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“In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics.” The teacher’s role is to “stimulate students to learn by setting up experiences and by guiding investigations.” – Teaching Children Mathematics, Clements, 1999 What is a rekenrek? • Dutch for “calculating frame” • Developed at the Freudenthal Institue in the Netherlands • Allows children to build on their innate ability to subitize small groups Example: 6 can be seen as 5 + 1 How is a rekenrek different than other manipulatives? “In the United States, the manipulatives most commonly used are single objects that can be counted – connecting cubes, bottle caps, counters, or buttons. While these manipulatives have great benefits in the very early stages of counting and modeling problems, they do little to support the development of the important strategies needed for automaticity. In fact, at a certain point they begin to reinforce low-level counting strategies.” - Contexts for Learning Mathematics, Fosnot & Uittenbogaard “For example, to solve 6 + 7 with cubes, children need to count out 6, then 7, and then either count on as they combine or (as is most common) count a third time. Because the materials have no built-in structure, they offer little support for the development of alternative strategies.” 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 5, 10, 13 How does a rekenrek work? • It is different than an abacus which is based on place value • There are two rows of ten, each broken into two sets of five (5 white beads, 5 red beads) • Beads pushed to the left represent amount being calculated • Beads pushed to the right are not being used. not being used What is a Rekenrek used for? • Counting: one to one correspondence • Cardinality: last number counted represents the group • Subitizing: to perceive the number of (a group of items) at a glance and without counting • Composing & Decomposing Numbers :a whole is made up of parts & these parts can be rearranged • Anchoring with 5 & 10 • Strategies of Addition & Subtraction • Doubling How do I teach with rekenreks? Minilessons! • Whole class or small group • Students sit in a “U” shape or semi-circle • Chart or whiteboard to represent math symbolically • Opportunity for pair talk • Encourages shared thinking Introducing Rekenreks • Inquiry Lesson: What do you notice about this rekenrek? How many red/ white beads? Can I turn it around? How many beads in all? Play with your rekenrek and tell me one thing you discovered. • Tips: start with only one row use consistent language to build independence: “start position” encourage students to slide beads in groups, not one by one “I need 4 beads to the left. Four Is one less than 5. So, I do not need all fie beads. I can leave one behind and slide four beads across.” Lessons to build Number Sense Quick Flash • Flash rekenrek and ask how many did you see? Copy Cat • Flash rekenrek and have students try to make the same How many moves? • Can you make 8 in 1 move? 2 moves? 3 moves? How many ways? • How many ways can we make 5? Guess My Way • I made 7. Can you guess my way? How is my way different than your way Make Five (or Ten) • Show 2 and ask how many more to make 5? • Show 7 and ask how many less to make 5? • Count On Mentally: 2, 3 Symbolically: 2+1=3 Mentally: 5, 6, 7 Symbolically: 2+ 5 = 7 • Commutative Property Mentally: 3, 4 Symbolically: 1+ 3 = 4 Mentally: 3, 4 Symbolically: 3+1=4 How are they different? How are they the same? • Doubles Prompts: What do you notice? How can you count? Big Ideas: Symmetry Skip counting Doubling Halving Doubles Activity Skills: – – – – Add two numbers to find sums to 20 Use 5’s and 10’s to anchor addition and subtraction facts See the usefulness of doubles Teach odd & even numbers Activity: 1. 2. 3. Show 10 frame Students try to build that number with rekenrek Challenge students to build the number as a double Variation: - Show two ten frames Identify numbers as odd or even • Make 5 and 10 • Guess my way – teacher hides or covers rekenrek • Turn around facts 6 + 4 = 10 • Use 2 rows 4 + 6 = 10 7 + 3 = 10 • Use 1 row 7 + 3 = 10 • Make 5 and 10 Follow-Up Activities • Building through 10 Mentally: 8, 10, 11 Symbolically: 8 + 2 + 1 = 11 8 + 3 = 11 What else can I use rekenreks for? Games Target Think Addition 1. 2. 3. Draw a number card (0 – 10) & build number Draw Target Number Card (11 – 20). This is the number they want to get to. Think of how many and which beads they will move. Partners share methods and then make moves. Add a Context Online Games • http://www.fi.uu.nl/toepassingen/0 0204/toepassing_rekenweb.xml?sty le=rekenweb&language=en&use=ga me • http://www.ictgames.com/resource s.html Math Rack App http://www.mathlearningcenter.org/web-apps/number-rack/ Questions • handouts