Teaching Addition and Subtraction for Meaning
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TEACHING ADDITION AND
SUBTRACTION FOR MEANING
Carissa Connell, Stacey Daly, Jennifer Maxwell
Mathematics SpecialistsMadison Public Schools
ATOMIC Fall Conference, Cromwell, CTDecember 3, 2013
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HOW WOULD YOU SOLVE THESE PROBLEMS?
326 + 497 = ? 800 – 537 = ?
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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.
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COMMON CORE STATE STANDARDS RELATED TO ADDITION AND SUBTRACTIONThird 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.
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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)
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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)
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Subitizing
Visualizing addends
Seeing patterns
Visual Models to Develop Meaning
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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
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USING TEN FRAMES“Concept of 10”
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NUMBER BONDS
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“Hide the Blocks” Balancing Equations
Missing Addend/ Subtraction
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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.
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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
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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
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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
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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
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ADDING WITH AN OPEN NUMBER LINE258 + 323= ________
+100 +100 +100 +20 +2 +1
258 358
458
558
578
580
581
or +300 +20 +2 +1
258 558
578
580
581
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SUBTRACTING WITH AN OPEN NUMBER LINE
257 - 125
- 5 - 10 - 10 - 100
132 137
147 157
257
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PARTIAL SUMS
48 + 37 70 +15 85
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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
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COMPENSATION (MAKING A FRIENDLY NUMBER)48 + 37
48 + 2 = 50
37 – 2 = 35
50 + 35 = 85
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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
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PARTIAL DIFFERENCES81 – 37 = ________
80 – 30 = 50 1-7 = -6
50 -6 = 44
Answer: 44
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ADDING UP TO SUBTRACT81 – 37 = ___
From Smaller to Larger Number
37 + 3 = 40 40 + 40 = 80 80 + 1 = 813 + 40 + 1 = 44
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COMPENSATION (MAKING A FRIENDLY NUMBER)
1000 - 892
1000 = 999 + 1999 – 892 = 107 107 + 1 = 108
Answer: 108
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WOULD YOU SOLVE THESE PROBLEMS DIFFERENTLY?
326 + 497 = ? 800 – 537 = ?
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DISCUSSION/COMMENTS/QUESTIONS
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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/
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CONTACT INFORMATION
Math SpecialistJeffrey School, MadisonE-mail: [email protected]
Math SpecialistRyerson School, MadisonE-mail:
Math SpecialistIsland Avenue School, MadisonE-mail:
Stacey Daly Carissa Connell
Jennifer Maxwell