What Is a Rekenrek?

A rekenrek is a bead rack with two rows of ten beads. Each row is 5 beads of one color followed by 5 of another, so a child can see a number instead of counting it: 7 is 5 and 2 more, and 13 is a full row and 3 more. The name is Dutch for “calculating frame”, and schools also call it a number rack or bead rack. Kindergarten and first-grade classes use it for numbers to 10 and 20, making ten, and doubles. Some preschools start with one row of five.

The most useful thing to do at home is to slide the beads across in one push and ask how many, without counting. You do not need to buy a rekenrek: a free paper rekenrek and a deck of “how many beads?” cards are in this guide.

What is a rekenrek?

A rekenrek is a frame with two wires, each holding ten beads: 5 of one color, then 5 of another, often red and white. The beads start at the right end of each wire, and a child slides them to the left to show a number. Only the beads on the left count.

The name means “calculating frame, or arithmetic rack”, in the words of Barbara Blanke’s 2008 guide for The Math Learning Center. Blanke credits its design to Adri Treffers (Adrian in her guide), a mathematics curriculum researcher at the Freudenthal Institute in the Netherlands. Schools that use the Bridges in Mathematics curriculum call it a number rack. A 100-bead rekenrek, with ten rows, works with bigger numbers.

A rekenrek is not an abacus, although it looks like one. An abacus’s rows are place-value columns, so a bead on one row can stand for 1 and a bead on the next for 10. On a rekenrek, every bead is 1, and the change of color after the fifth bead is the point. Blanke writes that it is “not based on place value columns or used like an abacus”. Like a ten frame, it shows numbers in fives and tens, with sliding beads instead of counters in boxes.

Why do schools use a rekenrek instead of counting one by one?

Schools use a rekenrek so that a child stops counting every bead and starts seeing numbers in groups of 5 and 10. With a rekenrek, writes Jeffrey Frykholm in his 2008 book of rekenrek lessons, “the child will see the number 7 as two distinct parts: one group of 5, and two more.”

Seeing in fives and tens is the basis of four strategies in the kindergarten and first-grade standards:

• Making ten. Show 8 on the top row and 2 beads are left at the start, so 8 and 2 make 10. Finding the partner that makes 10 is kindergarten standard K.OA.A.4.
• Teens as ten and some more. A full top row and 3 more is 13, which is how kindergarten standard K.NBT.A.1 describes the numbers from 11 to 19: “ten ones and some further ones”.
• Doubles and near doubles. Six beads on each row make 12, so 6 on top and 7 below is a double and 1 more, 13. First-grade standard 1.OA.C.6 lists “creating equivalent but easier or known sums” among the strategies within 20.
• Taking a number apart. The same 7 can be 5 and 2, or 4 and 3, depending on how the beads are pushed (K.OA.A.3).

A 2008 study tested the rekenrek with children who find math hard. Nelly Tournaki and colleagues gave 45 first graders with learning disabilities fifteen 30-minute one-on-one lessons over three weeks. The children taught with a rekenrek scored significantly higher on an addition and subtraction test within 20 than children given the same lessons without one, and than children with classroom teaching only. It is one small study: it shows the rekenrek helped these children, not that it beats every other method.

Counting still has a place: a child who sees 5 and 2 can check by counting. Seeing a small group at a glance is called subitizing, and the same fives are on two hands, where 7 is a whole hand and 2 fingers. The rekenrek is one of several models on your child’s homework that come from school curricula rather than the standards.

What age is a rekenrek for?

Children use a rekenrek from pre-K to first grade: one row to 10 at about age 4, numbers to 10 and making ten in kindergarten, and two rows to 20 in first grade.

Age or grade	What children do on a rekenrek	Common Core	Texas
Pre-K (age 4)	Use one row, or the first five beads: show 1–5, then up to 10; see small amounts at a glance	None	PK4.V.A.4, PK4.V.A.7
Kindergarten	Show 1–10 in one push; take numbers to 10 apart; make 10; see teens as ten and more	K.OA.A.3, K.OA.A.4, K.NBT.A.1	K.2(D), K.2(I)
1st grade	Use two rows to 20 for doubles, near doubles, and making ten to add and subtract	1.OA.C.6	1.2(A), 1.3(C), 1.3(D)

Texas makes seeing an amount without counting a standard in its own right. Its kindergartners “recognize instantly the quantity of a small group of objects” (K.2(D)), and its first graders “recognize instantly the quantity of structured arrangements” (1.2(A)). The 2022 Texas Prekindergarten Guidelines name bead sliding directly: a 4-year-old may “slide beads on a bracelet or abacus” to show 5 as 4 and 1, or 3 and 2.

A kindergartner who still counts every bead in the fall is on time. Blanke writes that with a rekenrek, kindergartners “can start making the transition about the middle of the school year” from counting by ones to using 5 and 10. Eureka Math’s kindergarten Module 1 lists 20-bead and 100-bead rekenreks in its materials and uses one in its first lessons.

How to make a rekenrek at home, or print one free

You do not need to buy a rekenrek: print one, make one, or use one on a screen.

1. Print the paper rekenrek. Our Paper Rekenrek is a frame with two printed wires and a “start” mark at the right. Its forty bead tokens cut out along straight lines: 5 dark and 5 light for each row, which your child slides along the wires, and a spare set. Its two counter mats need no scissors: put a bean or a piece of cereal on each printed bead.
2. Make one. Thread 10 pony beads onto each of two pipe cleaners or lengths of string, 5 of one color and then 5 of another. Tie or tape the two rows across a piece of cardboard or a shoebox lid, with room to slide.
3. Use one on a screen. The Math Learning Center’s free Number Rack app shows rows of beads that slide.

The How Many Beads? cards are the practice deck: one row to 10, two rows from 11 to 20, then doubles and near doubles. No card carries a numeral, so your child reads the beads, and the key after the cards matches each number to its card by position. Both PDFs print in black and white, with the fives told apart by dark and light beads, and each ends with a page of instructions for grown-ups. Other homemade math tools are in our guide to math manipulatives.

Free PDF · no sign-up

Free printable paper rekenrek and cards

Two free PDFs in black and white, with no account and no email, in teaching order: a paper rekenrek with counter mats, then How Many Beads? cards. Start with the rekenrek, and add the cards once your child can show a number on it. The cards have an answer key, and every PDF ends with a page of instructions for grown-ups on why, what for, and how to use it.

1. 1Paper Rekenrek (PDF)40 beads to cut out · 4 pagesDownload
2. 2How Many Beads? (PDF)32 cards · answer key included · 6 pagesDownload

How to use a rekenrek with your child

Use a rekenrek for a few minutes at a time, in six steps that take your child from pushing beads to seeing numbers to 20. The order follows Frykholm’s lessons, and his “Flash Attack” game, step 4, has a stated aim: “to wean students from their inclination to count every bead.”

1. 1

   Start position, and play

   Slide all the beads to the right end of each row. This is the start position, and only beads on the left count. Let your child play for a few minutes and find out that each row has two colors, with 5 beads of each.

2. 2

   Show me 1–5, in one push

   Say a number from 1 to 5. Your child slides that many beads to the left in one push, not one bead at a time, then returns them to the start. Use only the top row.

3. 3

   Show me 6–10 as 5 and more

   Ask for 7. Your child pushes all 5 dark beads and 2 light ones, and says how they knew: 5 and 2 more. If one push is hard, push 5 first and then the rest.

4. 4

   Flash and ask how many

   On a rekenrek, flashing means you push some beads to the left, show them for about two seconds, and cover them with your hand. Your child says how many and how they knew, such as 5 and 3. The short look is what stops your child counting every bead.

5. 5

   Make 10

   Show 8 on the top row and ask how many more make 10. The answer is the 2 beads still at the start, so 8 and 2 make 10.

6. 6

   Two rows to 20

   Use both rows. A full top row and 3 more is 13. Then show doubles, such as 4 on each row for 4 + 4, and near doubles, such as 4 on top and 5 below, which is a double and 1 more.

Steps 3 and 5 show a number as two parts, the idea behind a number bond. Making 10 is also how your child adds past 10. For 8 + 6, show 8 on the top row and 6 below. The top row needs 2 more to make 10, so the 6 splits into 2 and 4, and the answer is 10 and 4. It is the Common Core’s own example for making ten, “8 + 6 = 8 + 2 + 4 = 10 + 4 = 14”.

Rekenrek games and activities to do at home

Four rekenrek games use the cards or the beads for a few minutes at a time, and each ends with your child saying how they knew the number.

• How many beads? Turn over a card, say how many beads are on the left, and check on the key.
• Snap the same number. Find two cards that show one number two ways, such as 8 on one row and 4 on each row.
• Hide and guess. Slide 10 beads to the left, cover some with your hand, and ask how many are hidden.
• Race to 20. Take turns rolling a die and sliding that many more beads. Say each total as ten and some more, such as “ten and four”, and the first to fill both rows wins.

Common rekenrek mistakes

Five mistakes are common on a rekenrek, and each has a fix you can make on the spot.

• Counting every bead. Your child touches each bead and counts from 1. Flash the beads for two seconds instead, and ask “how many dark ones?” first.
• Pushing one bead at a time. Ask for the number in one push, and count to three out loud before the push.
• Starting from the wrong side. Your child counts the beads on the right. Say “start position” every time, and remind them that only the left side counts.
• Two rows too soon. Your child mixes up the rows before 1–10 is quick. Stay on the top row until it is.
• Reading the colors as the number. Your child says “three white” for 8. Ask for the dark beads first: “5 and how many more?”

When a rekenrek is hard, make it smaller: Frykholm suggests one row of five or ten beads for the youngest children. Slow the flash down, too. If counting a group of objects to 10 is still hard, practice that counting first and come back to the rekenrek later.