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
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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
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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.
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“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