TEACHING ADDITION AND

SUBTRACTION FOR MEANING

Carissa Connell, Stacey Daly, Jennifer Maxwell

Mathematics SpecialistsMadison Public Schools

ATOMIC Fall Conference, Cromwell, CTDecember 3, 2013

HOW WOULD YOU SOLVE THESE PROBLEMS?

326 + 497 = ? 800 – 537 = ?

COMMON CORE STATE STANDARDS RELATED TO ADDITION AND SUBTRACTION 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.

COMMON CORE STATE STANDARDS RELATED TO ADDITION AND SUBTRACTION

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.

ADDITION & SUBTRACTION FLUENCY

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)

INVOLVE ME AND I UNDERSTAND . . .

Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand. (Native American Proverb)

Subitizing

Visualizing addends

Seeing patterns

Visual Models to Develop Meaning

NUMBER RACKS OR REKENREKS

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

USING TEN FRAMES

“Concept of 10”

NUMBER BONDS

“Hide the Blocks” Balancing Equations

Missing Addend/ Subtraction

ADDING WITH BASE TEN BLOCKS17 + 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.

ADDING WITH BASE TEN BLOCKS CONT.

Next add the tens which results in a total of 5 tens. The final answer is 5 tens and 1 one.

Answer 51

SUBTRACTING WITH BASE TEN BLOCKS34 – 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

USING THE HUNDRED CHART

Looking at patterns on the hundred chart

Skip counting by 10 from any number

Adding and subtracting using the hundred chart

ADDING WITH AN OPEN NUMBER LINE

58 + 33= ________

+10 +10 +10 +2 +1

58 68

78

88

90

91 or

+30 +2 +1

58 88

90

91

ADDING WITH AN OPEN NUMBER LINE

258 + 323= ________

+100 +100 +100 +20 +2 +1

258 358

458

558

578

580

581

or +300 +20 +2 +1

258 558

578

580

581

SUBTRACTING WITH AN OPEN NUMBER LINE

257 - 125

- 5 - 10 - 10 - 100

132 137

147 157

257

PARTIAL SUMS

48 + 37 70 +15 85

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 Value Incremental Adding

COMPENSATION (MAKING A FRIENDLY NUMBER)48 + 37

48 + 2 = 50

37 – 2 = 35

50 + 35 = 85

SUBTRACTING IN STEPS 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

PARTIAL DIFFERENCES

81 – 37 = ________

80 – 30 = 50 1-7 = -6

50 -6 = 44

Answer: 44

ADDING UP TO SUBTRACT

81 – 37 = ___From Smaller to Larger Number

37 + 3 = 40 40 + 40 = 80 80 + 1 = 813 + 40 + 1 = 44

COMPENSATION (MAKING A FRIENDLY NUMBER)

1000 - 892

1000 = 999 + 1999 – 892 = 107 107 + 1 = 108

Answer: 108

WOULD YOU SOLVE THESE PROBLEMS DIFFERENTLY?

326 + 497 = ? 800 – 537 = ?

DISCUSSION/COMMENTS/QUESTIONS

RESOURCES Arizona State Content Standards @ http://www.azed.gov/standards-practices/common-standards/

Common Core State Standards (2010) @ http://www.corestandards.org/

First Steps in Mathematics @http://www.stepspd.com/au/courses/firststepsmath.htmMath Learning Center @ 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/

CONTACT INFORMATION

Math Specialist

Jeffrey School, Madison

E-mail: dalys@madison.k12.ct.us

Math Specialist

Ryerson School, Madison

E-mail: maxwellj@madison.k12.ct.us

Math Specialist

Island Avenue School, Madison

E-mail: connellc@madison.k12.ct.us

Stacey Daly Carissa Connell

Jennifer Maxwell