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:

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 15 are shown below.
Possible 1st Grade Place Value Strategies:
Draw Base 10 blocks: 33 + 20 = 53 
45 + 30 =75 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: 
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 becomes 500 + 100 + 14
 300 + 20 + 5  400 + 50 + 9  400 + 50 + 9
200 + 20 + 3 = 223 100 + 50 + 5= 155
Possible 3rd Grade Place Value Strategies: 632 

Use multiplication facts and place value to multiply by multiples of ten: 9 x 80 = 
Use the distributive property to multiply within 100: 
Possible 4th Grade Place Value Strategies:
Partial Products: (2 digit x 2 digit) 
Area Model: (2 digit x 2 digit) 
Partial Quotients: 7725/6 
Partition the Dividend: Partition the dividend into multiples of the divisor. 
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) 
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: 
Draw BaseTen Blocks: Division with decimals 
Area Model: Multiplying decimals 
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 12 focus strategies per grade for each operation: