Maths · Kindergarten to Grade 2
Free rekenrek worksheets
Seven free printable rekenrek worksheets (arithmetic rack), each with an answer key: read the number from eight pictured racks, color the beads to show ten numbers, making five, making ten, addition within 10 on one row, addition within 20 using both rows, and subtraction with the beads pushed back.
Read the rekenrek: what number is shown? (answer key)
What a rekenrek shows, with a labeled rack explaining the five red and five white beads in each row, then eight pictured racks to read, from 2 up to 17. Answer key on page 2. Free printable PDF.
Show the number: color the beads (answer key)
Ten numbers from 1 to 10, each with an empty rack: color the beads on the top row to show the number, reds first then whites. Answer key on page 2. Free printable PDF.
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Making five on the rekenrek (answer key)
Ten items on the five red beads: six pictures asking how many more make five, then four take-away items with beads pushed back. Answer key on page 2. Free printable PDF.
Making ten on the rekenrek (answer key)
Ten racks showing 0 to 10 beads pushed across: write how many more beads it takes to make ten. The beads still on the right are the answer. Answer key on page 2. Free printable PDF.
Addition within 10 on the rekenrek (answer key)
Eight additions shown on one row, with a dashed line splitting the beads into the two numbers: 3 + 4, 2 + 5, 1 + 6, 4 + 5, 5 + 3, 2 + 7, 6 + 2 and 4 + 4. Answer key on page 2. Free printable PDF.
Addition within 20 using both rows (answer key)
Eight additions with the first number on the top row and the second on the bottom row, totals from 11 to 20. Answer key on page 2. Free printable PDF.
Subtraction on the rekenrek (answer key)
Eight take-away facts within 10: the beads pushed back to the right are crossed out, so count what is left. Answer key on page 2. Free printable PDF.
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A rekenrek, or arithmetic rack, has two rows of ten beads, and each row is five red beads then five white ones. That split is the whole point: a child pushes seven beads to the left and sees five and two instead of counting one bead at a time. Beads are always pushed to the left on these sheets, so numbers up to five use only the red beads and six to ten are five reds plus some whites.
What is on each sheet
- Read the rekenrek. A labeled rack explaining the five and five split, then eight pictured racks to read, from 2 up to 17. The last two use both rows. Answer key on page 2.
- Show the number. Ten numbers from 1 to 10, each with an empty rack: color the red beads red and ring the white beads you use. Answer key on page 2.
- Making five. Ten items on the red beads only. Six pictures ask how many more make five, then four show all five reds with some pushed back for 5 minus 1 through 5 minus 4. Answer key on page 2.
- Making ten. Ten racks showing 0 to 10 beads pushed across, with the partner to write. The beads still waiting on the right are the answer, so there is no counting up. Answer key on page 2.
- Addition within 10. Eight sums on one row with a dashed line splitting the beads into the two numbers: 3 + 4, 2 + 5, 1 + 6, 4 + 5, 5 + 3, 2 + 7, 6 + 2 and 4 + 4. Answer key on page 2.
- Addition within 20. Eight sums with the first number on the top row and the second on the bottom row, totals from 11 to 20, including 10 + 10. Answer key on page 2.
- Subtraction on the rack. Eight take away facts within 10, where the beads pushed back to the right are crossed out so the child counts what is left. Answer key on page 2.
Every rack is drawn the same way, with the moved beads at the left end and the rest waiting at the right, so a child who has used a real rekenrek will recognize the pictures straight away.
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Complete pack · $2.99
All 7 sheets above, plus 5 bonus sheets you will not find on this page
7 free sheets + 5 bonus sheets in one print-ready PDF with a contents page. Instant, no ads, no account; the link is emailed to you so it works on any device. The 7 sheets above stay free.
- BonusDoubles to twenty on the rekenrek
- BonusMake ten to add: 8 + 5 and friends
- BonusRekenrek matching cards to cut out
- BonusBlank racks and how to build one
- BonusRekenrek test, 16 marks
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- Bonus
Doubles to twenty on the rekenrek - Bonus
Make ten to add: 8 + 5 and friends - Bonus
Rekenrek matching cards to cut out - Bonus
Blank racks and how to build one - Bonus
Rekenrek test, 16 marks
Teaching tips and common mistakes
How to use these worksheets
Print at 100% on A4 or US letter paper. A red pencil helps on the coloring sheet. These are recording sheets: the rack comes first, the paper second.
- Work with five, not one. Ask “how did you know?” and listen for “five and two” rather than counting from one. Seeing the group is the skill the rack is for.
- Flash the rack. Show a number for two seconds and cover it. Two seconds is on purpose: it is too short to count, so the child has to use the five and the ten.
- Say the number sentence out loud. “Six and four make ten.” Saying it while the beads are still in place is what links the picture to the fact.
- Order of the sheets. Read the rack, show the number, making five, making ten, addition within 10, addition within 20, subtraction. Making five and making ten are the two that pay off later, so do not rush past them.
- No rack at home? Twenty beads, two pipe cleaners and a shoebox lid make one in ten minutes. Keep the color order, five red then five white, or the five stops being visible at a glance.
Common mistakes to watch for
- Counting every bead. The commonest one. If a child counts one to seven every time, go back to the flash routine and to the making five sheet.
- Counting the beads on the right. Only the beads pushed to the left are being shown. The ones at the right are still waiting, which is also why they are the answer on the making ten sheet.
- Pushing from both ends. Always start from the left, or the red beads stop marking five.
- Starting again from one on the second row. On the addition within 20 sheet the top row is ten, so count on from ten rather than from one.
- Coloring the whole row. On the show the number sheet, only the beads being moved get colored, starting at the left.
- Treating the crossed beads as part of the answer. On the subtraction sheet a crossed bead has gone back to the right, so it is not counted.
Frequently asked questions
What is a rekenrek?
A counting frame with two rows of ten beads, five red and five white in each row. It was developed in the Netherlands by Adrian Treffers, and the name means calculating rack. Beads are slid to the left to show a number.
Why five red and five white?
So that five and ten can be seen without counting. Seven shows up as five reds and two whites, which is how children learn that seven is five and two, and later that eight and six is ten and four.
What age is a rekenrek for?
Kindergarten through grade two, roughly ages five to eight. The making five and making ten sheets suit the first year, and the addition within 20 and subtraction sheets the second and third.
Is a rekenrek the same as an abacus?
No. On an abacus the beads carry place value. On a rekenrek every bead is one, and the colors mark groups of five, so it is built for number sense rather than for calculation.
Can I use these without a real rack?
Yes, every sheet is a picture of a rack. A real one is still worth the ten minutes it takes to make, because pushing the beads is what makes the five stick.
More number sense printables
The other model that shows five and ten at a glance is the ten frame, on the ten frame worksheets page. For the color coded Montessori version of the same idea, see the Montessori bead stair worksheets. When the facts to twenty are secure, the next step is on the 2 digit addition worksheets page.
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