One of the best things about Montessori math is that materials can be used over and over for a variety of activities.
Here’s a beginning set up for 6-9 math:
Addition strip board, charts, & equations
Subtraction strip board, charts & equations
Box of bead bars (55 of each, if possible)
Large & small number cards
Math symbols (+, -, x, ÷, >, =)
An addition strip board can be used for addition, obviously, with the child taking a few equations (10-20) at a time and using the board to calculate the answers. It’s important that after putting the answer tiles down and checking the work with a finger chart, that the child write some of the equations. Some kids might want to write all of them, but at the very least they should write any that they got wrong. If they didn’t miss any, they can pick their favorite equation out of all the ones they did to write down.
An addition strip board can also be used for number analysis. For this, a child picks a certain number and sees how many different strip combinations they can use to make it. For 6, for instance, they would see that they could use 5 + 1, 4 + 2, and 3 + 3. On their own, they may discover that as blue strips increase, red strips decrease and vice versa. Also, they may notice that they reverse two of those equations (1 + 5 and 2 + 4) and get the same result. You can point out that when they use the 6 strip of either color, the missing symbol in the equation is 0.
One addition strip board activity is to have the child use the two pairs of strips to calculate all the doubles of numbers (1 + 1, 2 + 2, 3 + 3, etc.) Finger charts can be used to check any of the above activities, as well as for practice with math facts. Answer tiles can be used to fill in the answers on the blank chart.
The bead bar box is incredibly versatile. A child can choose two random beads (have them omit 1s and 10s) and make their own equations, counting the beads to get the answers. Or, they can choose 3 or 4 at a time and have triple or quadruple addends.
Using slips of paper with greater than/less than signs, the child can pick any two different beads and place them accordingly. An equal sign can be used when any two of the same bead bars are chosen. The beads can also be used to make ten and teen numbers; if you’d like, you can have the child write each ten and teen number on a slip of paper and place it next to the bead bar combinations.
You’ll need the larger bead box for this one, but kids really like making multiplication tables with bead bars. To do this, choose one number (say, 3) and put out one 3 bar horizontally. Then, since 3 x 1 is 3, put one three bar under the horizontally placed bar, vertically this time. Then, put out two 3 bars horizontally (go from left to right with these). Count 3 x 2, then get a 6 bar and put it vertically under the two 3 bars. Continue until you reach 3 x 10. The child can write these equations in a table. See example (I’ve only shown through 3 x 3):
Bead bars can also be used for Making 10, the snake game, binomial equations, balancing numbers, the checkerboard and I’m sure many more math activities. If you’re homeschooling and you want to purchase one Montessori math material, I would recommend a bead bar box. The beads bars can also be made and stored in a tackle box; you can Google for instructions on how to make them.
I like to use the small number cards for greater than/less than. Start with just the units and tens cards. Let the child make various combinations of the units and tens in pairs going down a rug. Then give them greater than/less than signs to put in between (you can write these on slips of paper or cardstock). When they’ve mastered that, let them add the hundreds and make numbers using hundreds, tens, and units cards. Then, they can add the thousands and do greater than/less than with thousands, hundreds, tens, and units.
These cards are also great for place value. Using the large number cards, have the child make numbers with thousands, hundreds, tens, and units in any combination. Then, have them put a stick (I find small sticks at craft stores, or you can use toothpicks) under just one number. For example: 8645. Have them identify where the stick was placed; in my example, it would be in the 10s. Let them write at least one combination of numbers and draw the line under one place and identify if its place is units, tens, hundreds, or thousands.
For odd and even work, using either the large or small number cards, let the child randomly combine the cards into 4-digit numbers. Have them identify whether the number is odd or even. They may realize (or you can point out) that only the last number in the series determines “odd” or “even”.