Mathematics

More rekenrek ideas: developing fluency with multiples

The rekenrek, a simple Dutch counting frame, is seeing rapidly increasing popularity in the world of education. 

In this blog, I’ll show how you can use it to build a child’s number sense and their fluency in working with multiples.

In my previous blog I explained the value of this simple tool for early mathematics. For me, introducing my granddaughter Daisy to the rekenrek highlighted just how useful it can be for early years arithmetic.

In that same blog I underlined three very important ground rules for using the rekenrek. I also explained how it can be used to build familiarity with number bonds from 1 to 20.

Two steps forward

The rekenrek or ‘calculating rack’ is an effective tactile tool for helping children to visualise number patterns and amounts. 

To build on Daisy’s experiences using her rekenrek frame for number bonds, next we used it for activities involving counting forwards and counting backwards.

The ability to count forwards and backwards in 2s, 5s and 10s becomes a very useful tool in addition, subtraction and multiplication.

Working with numbers in 2s, 5s and 10s from different multiples means that a child develops a feel for numerical rhythms and starts to recognise some useful and memorable patterns in the number system, including odd and even numbers.

Daisy is very capable when counting forward. This activity was intended to help her practise her skills in counting both forwards and backwards and build some fluency in working with whole numbers.

Here I’d like to add a quick reminder that we were using a 20-bead frame, with the 10 beads on the top row (5 red and 5 white) and 10 on the bottom in the same configuration. Unlike with other abacuses, every bead on the rekenrek has an identical unit value of one.

Frame of reference

I began by asking Daisy to slide the beads to the left in groups of 5, and to count as she did so, starting on the top row and moving to the bottom: 5, 10, 15, 20.

This was counting forwards in 5s

Then I asked Daisy to move the beads back to the right, in groups of 5, counting backwards in 5s: 20, 15, 10, 5.

Daisy repeated this counting forwards and backwards and she seemed quite confident.

A child slides some two beads along the top row of Dutch counting frame called a rekenrek

With the frame reset and all beads back on the right, I asked Daisy to slide 2 beads across a row and to count in 2s as she did so (2, 4, 6, 8, 10) and then continue onto the second row (12, 14, 16, 18 and 20) which was counting forwards in 2s.

Counting forwards in 2s seemed quite easy. The next step was for Daisy to move the beads back to the right, counting backwards in 2s, from 20. 

This is more of a challenge but the Rekenrek frame is helpful here: it offers the visual representation of the numbers, with beads in their groups of 5. 

Visualising number patterns

When Daisy moved 2 beads away to the right of the frame she could see the remaining beads on the left, 10 on one row with 5 red beads and 3 white beads on the other row. 

I helped Daisy to count these and see that, counting backwards in 2s from 20, the next number was 18. 

Move two more beds to the right and Daisy can see 10 beads together on one row and, on the other, 5 red beads and 1 white bead: 16. 

Daisy continued moving two beads away to the right and we counted the beads on the left for 14 and then 12. Continuing to count backwards in 2s from 10 was easy for Daisy.

We’ll need to repeat the counting backwards in 2s from 20 before Daisy becomes familiar with the pattern without needing the frame.

Granny Smith says…

  • One way to support this activity is by encouraging your child or grandchild to write down the numbers. When counting forwards in 2s and counting backwards in 2s from 20, they can see a number pattern of even numbers. When counting forwards in 5s and counting backwards in 5s from 20, they can see a number pattern of alternating odd and even numbers.
  • This is my 150th blog! I started blogging when my granddaughter was just 15 months old, and now she’s six. If you’re interested in exploring other educational topics covered on the site, then a great place to start is the categories page. I hope you find something that interests you!

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