Allison Payne, Math FacilitatorJana Clark, Kindergarten Teacher

Bonnie Grimes Elementary

What the heck? Rekenreks?Learning to Think Mathematically with

the Rekenrek

Multiply the Magic Elementary ConferenceRogers Public SchoolsFebruary 18, 2013

Goals…Understand the use and application of

Rekenreks in grades K-2 to support number sense.

To provide practical applications for classroom use through materials and resources.

What are Rekenreks?Directly translated from Dutch, rekenrek

means “counting rack.”Developed by mathematics education

researchers in the Netherlands. Provides a visual model that encourages

building numbers in groups of 5 and 10, to use doubling and halving strategies, and to count-on from known relationships.

Combines features of the number line, counters, and base-10 models.

RekenreksHow is it different than an abacus?The rekenrek looks like an abacus, but differs

in that it is based on a five-structure and not a ten-structure system. It is comprised of two rows of 10 beads, each broken into two sets of 5 by color (i.e., in each row the first 5 beads are red and the next 5 are white).

Let’s warm-up with some problems!

8 + 7 = ?

What mental adjustments did you make as you solved this problem? Double 8, subtract 1? (8 + 8 = 16; 16 - 1 = 15)Double 7, add 1? (7 + 7 = 14; 14 + 1 = 15)Make 10, add 5? (8 + 2 = 10; 10 + 5 = 15)Make 10 another way? (7 + 3 = 10; 10 + 5 = 15)Other strategies?

Next problem…

5 + 8 = ?What mental adjustments did you make as

you solved this problem? Make 10, add 5? (5 + 5 = 10; 10 + 3 = 13)Make 10 another way? (8 + 2 = 10; 10 + 3 = 13)Use another fact? (If 8 + 4 = 12, then 8 + 5 = 13)Other strategies?

Next problem…

9 + 7 = ?What mental adjustments did you make

as you solved this problem? Make 10, add 6? (9 + 1 = 10; 10 + 6 = 16)Other strategies?

With the rekenrek, young learners learn quickly to “see” the number 7 in two distinct parts: One group of 5, and 2 more.

Similarly, 13 is seen as one group of 10 (5 red and 5 white), and three more.

A group of 10

3 more

Rekenreks…Rekenreks support the learning of skills of automacity, subitization and flexibility which contribute to students ability to learn number sense by making connections in mathematics based on experiences with a concrete and pictorial representation.

http://nycdoeit.airws.org/pdf/Rekenrek.pdf

Rekenreks reinforce…Automatici

tySubitizatio

nFlexibility

… the ability to produce answers in a few seconds by relying on thinking of the relationships among the operations rather than recalling answers (e.g., 3+5=8).

… the ability to recognize the number of objects in a set without actually counting them.

… is an advanced stage of general number sense and involves understanding how to add and subtract with strategies.

What else do rekenreks reinforce?Read excerpt, pgs. 3-4 of

Learning to Think Mathematically with the Rekenrek, J. Frykholm (2008)

As you read, think about how you have traditionally taught these concepts and share out.

Is there a place for the rekenrek as an additional teaching tool?

Research findingsTournaki, N., Bae, Y.S., and Kerekes, J. (2008). Rekenrek: A

Manipulative Used to Teach Addition and Subtraction to Students with Learning Disabilities. Learning Disabilities: A Contemporary Journal, v6 n2, p41-59.

This quasi-experimental study supports the use of the strategy. The study participants included 45 first-grade students with documented learning disabilities who were at least two years behind in both mathematics and reading. Participants were divided into a control and two treatment group. Only the treatment group 1 used the rekenrek, while the treatment group 2 had pencils and paper, plastic counters, and a laminated sheet that provided tables for organizing discussions and the control group had the usual classroom instruction. Findings showed a significantly positive effect on the students’ post-test scores and understanding of number sense.

Example 1: One SecondHow many Red beads?

Example 2

Example 3

Example 4

THE BEST THINGS ABOUT A REKENREK

It is contained. There will be no beans, blocks, cubes, counters or bears to pick up around the room for weeks after using them.

It is coded for easy recognition of working in the base 10 system. The beads are

color coded in groups of 5 which enable students to see numbers quickly. Each row contains 10 beads which also lends to quick number identification and manipulation.

http://www.dilly-dabbles.com/2012/04/magnificent-math-tool-rekenrek.html

THE BEST THINGS ABOUT A REKENREK…It is kinesthetic

and visual.Students physically

manipulate the beads and see the numbers. This is an added help that is not given to students when using a number line.

It is available in three sizes: a single 10 row for preK-K

students or for students who may need extra support,

a double row containing 20 beads for K-2 students easily facilitates working with all problems within sums/differences within 20

a ten row board containing 100 beads for use with all students allows many options for number work.

Students and Teachers in action

Students in ActionMaking 5 on a Rekenrek—YouTube

Connecting to the classroom…How important is it for students to have an

understanding of place value?How important is it for students to know

5’s?How do you teach and develop the concept

of grouping 5?How important is it for students to have an

understanding of 10?

Common Core Standards…

Kindergarten Standards

Common Core Standards…

1st grade Standards

Rekenrek Number TalkWhat mathematical

understandings and misconceptions are being addressed?

How does the rekenrek provide opportunities for differentiation within the number talk?

K Rekenreks from Number Talks book

What instructional strategies does the teacher use to engage the students in the mathematics?

How does the teacher use rekenreks as a tool to build fluency with small numbers?

What role does the game “Can You Guess My Way? Play in the number talk?

Curricular Activities SequenceWeek 1: Number Sense Zero to Five

Day 1. 1. “Five Little Monkeys” song

(with showing fingers) 2. “Five Frame” activity:

demonstration of counting with “Five Frame” paper and plastic counters

3. “Five Fingers” activity: counting student’s five fingers in different ways (e.g., one thumb and four fingers, two fingers in one hand and three in the other)

4. Introducing rekenrek and comparison of rekenrek with “Five Frame” and with student’s 10 fingers and toes

Day 2.

1. “Five Little Monkeys” song (with showing fingers)

2. “Five Frame” activity – “What Is Five Made Of” activity: using the “Five Frame” and counters, student fills the frame in different ways (e.g., teacher says “if I put 2 chips on the frame, how many counters do you have to put on the frame to make 5?”)

3. “Five Fingers” activity: showing and counting two fingers in many different ways

4. Identification of the five structures on the rekenrek by mentioning the two different colors (red and white). Comparison of the five structure of rekenrek with student’s fingers and toes.

Source: Tournaki, N., Bae, Y., & Kerekes, J. (2008). Rekenrek: A Manipulative Used to Teach Addition and Subtraction to Students with Learning Disabilities. Learning Disabilities -- A Contemporary Journal, 6(2), 41-59.

Curricular Activities Days 3-5Day 3. 1. “Five Little Monkeys” song (with

showing of fingers) 2. “Five Frame” activity – same as Day 2 3. “Five Fingers” activity: showing and

counting three fingers in many different ways

4. “Count by Fives” activity: figuring out that there are four of fives in a rekenrek (comparing it with fingers and toes)

Day 4. 1. “Five Little Monkeys” song:

Teacher and student taking turns counting down from 5 to 0 (student semi-independent)

2. “Five Fact Family” activity: on a piece of paper teacher writes “5” and student completes (e.g., 4 and 1, or 2 and 3.The “Five Frame” is available for assistance)

Day 4…3. “Five Fingers” activity: showing

and counting four fingers in many different ways

4. Show and tell of the “Five Little Monkeys” song with the rekenrek (practicing more/less, part/whole

Day 5. 1. “Five Little Monkeys” song –

same as Day 4 2. “Five Fact Family” activity – same

as Day 4 3. “Five Fingers” activity – showing

(without counting) five fingers in many different ways

4. “Five Fact Family” activity: on a piece of paper teacher writes “5” and student completes (e.g., 4 and 1, or 2 and 3.The rekenrek is available for assistance)

Source: Tournaki, N., Bae, Y., & Kerekes, J. (2008). Rekenrek: A Manipulative Used to Teach Addition and Subtraction to Students with Learning Disabilities. Learning Disabilities -- A Contemporary Journal, 6(2), 41-59.

CGI and RekenreksUsing the handout of CGI type problem

starts, let’s model the problems using the rekenrek.

Classroom Considerations…Procedures for handing

out materialsHow will you teach kids

how to position them?Sliding vs. tipping

beadsNoiseCleaning them!StorageCommercial vs.

HandmadeFormative assessment

Classroom seating…carpet/desk

Collaboration…shoulder partners/talking partners

Math Journals/Notebooks

Desk work—drawing their own rekenrek models

ResourcesNumber Sense Routines: Building Numerical Literacy Every Day in Grades K-3 by Jessica Shumway

Chapter 3

Number Talks: Helping Children Build Mental Math and Computation Strategies by Sherry Parrish

Chapter 3 & 4

Blanke, B. (2008). Using the rekenrek as a visual model for strategic reasoning in mathematics. The Math Learning Center: Salem, OR.

GRANT OPPORTUNITIES

Rogers Early Risers Rotary Club and the Rogers Public Education Foundation; 3/15 deadline

Internet ResourcesVirtual Rekenrek w/directions up to 10 rows

Free App on iTunes!

Dreambox Tools

Let’s make some RekenreksMake a simple rekenrek with basic items for

individual student use.

Let’s Revisit our Goals…Understand the use and application of

Rekenreks in grades K-2 to support number sense.

To provide practical applications for classroom use through materials and resources.

How did we do?