Place Value Strategies
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.
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.
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:
207
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 Differences: Each number is
Partial Sums: Expanded Form layout as above
or vertical format.
represented using expanded notation. Like
place values are grouped and subtracted.
Negative place values may result.
632+325=
632
+ 325
900
752 - 436
523-259=
700 + 50 +2
500 + 20+ 3
- 400+30+6
300+ 20 - 4 = 316
- 200+ 50+9
300 - 30 - 6 = 264
50
7
957
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
= 72 tens = 720
9 x80 = 720
15 x 5 = (10 x 5) + (5x5)
= 50 + 25
= 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)
207
207
Partial Quotients: 7725/6
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)
207
126.4 - 58.7 =
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
207
207
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?