1. Number Lines and Rekenreks: Tools that COUNT!!
Presented by: Angela J. Williams
AMSTI Math Specialist

2. Number Lines

3. What can I do to prepare students to use a number line flexibly?

4. Creating a Number Line Use: 50 beads of 1 color
50 beads of a 2nd color
Alternate beads every 10.

5. Activities with the Number Line
Count the beads by 1s (forward and backward).
12 and 21 are two numbers. Find them on your number line and describe them to your partner.
Can you count from 16 to 31?

6. Activities with the Number Line
Where is 47? How many tens are in this number? How many ones?
Find 35. What is 10 more? 10 less?
Find 34. Is it closer to 30 or 40? How do you know?
Start at 3. Count forward by 10s. What is the last number you say?

7. Activities with the Number Line
Start at 82. Count back three 10s. Where do you end?
Find 36. How far are you from 100? Are you closer to 100 or 0?
Count by 5s. How many sets of 5 are in 100?

8. Activities with the Number Line
Find 53. Add 15. Where do you end?
= 68
Find 36. Find 61. What do you add to 36 to get to 61?
36 + ___ = 61
Add three 10s to 28. What number do you have?
= 58

9. Activities with the Number Line
Find 66. Take 31 away. Where are you?
66 – 31 = 35
Find 75. Find 58. How far apart are they?
75 – 58 = 17
Find 47. Find 19. What is the difference between them?
47 - ___ = 19

10. Research Says:
“The use of number lines increases students’ ability to use numbers flexibly, estimate, and visualize numbers and therefore increases number sense.”
(Wright, 2001)

11. Resources
bead-strings?parent_node=
books.google.com/books?isbn=
linegame_first/

12. If this is what I want…. WHERE DO I START?

13. What the heck is a rekenrek?
Like the 10-frame, this tool helps students see the quantity of five as a whole and develop strategies to solve equations like 5+2, etc. It is also useful with equations like 8+7 because students can solve this in multiple ways…..like or or even 10+5….this tool also helps build the counting on strategy
The Rekenrek is comprised of two strings of ten beads each, strategically broken into two groups: five red beads, and five white beads.  Readily apparent in this model is an implicit invitation for children to think in groups of five and ten.  The strings of red and white beads (in groups of 5) provide a visual model that encourages young learners to subitize, i.e., to build numbers based on groups of five and ten.

14. How will a rekenrek help my students?
developing one-to-one correspondence
ability to subitize
understanding of fives and tens
composing/decomposing numbers
recognizing the structure of our base-ten system
basic fact fluency
hierarchical inclusion (nestedness of numbers)
strategies for addition and subtraction

15. Let’s Make a Rekenrek! Use: 10 beads of 1 color
10 beads of a 2nd color
Top row: 5 beads of 1st color.
5 beads of 2nd color.
Bottom row: 5 beads of 1st color.

16. Rekenrek Activity #1
Making 5 and 10 Visible

17. Rekenrek Activity #2
Quick Images

18. Number sense strategies
Rekenrek Activity #3
Number sense
strategies

19. Multiple ways to Find a sum
Rekenrek Activity #4
Multiple ways to
Find a sum

20. Understanding doubles
Rekenrek Activity #5
Understanding
doubles

21. Think Addition: Missing addends
Rekenrek Activity #6
Think Addition:
Missing addends

22. Resources
nrek_0308.pdf
5mathteachingresources.com/Rekenrek.html
/Learning+to+Think+Mathematically+with+the+R ekenrek.pdf
5mathteachingresources.com/support- files/large10frames1-10.pdf