Montessori Mom

Negative Snake Game (Subtraction)

Ages

6 years and older — once the child is fluent with the Addition Snake Game, the Short Bead Stair, and the Golden Bead Material.

Purpose

Teach the concept of zero, and of negative and positive numbers. The negative snake game gives a concrete, hands-on picture of subtraction, and lays an early sensorial foundation for the higher-level algebra of equal quantities — where adding and subtracting equal amounts leaves a value unchanged.

Free Printouts

Download the Colored Bead Stair printout (PDF) — print and cut your own colored bead bars 1–9 if you don't yet own the material.

Download the blank Bead Stair outline (PDF) — a color-it-yourself version for the gray negative bars.

Download the Golden Bead Material printout (PDF) — ten-bars for exchanging.

Materials

• A box of colored bead bars
• A box of golden ten-bead bars
• A box of gray wooden negative bead bars — sets containing 1 through 9 (provide the same quantity of gold, colored, and negative bars for the first lesson)
• One set of black-and-white bead bars, 1 through 9
• Two empty boxes
• A pencil or pointer
• A felt mat or cloth place mat

Presentation

Spread a rug or long mat on the floor where the child has plenty of room to work. Place the negative and colored bead-bar boxes side by side at the upper corner of the mat. Set the black-and-white beads out in a triangle stair, with the box of golden ten-bars next to it at the other corner.

In this lesson the colored bead bars are added, the black-and-white bars are the remainders, and the gray negative bars are subtracted. Build the snake with the colored bead bars exactly as in the positive (addition) snake game, then continue the colored snake with the same quantities of negative bead bars.

A Worked Example

You need one colored bead-bar stair (1–9), one negative bead-bar stair (1–9), the black-and-white bead-bar stair (1–9), and four golden ten-bars. Arrange the colored and negative bars like this:

1 + 8 + 2 + 5 + 6 + 9 + 3 + 4 + 7 − 3 − 5 − 6 − 1 − 8 − 2 − 9 − 4

(+ are the colored bead bars; − are the gray negative bead bars.)

1. Count the colored bead bars from one end of the snake (left to right) until you reach 10. Rest the pencil point at 10, replace those beads with a golden ten-bar and a black bar for the remainder, and set the counted colored beads in an empty box. Continue until the snake is all golden ten-bars plus a final black-and-white remainder bar — just like the Addition Snake Game.
2. Now the first negative bar is reached (in the example, −3). Tell your child that 3 must be taken away from the black remainder bar.
3. Count backward 3, replace the 5 black bar with a 2 black bar, and put the −3 bar in the empty box.
4. Point to the next negative bar (−5) and count backward 5. The pencil point lands on the third bead of a golden ten-bar — so this time you exchange both the black bar and a golden bar.
5. Replace the golden ten-bar and the 3 black bar with a 7 black-and-white bar, and return the spent gold and black bars to their place at the edge of the mat.
6. Continue in this way until every bead has been removed and the snake is gone.

Checking Your Work

Lay each kind of bead bar back into a triangle stair — colored bars together, negative bars together — and match the negative beads to the positive beads to confirm the result.

Try This

Take a 5 colored bead bar and a −5 gray bead bar. Point to the colored bar and say "5," then place the negative 5 bar beside it: "take away 5 is 0." Repeat with the other pairs to make zero concrete.

Terms to Introduce

• Subtract
• Remainder
• Negative
• Positive
• Zero
• Add

Where to Buy the Material

If you'd like the ready-made bead materials rather than printing your own, these are the sets we use:

• Montessori colored & negative bead bar set (Amazon)
• Golden bead ten-bar material (Amazon)

Keep Exploring

Once subtraction with the snake clicks, move on with the Golden Bead Material, the Counting Chains, and more printable practice on the Math Printouts page. Browse the full Subtraction and Bead Materials collections for the next steps.