The Rekenrek

"Every strand in the mathematics curriculum relies on numbers."

The Ontario 2020 Mathematics Curriculum

A rekenrek is read from the left side. This rack represents 6 on the top row. 

A rekenrek combines some of the key features of number lines, counters, and base ten materials. This tools consists of rows of ten beads, strategically broken into groups of five: five red beads and five white beads. 

The tactile and visual nature of a rekenrek can lead students to notice and use key counting and quantity principles, such as:

• subitizing (instant, visual recognition of small quantities)

• cardinality (the understanding that the last object counted in a set represents the total number in the group)

• anchors of 5 & 10 (rekenreks help show the relationship between a number and 5 or 10 - e.g., 9 can be thought of as "5 and 4 more" or as "1 less than 10")

• part-part-whole relationships (understanding that a set may have two or more parts)

• doubling and halving strategies

• counting on & counting back strategies for problems involving addition and subtraction

• making 10 strategies

So that everyone reads and uses the rekenrek in the same way, there are a few conventions to explain to students:

• each bead represents “one”

• there are always 10 beads on each row - 5 red beads and 5 white beads (there can be multiple rows to represent larger numbers)

• we represent numbers by pushing the beads from the right side of the rack to the left side of the rack

• we ‘read’ the number using the beads on the left hand side

• when in 'staring position' (aka showing 0), the white beads should be on the right

See the online text "Learning to Think Mathematically with the Rekenrek"  from The Math Learning Centre for more information and lesson ideas.

Building Fluency lessons are an important instructional approach to support students as they deepen their understanding of number and explore mental math strategies.

• The resource “Minilessons for Early Addition and Subtraction” by Fosnot, available in all WRDSB schools, consists of a number of lessons built around strings of questions. "Number strings" are sets of questions to be posed one at a time with a discussion after each question. For each question, students have time to think and share their strategies with the group. Each question builds on the previous one to uncover important mathematical ideas. The collaborative conversations that arise during math talks are where the learning happens! Initial lessons in this resource focus on representing and reading numbers on the rekenrek. Later lessons have students compare numbers and represent addition and subtraction. Finally, students are encouraged to use the rekenrek to represent their mental math strategies - as a tool to communicate their thinking. 

• In addition, the "Number Talks" resource by Sherry Parrish - also available in all WRDSB schools, includes many examples of number talks structured around the rekenrek learning tool (pg. 82-89).