Kindergarten Materials Rekenreks, Ten Frames, and Interactive Boards September 2016 @HCPSSElemMath

Goal 1: Every student achieves academic excellence in an inspiring, engaging, and supportive environment. The instructional program is rigorous, globally-relevant, and aligned with international and/or nationally recognized college and career readiness standards. (Outcome 1.1) Students have equitable access to a rigorous instructional program. (Outcome 1.2) We’re doing this because we believe in this.

What is a rekenrek? Directly translated, rekenrek means calculating frame, or arithmetic rack. Developed by Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in Holland. Also called a math rack.

What is a rekenrek? It is comprised of two strings of 10 beads each, strategically broken into groups of five. As a result, the rekenrek helps students to think in groups of 5 and 10. The structure of the rekenrek offers visual pictures for young learners, encouraging them to “see” numbers within other numbers.

Rekenrek in action Watch the following short video: https://www.youtube.com/watch?v=B4_YvwpIQwU What do you notice about the progression the teachers use with the rekenreks? Discuss what they see and notice.

Let’s get started… Show 7 on your rekenrek. How do you think students will see and understand 7? Show 13 on your rekenrek. How do you think students will see and understand 13? If teachers show 5 reds and 2 whites in one row, then maybe they will say 5 and 2. Teachers might show 3 on the top and 4 on the bottom, so students could see that combination. The idea is that the rekenrek builds number relationships in many different ways. Do teachers think of 13 as 5+5+3 or do they see it as 10+3?

Early work with rekenreks Have students show a particular quantity between one and ten. With one row at first and then moving to representing numbers using two rows. Have students show 5 or 10. Have students show 11 through 20.

Not My Way Teacher makes a number. For example, the number 8, using top and bottom row. Students try to make the same configuration. Teacher gives meaningful clues to help students find the configuration. MST- model this game with the participants before you show the bullet points Adapted from Sherri Parrish, Number Talks

Two Moves Teacher selects a number card from the 11-20 pile. Challenge students to make the number with just “two moves”. Why would we do this activity with students? MST is encouraged to play this game before showing direct instructions. Discuss the significance of two moves when making the number 14– seeing it as 10 and 4. Number cards 1-20 are available in the resource bank.

Can You Build It? Using the “one and two more cards”, teacher selects a card and reads the condition to students. Students build the number. How should students build the numbers (one row/both rows)? Does it matter mathematically? MST is encouraged to play this game before showing direct instructions. Again, the discussion is around one row or two rows and how students will understand the quantity. There are pros and cons to always filling the first row- may be the more basic idea, but it also reinforces the idea of 5 and 10. Two rows seems to represent a more flexible thinker, but in certain cases, like 13- seems like good math conversation to wonder if 10 and 3 or 6 and 7 is the “better way” to “see” that number. Idea and materials from Didax, Working with the Rekenrek, gr.K-1

Compare, Compare Shuffle a deck of 1-10 number cards and face down in a pile. Each student (in partners) draws a card from the pile and builds the number. They then compare their representations to see who has the larger quantity. That student wins the cards. Students play five rounds and the player with the most cards wins. How can you modify this game? MST is encouraged to play this game before showing direct instructions. One modification: as students advance they can play the game with cards 11-20. Number cards 1-20 are available in the resource bank.

Dominoes and Rekenreks Student selects a domino from a container. Student represents the quantity of pips on the domino on the rekenrek using the top and bottom rows. Student then records and solves the addition sentence in their math journal. What mathematics ideas are highlighted with this activity? MST is encouraged to play this game before showing direct instructions. Encourage teachers to understand that this activity helps students connect different visual models and makes connections to addition. Domino cards are available on the resource bank if unavailable.

Five Will Win Review the directions on the “Five Will Win” game board sheet. What will you look for as your students play this game? MST is encouraged to play this game before showing direct instructions.

Closest to 20 Player one rolls two numbers. Player should write those numbers on their own recording sheet and they should build the sum on their rekenrek. Student can decide if they want to roll for a third number, remembering that the goal is to be as close to 20 without going over. Player two take a turn. Both players compare their sums to determine who wins each “game”. Who is this game appropriate for in Kindergarten? MST is encouraged to play this game before showing direct instructions. The conversation here should be around students who are ready for 3 addends and reasoning about whether to take the third roll. Generally I see this as students who are working on 1st grade standards or closer to the end of the year for on grade level students. Idea and materials from Didax, Working with the Rekenrek, gr.K-1

Online Rekenrek Options http://www.mathlearningcenter.org/web-apps/number-rack/ Dreambox Teacher Tools If time permits, consider giving teachers time to explore both online options for rekenreks. With Dreambox, you will need them to log on to dreambox.com and click resources and then click teacher tools. Dreambox has a design where the link changes everyday so I can’t link it here in the powerpoint, and teachers will need to log in on any particular day they want to use it with students.

What do you notice? How are the rekenrek and the magnetic ten frames are alike and different? Both are visual models that connect to 5 and 10. Both models can help with student understanding of number relationships. Both models can support student understanding of addition and subtraction. Do both models support subitizing? Subitizing is “instantly seeing how many”, at glance without counting- do both models help with this?

Will it work? Consider the activities we just did with rekenreks: Not My Way, Two Moves, Can You Build It?, Compare Compare, Dominoes, Five Will Win, and Closest to 20. Can you do these same activities with the double ten frames? Allow participants to reflect on this question. The activities all work essentially the same way since we are dealing with two models that represent up to 20 and tie to 5 and 10.

Online Ten Frame Options http://illuminations.nctm.org/Activity.aspx?id=3565 Dreambox Teacher Tools If your teachers don’t already use this illuminations, give them a minute to explore. With Dreambox, you will need them to log on to dreambox.com and click resources and then click teacher tools. Dreambox has a design where the link changes everyday so I can’t link it here in the powerpoint, and teachers will need to log in on any particular day they want to use it with students.