Place Value Strategies
from: www.k-5mathteachingresources.com/Place-Value-Strategies.html
What are place value strategies and how do they relate to standard algorithms? The Common Core
Standards describe the requirements for fluent use of the standard algorithms for addition, subtraction,
multiplication and division as follows:
Grade
Standard
4
4.NBT.4 Fluently add and subtract multi-digit whole numbers
using the standard algorithm.
5
5.NBT.5 Fluently multiply multi-digit whole numbers using the
standard algorithm.
6
6.NS.2 Fluently divide multi-digit numbers using the standard
algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit
decimals using the standard algorithm for each operation.
Prior to developing fluency with standard algorithms the CCSS emphasize place value strategies. This strong
focus on place value strategies plays a critical role in the development of mental and written computation
strategies, while providing students with the opportunity to develop a deep understanding of how the
standard algorithms work. Common Core Standards explicitly referencing strategies based on place value
include 1.NBT4, 2.NBT.5, 2.NBT.6, 2.NBT.7, 3.NBT.2, 3.NBT.3, 4.NBT.5, 4.NBT.6, 5.NBT.6, and 5.NBT.7.
So, what do place value strategies look like? Many different strategies based on place value exist for both
written and mental computations. Some examples of written methods for Grades 1-5 are shown below.
Possible 1st Grade Place Value Strategies:
45 + 30 =75
Draw Base 10 blocks: 33 + 20 = 53
Draw jumps on an empty number line: 2 digit + multiple
of 10
Possible 2nd Grade Place Value Strategies:
Draw jumps on an empty number line:
349
Partial Sums (Expanded form layout): Each addend is represented using expanded notation. Like place
values are added or subtracted.
123 + 234 =
238 + 473 =
100 + 20 + 3
200 + 30 + 8
+ 200 + 30 + 4
+ 400 + 70 + 3
300 + 50 + 7 = 357
600 + 100 + 11= 711
548 - 325
614 - 459
500 + 40 + 8
600 + 10 + 4
- 300 + 20 + 5
- 400 + 50 + 9
becomes
200 + 20 + 3 = 223
500 + 100 + 14
- 400 + 50 + 9
100 + 50 + 5= 155
Possible 3rd Grade Place Value Strategies:
Partial Sums: Expanded Form layout as above
or vertical format.
632+325=
632
+ 325
900
50
7
957
Partial Differences: Each number is represented
using expanded notation. Like place values
aregrouped and subtracted. Negative place values
may result.
752 - 436
523-259=
700 + 50 +2
500 + 20+ 3
- 400+30+6
- 200+ 50+9
300+ 20 - 4 = 316
300 - 30 - 6 = 264
Use multiplication facts and place value
Use the distributive property to multiply within
to multiply by multiples of ten: 9 x 80 =
100: 15 x 5 =
9 x80 = 9 x 8 tens
15 x 5 = (10 x 5) + (5x5)
= 72 tens = 720
= 50 + 25
9 x80 = 720
= 75
Possible 4th Grade Place Value Strategies:
Partial Products: (2 digit x 2 digit)
Area Model: (2 digit x 2 digit)
32
x 34
900 (30 x 30)
120 (30 x 4)
60 (2 x 30)
8
(2 x 4)
1,088
Area Model: (1 digit x 3 digit)
Partial Quotients: 7725/6
349
Partition the Dividend: Partition the dividend into
multiples of the divisor.
1204 r 1
6) 7225
292/4
- 6000 ( 1000 x 6)
1225
- 1200 (200 x 6)
25
- 24 (4 x 6)
1
70 + 3 = 73
4) 280 + 12
Possible 5th Grade Place Value Strategies:
Add decimals on an empty number line:
35.8 + 8.3 =
Subtract decimals on an empty number line: (Count
up to find the difference)
126.4 - 58.7 =
349
Start at 58.7 and jump up 1.3 to 60, then jump 40 to 100,
then jump 26.4 to 126.4. Add the jumps:
40 + 26.4 + 1.3 = 67.7
Draw Base-Ten Blocks: Division with decimals
Area Model: Multiplying decimals
349
349
Regardless of which place value strategies are taught it is important that there is consistency across each
grade level, and that a clear progression is maintained from one grade level to the next within a school.
Time needs to be allocated to school wide discussions to ensure that place value strategies are being used
or adopted. The following questions can be used to promote discussion and the selection of 1-2 focus
strategies per grade for each operation:

Which written methods for addition, subtraction, multiplication and division do we currently teach as
a school?

Do we have enough emphasis on place value strategies throughout the school?

Are there written methods we don’t use at the moment? Do we need to adopt them?

What mental calculation skills are needed in order for students to use written methods based on
place value? Do our students have the necessary mental calculations skills needed?

How can we develop whole school agreement on the written methods that we will teach for addition,
subtraction, multiplication and division? How will consistency and progression be maintained?