1. Rekenreks & Number Talks Just For Giggles...

2. Number Talks Sherry Parrish Sherry Parrish: Number Talks: Building Numerical Reasoning

3. Solve Mentally 38 + 37

4. Number Talks Classroom conversations around purposefully crafted computation problems that are solved mentally Problems focus on number relationships and number theory Five to fifteen minutes Allow students to construct and make sense of important foundations in numbers and number relationships

5. Key Components of Number Talks 1.Classroom environment and community 2.Classroom discussions 3.The teacher’s role 4.The role of the mental math 5.Purposeful computation problems

6. 1. Classroom Environment and Community Building a cohesive classroom community is essential for creating a safe risk- free environment for effective number talks. Students should feel comfortable sharing responses Culture of the classroom should be one of acceptance- accept, respect and consider all answers This all takes time to establish Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions.

7. 2. Classroom Discussions Allows students the opportunity to… Clarify their own thinking. Consider & test other strategies to see if they are mathematically logical Investigate & apply mathematical relationships. Build a repertoire of efficient strategies. Make decisions about choosing efficient strategies for specific problems.

8. 3. The Teacher’s Role Shift from being the sole authority in imparting information to the role of facilitator, questioner, listener, and learner. Need to listen to students’ thinking Shift from “What answer did you get?” to “How did you get your answer?” Provide appropriate wait time for the majority of the students to access the problem.

9. 4. The Role of Mental Math Mental computation is a key component because it encourages students to build on number relationships to solve problems instead of relying on memorized procedures. No paper pencil Helps strengthen students’ understanding of place value

10. 5. Purposeful Computation Problems Crafting problems that guide students to focus on mathematical relationships is essential Careful planning is necessary to design “just right” problems for students

11. Number Talks - Hand Signals Encourage student communication

12. Four goals for K-2 Number Talks 1.Developing Number Sense 2.Developing fluency with small numbers 3.Subitizing 4.Making tens

13. Eight Common Strategies for Addition 1.Counting All (K and beginning of 1 st - not yet able to add on to another number) 2.Counting On (start with one of the addends and counts on) 3.Doubles/Near Doubles (making closest double- 19+18, 20+20=40, then subtract 3 4.Making Tens (8+9, decompose 8 into 7+1, then add 1 to 9 to make ten, then 10+7) 5.Making Landmark or Friendly Numbers (numbers easy to use in mental computation 23+48, 23+50 = 73, then subtract 2 = 71) 6.Compensation (add to one addend and subtract same amount from other addend 36+9, add 1 to make 10, then subtract 1 from 36, which makes 35+10) 7.Breaking Each Number into its Place Value 19+18, (10+9)+(10+8)= 20+17, 20+10=30+7=37, or just add tens and then ones 8.Adding up in Chunks (45 + 28, 45 + 20 = 65, 65 +8 =73)

14. Your Turn Use one of the addition strategies that we just discussed to solve 17+16

15. 2 Common Strategies for Subtraction 1.Adding up (on number line) 2.Removal (counting back in chunks) or Counting Back (one number at a time)

16. Goals of 3-5 Number Talks 1.Number Sense 2.Place Value 3.Fluency 4.Properties 5.Connecting mathematical ideas

17. Strategies for Multiplication 1.Repeated Addition 2.Skip Counting 3.Partial Products 4.Making Landmark or Friendly Numbers (9x15, 10x15, then subtract one group of 15) 5.Doubling and Halving (1x16, 2x8, 4x4, 8x2, 16x1 with arrays) 6.Breaking Factors into Smaller Factors 12x 25 (4x25) (4x25) (4x25)

18. Strategies for Division 1.Repeated Subtraction or Sharing/Dealing Out 2.Multiplying Up (384/16 10x16=160, 10x16 =160, 160+160 = 320…keep going…2x16 =32, 320+32= 352….keep going…2x16=32, 352+32=384, so 10+10+2+2=24, 384/16=24) 3.Partial Quotients 4.Proportional Reasoning (384/16 divide both by 2= 192/8, divide both by 2=96/4, divide both by 2=48/2 = 24….384/16=24)

19. Video Examples of Number Talks Kinder rekenrek https://www.youtube.com/watch?v=oUI05UQmYz8https://www.youtube.com/watch?v=oUI05UQmYz8 Another Kinder rekenrek https://www.youtube.com/watch?v=pk9TbuAPQ7Ehttps://www.youtube.com/watch?v=pk9TbuAPQ7E Kinder 10 frame https://www.youtube.com/watch?v=8D-qejdIlFghttps://www.youtube.com/watch?v=8D-qejdIlFg 1st Grade https://www.youtube.com/watch?v=X18cQkKMlhshttps://www.youtube.com/watch?v=X18cQkKMlhs 2nd Grade https://www.youtube.com/watch?v=RCPo334nPbQhttps://www.youtube.com/watch?v=RCPo334nPbQ 3rd Grade https://www.youtube.com/watch?v=YV4o_U8K9aAhttps://www.youtube.com/watch?v=YV4o_U8K9aA 4th Grade https://www.youtube.com/watch?v=2Stg60boc8Qhttps://www.youtube.com/watch?v=2Stg60boc8Q 5th Grade division https://www.youtube.com/watch?v=DQtgFaVqv7chttps://www.youtube.com/watch?v=DQtgFaVqv7c (It's a good example of the number talks, but the teacher keeps saying add the zero instead of multiply by ten!)

20. Rekenrek A Visual, Concrete Model for Strategic Reasoning in Mathematics and used to discover number relationships and develop automaticity From the Netherlands - also known as Arithmetic Rack, Calculating Frame, Math Rack Reken - to do Math In English - to reckon: calculate, add up, total, count Used to develop number sense and to conceptualize numbers Concrete, Visual, Kinesthetic

21. What Do You Notice?

22. Rekenrek - What the Heck? Two rows of stringed beads, 10 in each row Repeating pattern of 5 beads of one color and 5 beads of another color on each row Groups of 5 allow students to subitize: see numbers as a group without counting one by one Use one row to develop fluency to 10 Use two rows to develop fluency to 20

23. Why? Supports The 8 Mathematical Practices

24. Why? Content Standards Counting and Cardinality (Numbers 0-20) Know number names and the count sequence Count to tell the number of objects Compare numbers Operations and Algebraic Thinking (Numbers 0-20) Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from Numbers and Operations in Base Ten Work with Numbers 11-19 to gain foundations for place value Sherry Parrish video - YouTube video min.YouTube video

25. 4 Relationships to gain number sense... John Van de Walle (2006) describes four relationships that need to be developed for children to gain number sense with numbers up to 20 so they can use those numbers but also understand them: Spatial relationships – having a visual picture of an amount, also recognizing how many without counting by seeing a visual pattern (subitizing). One and two more, one and two less – this is not the ability to count on two or count back two, but instead knowing which numbers are one and two less or more than any given number by understanding the pattern of numbers. Benchmarks of 5 and 10 – because ten plays such an important role in our number system, and two fives make up ten, students must know how numbers relate to five and ten. Part-Part-Whole – seeing a number as being made up of two or more parts.

27. Skills Counting Visualizing numbers Developing number sense strategies using 5 and 10 Composing/Decomposing Doubles/Near Doubles Adding/Subtracting within 10 and 20 Finding unknowns Developing problem-solving strategies Building fluency with facts

28. How To For most applications: begin with all beads on the right side Move beads to the left Count, then move beads as a group, not one by one Use 5 and 10 as “anchor numbers” Video Link: How To Use a Rekenrek

29. Vocabulary Right - the right side of the Rekerek can be marked with a dot or star if needed Return - slide all beads to the right so that they are ready for the next task Slide - to move the beads Move - one move, two moves, etc… Ex: Build the number 7 with one move

30. Composing - Decomposing Numbers to Ten Separate beads - 5 on left, 5 on right Slide beads to center to represent a number Ex: Represent 4 Show another way… Show another way... Video - Decomposing Numbers on a Rekenrek

31. Resources on the Web - Google it!! Click Here for info about Number Rack Free App for iPadNumber Rack Free App for iPad Click Here for Number Sense Technology Tool - FreeNumber Sense Technology Tool - Free Click Here for Free Prompt Cards from TPTFree Prompt Cards from TPT Click Here for Electronic Copy of HandoutElectronic Copy of Handout Click Here for “Got Rekenek?” - a 13 minute video presentation with student videos“Got Rekenek?” - a 13 minute video presentation with student videos You Tube - search Rekenrek for teacher-made demos and student use Pinterest - how to make class sets - lots of great ideas!!