Incorporating the
Common Core State Standards
for Addition, Subtraction,
Multiplication & Division
The Standard/Traditional Subtraction Algorithm:
3 0
- 1 2
The Standard Subtraction Algorithm:
2 3 10
-1 2
1 8
* A major strength of the Common Core is its unity of teaching
strategies and alternative algorithms.
* This presentation highlights the changes in teaching:
Addition
Subtraction
Multiplication
Division
Standards for Mathematical Teaching Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of
others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
The Four BIG tools
for Adding and Subtracting:
1)
2)
3)
4)
Ten Frames
Hundreds Charts
Number Lines
Alternate Algorithms
The skill of subitizing is essential to
understanding numbers.
Kindergarten Center
Connecting Subitizing to Addition and Subtraction
8+7=
8 + 7 = 15
8 + 7 = 15
10 + 5 = 15
*1st Grade Center
26
+10
26
+13
30
-12
2nd
Grade
Center
Decomposing
34
65 - 34 = 31
3rd Grade Center
28 + 5 = 33
54 + 8 = 62
2nd Grade Center
Non-Traditional Algorithms
• Based on use of tools
• Use structure of the number
system
• Lead to traditional algorithms
An example of the Partial Sums Algorithm:
18
+17
20
the sum.
Step 1: Add the tens (10 + 10 = 20) and write
NBT standards based on place value
An example of the Partial Sums Algorithm:
18
+17
20
15
Step 1: Add the tens (10 + 10 = 20) and write the sum.
Step 2: Add the ones (8 + 7 = 15) and write the sum.
NBT standards based on place value
The PARTIAL SUMS ALGORITHM…
18
+17
20
+15
35
Step 1: Add the tens (10 + 10 = 20) and write the sum.
Step 2: Add the ones (8 + 7 = 15) and write the sum.
Step 3: Add the partial sums to get 35
The PARTIAL SUMS ALGORITHM…
18
+17
20
+15
35
1
18
+ 17
35
Step 1: Add the tens (10 + 10 = 20) and write the sum.
Step 2: Add the ones (8 + 7 = 15) and write the sum.
Step 3: Add the partial sums to get 35
The STANDARD ALGORITHM…
Step 1: Add the ones and regroup the ten
Step 2: Add the tens
The Three BIG Tools
For Multiplying and Dividing:
1) Arrays
2) Area
3) Non-Traditional Algorithms
Arrays
2 x 7 is 14…
2 rows of 7
and 7 x 2 is 14
7 rows
of 2
If 2 x 7 is 14… then 4 x 7 =28
3rd Grade Center
Area Model
5x7=
7
5
5 x 7 is the same as…
5 x 5 + 5 x 2 = 25 + 10 = 35
5
5
5 x 5 = 25
2
5 x 2 = 10
27 x 35
30
5
20
20 x 30= 600
20 x 5 = 100
7
7 x 30 = 210
7 x 5 = 35
27 x 35 = 945
30
20
7
5
20 x 30=
600
20 x 5 = 100
7 x 30 =
210
7 x 5 = 35
600 + 100 + 210 + 35 = 945
X
35
27
35
210
100
600
945
Partial Products Algorithm
7x5
7 x 30
20 x 5
20 x 30
30
=
=
=
=
5
20
20 x 30= 600
20 x 5 = 100
7
7 x 30 = 210
7 x 5 = 35
35
210
100
600
X
35
27
35
210
100
600
945
Partial Products Algorithm
7x5
7 x 30
20 x 5
20 x 30
30
=
=
=
=
5
4th
Grade
Center
35
210
100
600
Standard Algorithm
13
20
20 x 30= 600
20 x 5 = 100
7
7 x 30 = 210
7 x 5 = 35
35
x 27
245
+ 700
945
Partial Quotients Algorithm
305 ÷ 5
?
5
305
305 ÷ 5
5
60 + 1 = 61
60
+ 1
300
5
Partial Quotients Algorithm
62
3 186
- 180 3 x 60
6
6 3x 2
Partial Quotients Algorithm
62
3 186
- 180 3 x 60
6
6 3x 2
0
5th
Grade
Center
LONG
62
DIVISION: 3 186
- 18
06
-6
0
* WHY ARE WE TEACHING THESE NEW WAYS?
• We teach students to apply the Standards of Mathematical Practice
to THINK LIKE MATHEMATICIANS and internalize the structure of the
mathematical tools they are using while “DOING” mathematics.
• We want students to be FLEXIBLE in their thinking so they can solve
problems MENTALLY with a deeper understanding of place value
which will lead to FEWER ERRORS and less re-teaching.
• We are supporting students with tools and explicitly teaching them to
use structure and repeated reasoning will allow students the ability
to access and solve more complicated problems.
* WHEN ARE STUDENTS READY FOR THE
STANDARD ALGORITHMS?
Exploring Strategies and
Non Traditional Algorithms
Teaching the
Standard Algorithm
Addition
Kindergarten, 1st Grade
& 2nd Grade
Introduced in
3rd Grade &
Mastered in 4th
Grade
Subtraction
Kindergarten, 1st Grade
2nd Grade & 3rd Grade
Introduced in
3rd Grade &
Mastered in 4th Grade
Multiplication
2nd Grade, 3rd Grade
& 4th Grade
Division
2nd Grade, 3rd Grade,
4th Grade & 5th Grade
5th Grade
Introduced in
5th Grade &
Mastered in 6th Grade
You Can Visit Centers:
BY
OR BY
GRADE
TOPIC
K
In Media Center
Subitizing
& Ten Frames
1 and 2
In Math Room
Linking Subitizing to Addition
Additon Strategies, Games
3
Subtraction Strategies &
Multiplication and Division Fact Strategies
Games
4
Mental Multiplication Games &
Partial Product Multiplication
5
Mental Division Games &
Partial Quotient Division