1. T EACHING A DDITION AND S UBTRACTION FOR M EANING Carissa Connell, Stacey Daly, Jennifer Maxwell Mathematics Specialists Madison Public Schools ATOMIC Fall Conference, Cromwell, CT December 3, 2013

2. H OW WOULD YOU SOLVE THESE PROBLEMS ? 326 + 497 = ?800 – 537 = ?

3. C OMMON C ORE S TATE S TANDARDS R ELATED TO A DDITION AND S UBTRACTION Kindergarten: CC.K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. CC.K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, etc. First Grade: CC.1.NBT.4 Add within 100, including a two-digit number and a one-digit number, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Second Grade: CC.2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

4. C OMMON C ORE S TATE S TANDARDS R ELATED TO A DDITION AND S UBTRACTION Third Grade: CC.3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Fourth Grade: CC.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm (limited to whole numbers less than or equal to 1,000,000.) A range of algorithms may be used.

5. A DDITION & S UBTRACTION F LUENCY Explanations and Examples state: “Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.” Mathematics Arizona Academic Content Standards (2010)

6. I NVOLVE M E AND I U NDERSTAND... Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand. (Native American Proverb )

7. Subitizing Visualizing addends Seeing patterns Visual Models to Develop Meaning

8. N UMBER R ACKS OR R EKENREKS Teacher Demonstration Size Student Created Version – pipe cleaners & pony beads Free App! https://itunes.apple.com/us/app /number-rack-by-math- learning/id496057949?mt=8 https://itunes.apple.com/us/app /number-rack-by-math- learning/id496057949?mt=8

9. U SING T EN F RAMES “Concept of 10”

10. N UMBER B ONDS

11. “Hide the Blocks” Balancing Equations Missing Addend/ Subtraction

12. A DDING WITH B ASE T EN B LOCKS 17 + 34 = ? Begin by taking 1 tens rod and seven ones. Below that amount place 3 tens and 4 ones. Start with the ones and add the 7 ones to the 4 ones getting 11 ones. Then, regroup ten ones for a tens rod. This is done because in our place value system you cannot have more than 9 items in a given place. The ten rod should be placed in the tens column.

13. A DDING WITH B ASE T EN B LOCKS C ONT. Next add the tens which results in a total of 5 tens. The final answer is 5 tens and 1 one. Answer51

14. S UBTRACTING WITH B ASE T EN B LOCKS 34 – 18 = ? Begin by taking 3 tens rods and 4 ones rods. In order to take away 8 ones, you need to regroup a ten for ten ones. Now you have 2 tens and 14 ones (still 34). Subtract the ones. Subtract the tens. Answer. 16

15. U SING THE H UNDRED C HART Looking at patterns on the hundred chart Skip counting by 10 from any number Adding and subtracting using the hundred chart

16. A DDING WITH AN O PEN N UMBER L INE

18. S UBTRACTING WITH AN O PEN N UMBER L INE 257 - 125

19. P ARTIAL S UMS 48 + 37 70 +15 85

20. 48 + 37 40 + 30 = 70 And 8 + 7 = 15 And 70 + 15 = 85 (Breaking one number into tens and ones) 48 + 10 = 58 58 + 10 = 68 68 + 10 = 78 78 + 7 = 85 Adding by Place ValueIncremental Adding

21. C OMPENSATION (M AKING A F RIENDLY N UMBER ) 48 + 37 48 + 2 = 50 37 – 2 = 35 50 + 35 = 85

22. S UBTRACTING I N S TEPS 81 – 37 = ___ 81 – 10 = 71 71 – 10 = 61 61 – 10 = 51 51 – 1 = 50 50 – 6 = 44 81 – 30 = 51 51 – 7 = 44 Incremental Subtracting Subtracting by Place Value

23. P ARTIAL DIFFERENCES 81 – 37 = ________ 80 – 30 = 50 1-7 = -6 50 -6 = 44 Answer: 44

24. A DDING U P TO S UBTRACT 81 – 37 = ___ From Smaller to Larger Number 37 + 3 = 40 40 + 40 = 80 80 + 1 = 81 3 + 40 + 1 = 44

25. C OMPENSATION ( MAKING A F RIENDLY N UMBER ) 1000 - 892 1000 = 999 + 1 999 – 892 = 107 107 + 1 = 108 Answer: 108

26. W OULD YOU SOLVE THESE PROBLEMS DIFFERENTLY ? 326 + 497 = ?800 – 537 = ?

27. D ISCUSSION /C OMMENTS /Q UESTIONS

28. R ESOURCES Arizona State Content Standards @ http://www.azed.gov/standards-practices/common- standards/ Common Core State Standards (2010) @ http://www.corestandards.org/ http://www.corestandards.org/ First Steps in Mathematics @ http://www.stepspd.com/au/courses/firststepsmath.h tm Math Learning Center @ http://www.mathlearningcenter.org/ http://www.mathlearningcenter.org/ NCTM: Developing Essential Understanding of Addition and Subtraction (2011). NCTM Illuminations @ http://illuminations.nctm.org/ SMARTER Balanced Assessment Consortium @ http://www.k12.wa.us/smarter/ http://www.k12.wa.us/smarter/

29. C ONTACT INFORMATION Math Specialist Jeffrey School, Madison E-mail: dalys@madison.k12.ct.usdalys@madison.k12.ct.us Math Specialist Ryerson School, Madison E-mail: maxwellj@madison.k12.ct.usmaxwellj@madison.k12.ct.us Math Specialist Island Avenue School, Madison E-mail: connellc@madison.k12.ct.usconnellc@madison.k12.ct.us Stacey DalyCarissa Connell Jennifer Maxwell