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Learning to Think Mathematically with the Rekenrek - Jeff Frykholm, Ph.d. THE REKENREK ABC MATH What is A more than E? What is B less than AO? There are B ducks on a pond. D more ducks waddle into the pond. How many ducks are there now? Do you have “D-ness”? Do you have “letter sense”? Meet the Rekenrek From start position…..what do you see? Allow students to come up with a discovery about the Rekenrek Cardinality, Subitizing, Decomposing and a understanding of 5 and 10 Rekenrek is a DYNAMIC ten frame The rule is to slide in groups rather than one by one Show Me….1-5 and Make 5 The importance of helping young children anchor on 5 and 10 cannot be stated strongly enough….this helps with mental math strategies for add/sub Show me 1, then 2, then 3, then 4, then 5 Move 2 on top…how many more do we need to move over to make 5? Show me 3…..now make 5 Do this with all combinations of 5 Then try it using two rows Show me 2 on the top row, how many on the bottom row do you need to make 5? Why would students need to move to using the bottom row? Show Me 5-10 This will help students understanding of cardinality. Ex. 5+1….they have to count all to get the answer…they don’t understand to start with 5 and add one more Slide 5 in one move. How did you know to do that? Then continue with this pattern 10, 9, 5, 7, 8, 6, 9, 10, 7 Now use two pushes and the bottom row to show me 8 Make 10, Two Rows Move 5 to the left….then make 10 Students should now know that 5 red beads and 5 white beads make 10 Show me 7….Now what do I need to make ten? You could do the last three on the top….OR…3 on the bottom I will show you a move…show 8 and cover the remaining ones. How many more do I need to make 10? Flash Attack Game This game will wean students from wanting to count every bead Show 6 for 2 seconds, then cover….How many did I show and how did you know? Show 19 for two seconds Then play Flash Attack with top and bottom row Doubles Slide one on top and one on bottom…. Then slide two on top and two on bottom…How many do you see? Demonstrate all the way up to 5. Let’s think about 7 and 7….They may see two sets of doubles. First, they will recognize that two groups of 5 red beads is 10. Next a pair of 2’s is 4. Hence, 7+7= (5+5)+(2+2)= 10+4=14 Almost a Double (Doubles +1) Show three on top and two on bottom…where is the double? 2+2…now what can you tell me about doubles +1? Pose these questions for students to figure out on the rekenrek Does 6+7=12+1? Does 3+2 = 4+1? Part Part Whole Move 6 beads to the left and cover the others…How many are on the top row? What could students say? “5 and 1 more is 6. I counted up to 10….7,8,9,10. 4 are covered” “I know that 6+4 =10. I see 6 so 4 more are covered. “I know that there are 5 red and 5 white beads on a row. I only see one white, so there must be 4 more”. Part Part Whole Continued Move 9 over (6 on top and 3 on bottom) and cover the rest. How many are missing? What could the students say? “5 whites and 2 reds are missing on the bottom. 4 whites are missing on top. 7 and 4 is 11.” “If I slid the 3 red beads under the cover, and slid 3 white beads to the left, then there would be 5 red and 5 white hidden on the bottom, and 1 white hidden on the top. So that is 11 hidden. “Well, 10 and 10 are 20. Right now I can see 9 which is close to 10. Since it is 1 less than 10, then 11 must be covered up.” Rekenrek Recording Paper It’s Automatic…Math Facts Give them 4+5….Show me 4 and then add 5 more beads anyway you want. Without having to count each bead, how do you know that there are 9 beads? You can also use flashcards that show the beads on the rekenrek Subtraction – Take Away Model I have 14 balls. You take away 6. How many are left? How could you show that on a rekenrek? Show 14 and cover the rest…(10 on top and 4 on bottom)…Then take away 6 (4 on bottom and 2 more on top). That leaves 8! Subtraction – Comparison Model I have 8 dollars and you have 6. How much more do I have? How can we show this on the rekenrek? 8 on top and 6 on bottom.. Compare the two rows. Find the beads that are in common on both rows. How many beads are left over? How many more beads on the top row? You can use your pencil to separate them… Game – Roll Three for 20 or Bust! Use 3 dice One red (0,1,2,3,4,5) One blue (2,3,4,5,6,7) One green (4,5,6,7,8,9) Roll the dice to determine the first three numbers to add…”I rolled a 6,7 and 4” Use rekenrek to show how I added these together (Move 6 and then 4 over. That makes 10. Then on the bottom move 5 red and 2 white which is 7. 10 plus 7 equals 17.) Roll 3 for 20 or Bust! Con.. Students must then decide to stay put or roll 1,2,3 dice to add more to the sum they have so far to come close or equal to 20 without going over. “I am going to try again…but I will use the red dice because I am only 3 away from 20” I rolled a 4! Oh that is too much. I went Bust! Play 4 rounds…the person with the highest sum wins…. TENS OR ONES GAME Choose a card from the 11-19 number cards. “I chose 19” Show that on the rekenrek Then draw a card from the take away tens or run away ones cards. “I chose a take away ten card” Move ten beads back to the right. That leaves 9. 19-10 is 9! I drew a 16 and a take away ones. I take the 6 ones away and it leaves 10. 16-6=10 Brainstorm…what is early number sense? What is Early Number Sense? Counting Cardinality Comparing Relationships Among Numbers (Spatial, 1 more/1 less 2 more 2 less, Anchors of 5 and 10, Part Part Whole) Pre Place Value (tens and ones) Place Value