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

Number Lines

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

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

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?

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?

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?

Activities with the Number Line Find 53. Add 15. Where do you end? 53 + 15 = 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? 28 + 30 = 58

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

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)

Resources http://nzmaths.co.nz/resource/number-lines-and- bead-strings?parent_node= books.google.com/books?isbn=0826486878 http://www.smartfirstgraders.com/number-line.html http://www.education.com/activity/article/number linegame_first/

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

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 5+5+2+3 or 7+7+1 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.

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

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.

Rekenrek Activity #1 Making 5 and 10 Visible

Rekenrek Activity #2 Quick Images

Number sense strategies Rekenrek Activity #3 Number sense strategies

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

Understanding doubles Rekenrek Activity #5 Understanding doubles

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

Resources http://bridges1.mathlearningcenter.org/media/Reke nrek_0308.pdf http://www.therekenrek.com/2013/ http://www.k- 5mathteachingresources.com/Rekenrek.html https://cesa5mathscience.wikispaces.com/file/view /Learning+to+Think+Mathematically+with+the+R ekenrek.pdf http://www.k- 5mathteachingresources.com/support- files/large10frames1-10.pdf