Cuisenaire Rods: Free Virtual Cuisenaire Rods Online

What Cuisenaire rods teach

Cuisenaire rods teach number as length. A child who puts a red rod and a light green rod end to end and finds that the train matches the yellow rod has discovered 2 + 3 = 5 without counting a single thing. The rods have no marks on them. The idea is to compare lengths and notice relationships, not to count units.

Each rod is 1 cm square in cross-section and from 1 to 10 cm long, and every length has its own color. Colors run in families: red, purple and brown (2, 4 and 8) are related by doubling; light green, dark green and blue (3, 6 and 9) are multiples of 3; yellow and orange (5 and 10) go together.

The rods are named for Georges Cuisenaire, a Belgian primary teacher who began experimenting with colored rods in 1931 and described his method in the 1952 book Numbers in Color. The educator Caleb Gattegno saw them in use in 1953, gave them their name and built a worldwide following for them.

How to use Cuisenaire rods on this board

Drag rods from the tray onto the grid. Each square of the grid is one white cube, so every rod snaps to whole centimeters and rods never overlap. A row of rods touching end to end is a train, and the board adds it up for you: the total appears at the end of the train and in the readout.

• Compare. Put two trains in neighboring rows, lined up on the left, to see which is longer.
• Find the difference. Put blue above yellow and find the rod that fills the gap: purple, so 9 − 5 = 4.
• Stand rods up. Rotate turns a rod on end, which is useful for building rectangles and walls.
• Change the whole. One whole is sets the rod worth 1, and every value in the readout changes to match.

Adding and subtracting with trains

Rods make number bonds visible. Ask for every two-rod train as long as yellow and children find white + purple and red + light green (and their turnarounds). Do the same for orange and they find all the ways to make 10: 9 + 1, 8 + 2, 7 + 3, 6 + 4 and 5 + 5.

The Common Core standards ask kindergartners to decompose numbers to 10 in more than one way (K.OA.A.3) and to find the number that makes 10 with any number from 1 to 9 (K.OA.A.4). First graders add and subtract within 20 using strategies like making ten and the relationship between addition and subtraction (1.OA.C.6), and they use properties such as the commutative property (1.OA.B.3). Each of these has a direct rod model:

1. Making ten. Orange is ten. 8 + 5 becomes a brown and a yellow; swap the yellow for a red and a light green, and the brown and red make orange: 10 + 3.
2. Missing addend. Dark green + ? = blue. Line them up and the gap is light green.
3. Turnaround facts. Light green + purple and purple + light green are both as long as black.

Multiplying with rods

Trains of one color are repeated addition. Three purple rods in a row are 4 + 4 + 4 = 12, and so are four light greens. Stack the three purples in three rows and you have a 3 by 4 rectangle covering 12 white cubes, the array model second and third graders use for multiplication (2.OA.C.4, 3.OA.A.1). Task card 8 asks for three different one-color trains of 12: it leads straight to the factors of 12.

Cuisenaire rods for fractions

Fractions are where Cuisenaire rods shine past 1st grade, because any rod can be the whole. With orange as one whole, five reds fill it, so red is 1/5; three reds are 3/5. Change the whole to brown and red becomes 1/4, purple 1/2.

On this board, set One whole is and switch Labels to Values. Every rod shows its fraction, and trains add exactly: with orange as 1, light green + black is 3/10 + 7/10 = 1. The Common Core standards define a fraction as parts of a whole in 3rd grade (3.NF.A.1) and ask students to explain equivalent fractions with visual models (3.NF.A.3). Rods let children build 1/2 = 2/4 = 4/8 with brown as the whole: one purple, two reds, four whites.

Cuisenaire rods by grade

Activities to try

• Staircase. Build the stair from white to orange, every rod lined up on the left. What do you notice about the steps?
• Rod families. Which rods can be made from reds alone? (The even ones.) From light greens alone? Which rods can only be made from whites? (Red, light green, yellow and black: 2, 3, 5 and 7 are prime.)
• Equal trains. Make a train with two rods. Make a different train, also of two rods, that's just as long. How many pairs can you find?
• Mystery rod. Hide the values, put a rod in a row and say "it's half of brown." A partner finds it.
• Fraction riddle. "If dark green is 1, what is light green?" Change the whole to check.
• Twelve ways. How many different trains of exactly two rods make 12? (Start with orange + red, then blue + light green, and keep going until the rods meet in the middle at dark green + dark green.)

Tips for teachers and parents

• Start with colors, not numbers. Gattegno's method names rods by color first. Turn labels off and talk about "the yellow" before calling it 5, so children focus on relationships.
• Ask "how do you know?" When a child says red is half of purple, ask them to show it: two reds alongside one purple. NCTM's teaching practices put this kind of reasoning at the center.
• Move from rods to drawings to equations. The What Works Clearinghouse practice guide on struggling students recommends moving from concrete objects to drawings to symbols. Build a train, sketch it on 1 cm graph paper, then write the equation.
• Keep real rods if you can. Wooden or plastic rods are hard to beat for small hands. Use this board for extra rods, exact fraction readouts, sharing and printing.

What makes these rods different

The board keeps the rods honest: they snap to a centimeter grid, never overlap, and add up as exact fractions of whatever whole you choose. It adds train totals at the end of each row, a staircase button, length, value and letter labels, rotation, pen and text labels, undo and redo, share links, a printable snapshot, keyboard controls and eleven self-checking task cards.

Families using Montessori materials can compare with the longer red-and-blue number rods. For fractions as lengths with numbers on them, try fraction tiles. Math programs that teach with rods or similar blocks are compared in the best homeschool math curriculum guide.