Transcript Teaching Addition and Subtraction for Meaning

TEACHING ADDITION
AND SUBTRACTION
FOR MEANING
Carissa Connell, Stacey Daly, Jennifer Maxwell
Mathematics Specialists
Madison Public Schools
ATOMIC Fall Conference, Cromwell, CT
December 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)
Visual Models to Develop Meaning

Subitizing

Visualizing addends

Seeing patterns
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-mathlearning/id496057949?mt=8
USING TEN FRAMES
“Concept of 10”
NUMBER BONDS
Missing Addend/ Subtraction

“Hide the Blocks”
Balancing Equations
ADDING WITH BASE TEN BLOCKS
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.
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 BLOCKS
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
USING THE HUNDRED CHART


Looking at patterns
on the hundred chart
Skip counting by 10
from any number
Name:
Hundreds Chart
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50

Adding and
subtracting using the
hundred chart
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Super Teacher Worksheets - www.superteacherworksheets.com
ADDING WITH AN OPEN NUMBER LINE
58 + 33= ________
+10
58
+10
68
+10
78
+2
88
or
+30
58
+2
88
+1
90
91
+1
90
91
ADDING WITH AN OPEN NUMBER LINE
258 + 323= ________
+100
258
358
+300
258
+100
or
558
+100
458
+20
+20
558
+2
578
+2
578
+1
580
581
+1
580
581
SUBTRACTING WITH AN OPEN NUMBER
LINE
257 - 125
-5
132
-10
137
-10
147
-100
157
257
PARTIAL SUMS
48
+ 37
70
+15
85
48 + 37
Adding by Place Value

40 + 30 = 70

And 8 + 7 = 15

And 70 + 15 = 85
Incremental Adding
(Breaking one number
into tens and ones)
 48 + 10 = 58
 58 + 10 = 68
 68 + 10 = 78
 78 + 7 = 85

COMPENSATION (MAKING A FRIENDLY NUMBER)
48 + 37
48 + 2 = 50
37 – 2 = 35
50 + 35 = 85
SUBTRACTING IN STEPS
81 – 37 = ___
Incremental Subtracting
Subtracting by
Place Value

81 – 10 = 71

81 – 30 = 51

71 – 10 = 61

51 – 7 = 44

61 – 10 = 51

51 – 1 = 50

50 – 6 = 44
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 = 81
3 + 40 + 1 = 44
COMPENSATION (MAKING A FRIENDLY
NUMBER)
1000 - 892
1000 = 999 + 1
999 – 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/commonstandards/
 Common Core State Standards (2010) @
http://www.corestandards.org/
 First Steps in Mathematics @
http://www.stepspd.com/au/courses/firststepsmath.h
tm
Math 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
Stacey Daly
Carissa Connell
Math Specialist
Math Specialist
Jeffrey School, Madison
Island Avenue School, Madison
E-mail: [email protected]
E-mail: [email protected]
Jennifer Maxwell
Math Specialist
Ryerson School, Madison
E-mail: [email protected]