Rekenreks Number Talks Just For Giggles Number Talks

Rekenreks & Number Talks Just For Giggles. . .

Number Talks Sherry Parrish: Number Talks: Building Numerical Reasoning

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

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

1. Classroom Environment and Community • Building a cohesive classroom community is essential for creating a safe riskfree 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.

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.

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.

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

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

Number Talks Hand Signals Encourage student communication

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

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)

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

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)

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

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

Strategies for Division 1. Repeated Subtraction or Sharing/Dealing Out 2. Multiplying Up (384/16 10 x 16=160, 10 x 16 =160, 160+160 = 320…keep going… 2 x 16 =32, 320+32= 352…. keep going… 2 x 16=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)

Video Examples of Number Talks Kinder rekenrek https: //www. youtube. com/watch? v=o. UI 05 UQm. Yz 8 Another Kinder rekenrek https: //www. youtube. com/watch? v=pk 9 Tbu. APQ 7 E Kinder 10 frame https: //www. youtube. com/watch? v=8 D-qejd. Il. Fg 1 st Grade https: //www. youtube. com/watch? v=X 18 c. Qk. KMlhs 2 nd Grade https: //www. youtube. com/watch? v=RCPo 334 n. Pb. Q 3 rd Grade https: //www. youtube. com/watch? v=YV 4 o_U 8 K 9 a. A 4 th Grade https: //www. youtube. com/watch? v=2 Stg 60 boc 8 Q 5 th Grade division https: //www. youtube. com/watch? v=DQtg. Fa. Vqv 7 c (It's a good example of the number talks, but the teacher keeps saying add the zero instead of multiply by ten!)

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

What Do You Notice?

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

Why? Supports The 8 Mathematical Practices

Content Standards Counting and Cardinality (Numbers 0 -20) Know number names and the count sequence Count to tell the number of objects Compare numbers Why? 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 - You. Tube video min.

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

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

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

Resources on the Web - Google it!! Click Here for info about Number Rack Free App for i. Pad Click Here for Number Sense Technology Tool - Free Click Here for Free Prompt Cards from TPT Click Here for Electronic Copy of Handout Click Here for “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!!