Virtual rekenrek (20-bead rack)

What a rekenrek is

A rekenrek, Dutch for "counting rack," is a frame with two rods of ten beads. On each rod the first five beads are red and the next five are white. Beads start on the right, and you push them to the left to show a number. Because the colors change at five, a child can see 7 as "five and two" without counting each bead.

On this page you tap a bead to push it and every bead to its left across together, or drag beads along the rod. Tap a bead that is already on the left to send it and the beads after it back. The Top row and Bottom row buttons do the same one bead at a time. The readout gives the total, the colors on each row, and points out doubles and near doubles.

Why it helps

The rekenrek nudges children away from counting by ones. The groups of five and ten make amounts recognizable at a glance, the way you recognize a face. Two rows invite doubles, such as 6 on top and 6 below, and near doubles: 6 + 7 is a double 6 and one more.

Common mix-ups

• Pushing beads one at a time and counting each one. Ask the child to show a number "in one push" so they think about fives first.
• Counting the beads on the right instead of the left. Agree that only beads pushed to the left count.
• Thinking 13 must be 10 on top and 3 below. It can also be 7 + 6 or 8 + 5; the Show me challenge asks for more than one way.
• Missing that a near double is a double plus or minus one. Make 7 and 7, then take one bead back and talk about what changed.

A 10-minute rekenrek routine

• Call out numbers from 1 to 10 and ask the child to show each on the top row in one push.
• Turn on Hide the total. Show an amount, ask "How many?" and "How did you see it?" before turning the total back on.
• Show a double, such as 4 and 4, then add one bead to the bottom row and ask for the new total.
• Press Show me a number. After the child builds it, ask for another way and watch the list of ways grow.

Where it fits by grade

• Kindergarten: split numbers up to 10 in different ways (K.OA.A.3), find the number that makes 10 (K.OA.A.4), and see 11 to 19 as ten ones and some more (K.NBT.A.1). In England, this is Year 1 work on numbers to 20.
• Grade 1: add within 20 using making ten and easier known sums, such as 6 + 7 = 6 + 6 + 1 (1.OA.C.6). In England, Year 2 children recall facts to 20.
• Grade 2: know all sums of two one-digit numbers from memory (2.OA.B.2).

Learning more

Adding and subtracting within 20 are skills on Eurekami's skill map, and Daily Practice brings them back when they start to fade. Lessons draw diagrams live from the numbers in each question, so a child sees the same tens and ones they built here.