1. STRATEGIES FOR TEACHING MATHEMATICS Strategies for Building Number Sense and Computational Fluency

2. INCREMENTAL REHEARSAL INTERSPERSAL WORKSHEETS INDIVIDUALIZED SELF-CORRECTION CHECKLIST COVER-COPY-COMPARE ‘ERRORLESS LEARNING’ WORKSHEETS TIME DRILLS GAMES USE BOOKS TO ENGAGE STUDENTS WRITING ACTIVITIES SOCIO-DRAMATIC PLAY MNEMONICS MANIPULATIVES MISCELLANEOUS IDEAS

3. INCREMENTAL REHEARSAL Flash cards (http://www.aplusmath.com/Flashcards/Flashcard_Creator.html)or index cards with problems students are expected to knowhttp://www.aplusmath.com/Flashcards/Flashcard_Creator.html Student is given two seconds to answer problems – correct answers into “known” pile, incorrect answers into “unknown pile”. Nine cards are selected from “known” pile; rest discarded. A review deck is started by teacher reading and answering one problem from the unknown stack; student repeats problem and answer Teacher chooses one “known” card and uses with “unknown” card having student say problem and answer to both; two card sequence continues until each answer is given within two seconds Additional “known” problems are added to the deck until all nine known problems are used with “unknown problem” Review deck now has nine “known” and one “unknown” problem; when each is answered in two seconds or less, one original “known fact is discarded and another “unknown problem is added following the same procedure as above Jim Wright http://www.interventioncentral.org/htmdocs/interventions/math/math_increm_rehearsal.p hp

4. INTERSPERSAL WORKSHEETS Teacher identifies challenging problems for a student Teacher identifies easy problems for a student Worksheet is prepared alternating two types of problems Worksheet Generator for Numbers at http://www.interventioncentral.org/htmdocs/tools/mathprobe/all mult.php http://www.interventioncentral.org/htmdocs/tools/mathprobe/all mult.php Jim Wright http://www.interventioncentral.org/htmdocs/interventions/math/math_interspersal.php http://www.interventioncentral.org/htmdocs/interventions/math/math_interspersal.php

5. INDIVIDUALIZED SELF- CORRECTION CHECKLIST Teacher meets with students to analyze mistakes Together develop way to avoid mistake Students use checklist when working independently Zrebiec Uberti, Mastropieri & Scruggs, 2004

6. COVER-COPY-COMPARE Jim Wright, http://www.interventioncentral.org/htmdocs/interventions/g enAcademic/ccc.php http://www.interventioncentral.org/htmdocs/interventions/g enAcademic/ccc.php Prepare worksheets with problems with answers on left, unsolved problems on right Student looks at worked problem Student covers correct problem, works problem on right and checks

7. ‘ERRORLESS LEARNING’ WORKSHEETS Timed worksheets with include an answer key at the top of the page Student locates answer to problem they cannot work and write it in Caron, T. A. (2007). Learning multiplication the easy way. The Clearing House, 80, 278-282. Jim Wright www.interventioncentral.orgwww.interventioncentral.org

8. TIME DRILLS TI-10/15

9. TIME DRILLS Textbook Worksheets Web Sources – http://www.interventioncentral.org/htmdocs/tools/m athprobe/allmult.php http://www.interventioncentral.org/htmdocs/tools/m athprobe/allmult.php – http://www.aimsweb.com/login.php http://www.aimsweb.com/login.php Extension Chart Progress Graph Progress

10. GAMES Mental Paper and Pencil Board Computer

11. MENTAL NUMBER GAMES A Minute or Less– start with a number and give students an operation and another number. Without telling them the answer, use that answer and give them another number and operation. Operations are performed in the order given. Make It More, Make It Less Number Sense and Operations Addenda Series Grades K-6, NCTM One-Out Navigating through Number and Operations in Prekindergarten-Grade 2, NCTM

12. PAPER AND PENCIL NUMBER GAMES Give students a number and have them come up with computational problems that fit that number. Give students a date and see how many problems they can write that uses all the digits in that date. Commercial Board and Computer Games

13. 1/14/96 0 = 4 + 6 – 9 – 1/1 0r 6 - 4 + 1/1 - √9 1 = 4 + 6 – 9 – 1 + 1 2 = √9∙√4 – 6 + 1 + 1 3 = 6 - 4 + √9 – (1+1) 4 = 5 = 6 + 4 - √9 – (1+1) 6 = 4√9 – 6 + 1 - 1 etc

14. Board Games WWC Quick Review of the Article “Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games" 1 1 What is this study about? This study examined whether playing number board games improved numeracy skills of low- income preschoolers. It included 136 preschool children from 10 urban Head Start centers. The children ranged in age from four to five-and-a-half years old. Seventy-two children were randomly selected to play a number board game with a trained experimenter. The other 64 children played a different version of the game using colors instead of numbers. Numeracy skills were assessed at the end of a two-week period and again nine weeks later. What did the study authors report? Children who played the number game had better counting and number identification skills than children who played the color game. Children who played the number game were also better at picking the highest number from a pair of numbers and identifying positions on a number line. The effects persisted nine weeks after the game sessions ended. Estimated effect sizes at that point ranged from 0.55 to 0.80. These effects did not differ by the age of the preschoolers. 1 “Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games.” Child Development, 79(2), 375-394. Geetha B. Ramani and Robert S. Siegler. 1

15. Games Chart showing the possible applications/modifications of nine commercial board games for teaching early numeracy. http://www.kentuckymathematics.org/docs/2 007/intervention/Game_chart.pdf http://www.kentuckymathematics.org/docs/2 007/intervention/Game_chart.pdf

16. BOOKS Remainder of One Annabelle Swift, Kindergartner Each Orange Had Eight Slices Two Ways to Count to Ten 12 Ways to get to 11 A Million Fish…More or Less How the Second Grade Got $8,205.50 to Visit the Statue of Liberty

17. WRITING ACTIVITIES Students write a letter to an absent student, parent, or student in another class to explain a process; include a problem to be worked using the process for the addressee to work Entrance/exit slips Media Campaign Middle School Mathematics Online Strategies for Teachers http://www.doe.virginia.gov/VDOE/middle-math- strategies/ http://www.doe.virginia.gov/VDOE/middle-math- strategies/

18. SOCIO-DRAMATIC PLAY Create Learning Stations Restaurant (menu, money, table numbers) Grocery (money, quantity, unit prices) Music (assign a number to instruments)

19. MNEMONICS FOR BASIC COMPUTATION (CAUTION) Don’t Miss Susie’s Boat Please Excuse My Dear Aunt Sally http://www.unl.edu/csi/math.shtml

20. MANIPULATIVES Base Ten Blocks Dominoes Number Lines Two sided chips, mat tiles, tile spacers Positive/Negative mats

21. MISCELLANEOUS IDEAS Position Paper Patterns in Math Cooperative Learning – I Have…Who Has… Color Coding Arithmetic Symbols Calculators Probes on Quantity Discrimination, Missing Number, Number Identification http://www.interventioncentral.org/php/numberfly/numberfly.php http://www.interventioncentral.org/php/numberfly/numberfly.php