe it, I decided to make one myself. I was actually pretty pleased with the result (and the total cost of under $5). However, I was a little disappointed with the amount of time he spent using it. I asked him to show me he could do it and he stacked the blocks in the correct order, but completely forgot about one of the blocks. I showed him he forgot one and he did it again correctly the second time.

In my opinion, his problem was more of an attention span issue than a stacking issue. Since he never really used them again, I’m hoping they’ll come in handy when my 2 year old is a little older.

Note that when I’d completed the tower, I basically just gave him the blocks and said, “Do it.” After all, he’d seen them at school. However, if you’re interested in introducing the pink tower to your child in a way that wouldn’t make Maria Montessori cringe, check out this tutorial on the correct way to present this learning tool from Carrots are Orange.

Recommended Age Range: Preschool
Time Required: ~3 hours
Difficulty: Fairly Easy (all the measuring with a ruler is time consuming and using the x-acto knife requires attention and care, but otherwise, the process is simple.)
Cost: Less than $5 in used supplies (I forget how much the large sheet of foam board cost, but I’m sure it was less than $5 and was the only real cost.)

Materials:

• Foam board (I used a 20″x28″x3/16″ or 508 x 711 x 5 mm sheet, but I had quite a bit left over)
• Tacky glue

Supplies & Tools:

• pencil
• ruler
• x-acto knife
• surface for cutting (I used a self-healing mat)
• marker or paint (unless you buy colored foam board, which would have saved time, or you want to leave it white)

Instructions:

1. The first step is to trace out all the square and rectangular shapes to be cut to make the blocks onto the foam board using a ruler and pencil. Going along with standard Montessori specifications, my largest cube was 10 cm on each edge and my smallest was 1 cm. Since the foam board itself has a thickness of half a centimeter, all the sides of each cube are not the same size. For example, the 10 cm cube is made of two 10 cm x 10 cm squares, two 10 cm x 9 cm rectangles, and two 9 cm x 9 cm squares. The 1 cm cube is made by stacking and gluing two 1 cm x 1 cm squares. Here is a diagram of the shapes that I drew onto my foam board in centimeters.



2. Cut out all the shapes using an x-acto knife on a safe cutting surface, like a self-healing mat.
3. Color or paint one side of each shape if desired. Although the standard Montessori tower is pink, I like blue better.
4. Glue the shapes together to make each cube. As stated before, the 10 cm cube is made of two 10 cm x 10 cm squares, two 10 cm x 9 cm rectangles, and two 9 cm x 9 cm squares. This diagram shows how they are assembled.



5. Similarly, assemble the 9 cm cube using two 9 cm x 9 cm squares, two 9 cm x 8 cm rectangles, and two 8 cm x 8 cm squares.
6. Assemble the 8 cm cube using two 8 cm x 8 cm squares, two 8 cm x 7 cm rectangles, and two 7 cm x 7 cm squares.
7. Assemble the 7 cm cube using two 7 cm x 7 cm squares, two 7 cm x 6 cm rectangles, and two 6 cm x 6 cm squares.
8. Assemble the 6 cm cube using two 6 cm x 6 cm squares, two 6 cm x 5 cm rectangles, and two 5 cm x 5 cm squares.
9. Assemble the 5 cm cube using two 5 cm x 5 cm squares, two 5 cm x 4 cm rectangles, and two 4 cm x 4 cm squares.
10. Assemble the 4 cm cube using two 4 cm x 4 cm squares, two 4 cm x 3 cm rectangles, and two 3 cm x 3 cm squares.
11. Assemble the 3 cm cube using two 3 cm x 3 cm squares, two 3 cm x 2 cm rectangles, and two 2 cm x 2 cm squares.
12. Assemble the 2 cm cube using two 2 cm x 2 cm squares, two 2 cm x 1 cm rectangles, and two 1 cm x 1 cm squares.
13. Assemble the 1 cm cube by gluing two 1 cm x 1 cm squares together.

Related Links

Homemade Montessori Learning
Best Books for Preschoolers
Pre-K Learning

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My 3 year old was not very good at doing these Montessori sound jars when I first made them, but I’m hoping that as he gets older, he’ll learn to distinguish between the different sounds. The idea is that you have two sets of jars (blue and red, in my case), each filled with the same objects (like rice, rocks, beans, etc.) The child would start by picking a red jar for example, then shake it, listen carefully to it, and try to find the blue jar that makes the same sound. Since I left the bottoms of the jars uncovered, the child could check to see if they guessed right by looking in the bottom of the jars to see if the contents match.

Recommended Age Range: Preschool, Kindergarten
Time Required: ~1 hour
Difficulty: Easy
Cost: For me, this was a very inexpensive project, because I got the spice rack for cheap at a garage sale and filled the jars with items I already had around the house. However, a brand-new similar spice rack (Affiliate Link) on Amazon is not cheap at all, so the cost of this project can vary widely.

Materials:

• glass jars (such as for holding spices)
• small quantities of various items (such as beans, puffed rice, quinoa, rice grains, rocks, peppercorns, salt, lentils, marshmallows, beads, etc.)
• two colors of construction paper

Supplies & Tools:

• scissors
• ruler
• glue stick

Instructions:

1. Measure the height of the jar and cut rectangles out of the construction paper such that they can be wrapped around the jars to hide the contents. Make half the rectangles one color and half a second color.
2. Glue one rectangle onto each jar.
3. For each item (rice, rocks, etc.), place an equal amount of that item in a jar of each color. In the end you should have a matching set of sound jars, with one set covered in one color and the second set covered in a different color.

Related Links

Montessori Learning Activities
Pre-K Learning Activities
Best Books for Preschool

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I decided to make the Montessori colored bead stair after I had already made my own imitation “golden” (actually white) beads. So far, the colored beads representing each number between 1 and 9 are not actually necessary, since the child can just count out the appropriate number of single golden beads. However, they are a handy shortcut that keep the child interested in whatever we’re doing.

If I expected my kid to count out 9 single beads every time he wanted to represent 9 (which I already know he’s capable of doing), he would get bored really fast and find the whole exercise too tedious. However, if he can just grab a 9-bar out of our set of colored beads, he’s likely to stay interested much longer.

Recommended Age Range: Preschool, Kindergarten, Early Elementary
Time Required: Each bar takes about 1-2 minutes to make depending on the length. With one 500 pack of beads of various colors, I was able to make ten each of 2-,3-,and 4-bars, nine 5-bars, six 6- and 7- bars, and five 8- and 9-bars, or about 60 bars. Therefore, the total time was approximately 1-2 hours. At some point I will likely buy another 500 pack of beads so that I can have 10 of each length for when my kids are learning multiplication. Completing my set will likely take less than an hour.
Difficulty: Easy
Cost: Less than $5 in used supplies (I had already bought fishing line and wire for the Montessori “Golden” Beads and only a minimal amount of each was used for this project. I used a 500 pack of faceted, 8 mm, plastic beads of various colors from my local craft store, which cost $2.69 after using a 40% off coupon. I will likely someday buy another pack so that I can have at least 10 of each length bar. A 900 pack of similar beads (Affiliate Link) are available on Amazon for $4.99 presently.)

Materials:

• 500-1000 pack of beads of various colors
• wire (I used a 175 ft spool of 20 gauge galvanized steel wire from the hardware store, but any similar gauge would likely work. I estimate to make 10 of each length bar using 8 mm beads would require less than 25 ft.)

Supplies & Tools:

• small diagonal wire cutters
• needle nose pliers
• ruler

Instructions:

1. First, sort all your beads by color. My variety pack had 12 colors, so I used an egg carton to sort them.
2. Decide which color will represent each length bar, using the most plentiful colors for the largest bars.
3. For each number bar, you could experiment to see what the desired length of wire is, then use a ruler to measure out the desired number of wire pieces for that length. However, I chose to first thread the desired number of beads onto the wire spool.



4. Curl the end of the wire using the tip of the needle nose pliers in order to hold the beads on the wire.



5. Cut the wire leaving an extra length to be curled. For me the ideal extra length was about the length of one bead (or around 1 cm), though this might vary from person to person depending on the tool and technique used to bend the wire.



6. Curl the end of the wire to hold all the beads together.



7. Repeat in order to have bars 2 to 9 beads long, with each length being represented by a different color. Make as many as you can of each length (up to 10) based on the number of beads you have of each color.

I made a special box to hold all my bead material, but they could be stored in a wide variety of ways (including in a Ziploc bag).

There are many things you can do with the colored beads. In addition to letting your child make them into a triangle, you could also use them with Montessori Number Symbol Cards or Seguin Boards.

Click here for more Counting and Number Recognition activities for kids.

Related Links

Montessori Learning Activities
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I briefly looked into purchasing a set, but that turned out to be cost-prohibitive. Undeterred, I decided to try making my own. Unfortunately, I quickly realized I had two options: pretty or cheap. While I really wanted to use perfectly round, hand-painted, wooden beads, I didn’t want to pay that much. Especially, when I wasn’t even sure how well the whole endeavor would work out. Therefore, I decided to go the cheap route. I bought faceted, plastic, 8 mm beads off Amazon in the least expensive color available at the time.

Next, I had a little trouble finding the plastic mesh/canvas that many people use to hold the hundred squares and thousand cubes together. I eventually found some at my local craft store, but by that time I had already made a hundred square by stringing together my ten bars with fishing line. As expected, my fishing line squares ended up floppy. Afterwards, I made one hundred square using the plastic mesh. Next, I spent a day trying to decide which I liked better. Both ways took about the same amount of time. Being a very organized, structured person, the rigidity of the plastic mesh appealed to me.

My husband on the other hand liked the floppy square better saying it was a more interesting object to manipulate. I ended up deciding to go with the floppy squares when my 4 year old squished one of the hundred squares in his hand and asked, “How many is it now?” I was a little surprised it wasn’t obvious to him. However, I was able to convince him that if it was a hundred beads when it was flat, it was still a hundred beads when you folded it in half, or rolled it up, or manipulated it any way you wanted. The floppy squares ended up being more useful conceptually.

The last decision was how many to make. I may add to my collection at some point, but for now, I decided to make 1 thousand cube (mainly just because you only need one to explain the concept of a thousand and they’re obviously very time-consuming to make), 10 hundred squares (to show how the hundreds add together to make a thousand), and 55 ten bars (which allows me to demonstrate 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 all at the same time). Making all of this required 2550 beads. Since I bought 3000 I have 450 left over to use as singles (minus some that my kids lost).

Recommended Age Range: Preschool, Kindergarten, Elementary
Time Required: For me, it took about 2 minutes to make one ten bar, 25 minutes to make one hundred square, and about 6 hours to make one thousand cube. Since I made 55 ten bars, 10 hundred squares, and 1 thousand cube, all together this took about 12 hours. Really, I worked on this for about 15 minutes a day or so for a couple months.
Difficulty: Fairly easy, but time-consuming. Tying the fishing line was at times a little challenging in poor lighting since it was so thin and hard to see. However, all the steps became fairly mindless after the first few attempts.
Cost: ~$25 (which made 1 thousand cube, 10 hundred squares, 55 ten bars, and 450 leftover single beads.) I already had the wire cutters and pliers, so all I had to buy was fishing line (~$3), wire (~$5) (neither of which I used anywhere close to all of), and beads. I paid about $18 for 3000 beads. The faceted, 8 mm, plastic beads (Affiliate Link) shown in this post were $5.77 for a 1000 pack on Amazon, though the price fluctuates daily. After I purchased my first pack I had to wait a couple weeks for the price to drop before I bought the remaining 2 packs. (I used camelcamelcamel.com to track the price and be notified when my target price of $6 had been reached.) However, I noticed that our local craft store (Michaels) sold similar beads at $4.49 for 500. With a 40% coupon, this would have been an even better deal.

Materials:

• 3000 “golden” beads (or whatever color you choose)
• fishing line (I used 6 lb monofilament fishing line, but any would probably work)
• wire (I used a 175 ft spool of 20 gauge galvanized steel wire from the hardware store, but any similar gauge would likely work. I estimate I used about 85 ft.)

Supplies & Tools:

• small diagonal wire cutters
• needle nose pliers
• ruler
• scissors

Instructions:

To Make Ten Bar
1. You could string the beads first, curl an end, cut, then curl the other end, in order to ensure the wire is the right length. However, I chose to cut the wire first, that way I could do the ten bars in groups of 10, assembly style. First, I cut wire measuring approximately 4″. This was perfect for me based on my 8 mm beads and how I curled the ends, but you’ll want to try it out to find the perfect length for you. Usually I just measured the first one with a ruler, then used that one as a reference to cut a few more.
2. Next I curled one of the ends of wire using the tip of my needle nose pliers.



3. String 10 beads onto the wire.
4. Curl the other end with the needle nose pliers.

To Make Hundred Square

To Make Thousand Cube

With 3000 beads, you will have enough to make 55 ten bars, 10 hundred squares, 1 thousand cube, and still have 450 beads leftover to use as singles (or use Montessori colored beads instead for the single digits). I chose to make a box to hold my Montessori math material.

There are lot of ways to use the “Golden” Beads. You can use the 3-period lesson to introduce the concept of a unit, ten, hundred, and thousand. You can ask your child to bring you a certain number to help with counting. You can also combine the beads with other Montessori math material such as the number symbol cards or Seguin boards.

Click here for more Mathematics activities for kids.

Related Links

Montessori Learning Activities
Math Activities
Best Books for Early Elementary

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