Division with Racks and Tubes
Materials:
Tray
7 racks of test tubes: 3 racks painted white for units, 3 racks painted gray for thousands, and 1 rack painted black for millions.
Each rack holds ten test tubes and each tube holds ten beads: in each of the first 2 racks one tube holds green beads for units, one tube holds blue beads for tens, and one tube holds red beads for hundreds; the black rack holds green beads for units of millions.
7 painted cups to match each rack: the outside color corresponds to white, gray or black and the inside color corresponds to the hierarchical colors green, blue or red
A board of the same pattern as the unit division board (green)
A set of green skittles
20 x 5 grid paper & pencil
Purposes: Continuation of the process of moving toward abstraction with division
Age: 6 and up
Preparation:
The child has worked with the Unit Division Board.
The child has been given all three presentations with the Wooden Hierarchy Material.
Presentation 1: Static Division
Invite the child to bring the racks and tubes, the division board, and a long paper.
Introduce the tubes and have the child count the beads in one. Explain the white racks represent the simple family, the gray is the thousand family, and the black is the million family.
Write an equation on the paper and read it with the child. Example: 48,628÷2=
Guide the child in determining which racks to take to build the number. Example: Units, tens, hundred, thousand and ten thousand.
Place a white or gray cup with the matching category color in front of each rack.
Place 4 ten thousand beads in the ten thousand cup and guide the child to do the rest to build the number. 8 thousand beads in the thousand cup, etc.
Explain that the beads are the dividend and the divisor is built with skittles on the board. Place the two skittles.
Remind the child the rules of division.
Start with the highest category. Move the rack above the board. The child shares 10,000’s and reads the board.
Records the 2 on the paper.
Replace the beads into the tube, move the 10,000 rack on the tray, and place the cup upside down on its tubes.
Move the thousands rack above the board and repeat. Continue in this way for the rest of the categories.
Read the whole equation conventionally with the child.
Presentation 2: Dynamic Division
Layout as before and write a dynamic division equation. Example: 485,297÷4=
Follow the same process as above except when exchanging is required.
Write what was shared equally.
Take the left-over bead(s) and place it/them in the next cup to the right (the next family lower). The beads on the board go to their tube and rack moved to the tray.
Next, exchange the bead from the higher category in the cup for ten of the current category. The exchanged bead goes back into its corresponding tube. At the end if there is a remainder, leave it in the cup. The child will document the remainder with a r.
Return remainder to tube and read the entire equation together.
Note: You can show the child to place the commas if necessary.
Control of Error: None, however, the child needs a good understanding of the process.
Pedagogical Notes:
The child becomes independent in this work at the dynamic level. As soon as they understand the process in static, move them on.
Many 3-6 classrooms do not have this material and borrow it from an elementary classroom.