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Student strategies
These various strategies are to help you as parents identify the method in which your child might be solving their problems and give you some familiarity with the strategies to engage in conversation with your child about their strategy.
These strategies are not to be seen as a linear progression towards the standard algorithm. In fact, I would argue that the standard algorithm is not the most efficient strategy and by no means the end goal when working with students on building their understanding of the four operations.
The strategies below all have their place depending on the problem posed and it is important that students have opportunities to solve problems and choose which strategy to use as they develop efficient and flexible uses for these strategies.
These strategies are not to be seen as a linear progression towards the standard algorithm. In fact, I would argue that the standard algorithm is not the most efficient strategy and by no means the end goal when working with students on building their understanding of the four operations.
The strategies below all have their place depending on the problem posed and it is important that students have opportunities to solve problems and choose which strategy to use as they develop efficient and flexible uses for these strategies.

Counting

Addition

Subtraction

Multiplication

Division
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COMING SOON! LOOK FOR THE Counting STRATEGies VIDEOS THIS SUMMER

Making Tens
Students break numbers apart to make tens. 
Landmark/Friendly Numbers
Students adjust one or both addends to make numbers that are easier and friendlier to use. 


Place Value
Students break apart each addend according to place value and combine quantities. Students may start combining from the highest value to lowest or from lowest to highest value. 
Compensation
Students manipulate the numbers into easier, friendlier numbers by removing a specific amount from one addend and adding it to the other addend. 


Adding in Chunks
Students keep one addend whole and break one addend into friendlier to use chunks. 
Expanded Algorithm 1
Students expanded each number according to place value and add. This ensures place value stays at the forefront of addition and explicitly shows what is occurring throughout the algorithm. 


Expanded Algorithm 2
Students begin to place numbers vertically but continue to explicitly show place value throughout the algorithm. 
Standard Algorithm
Students may use the standard algorithm once they have built their understanding of what is taking place throughout. 


Adding Up
Students build on their understanding of addition by adding up from the number being subtracted to the whole. 
Removal / Counting Back
Students may count back from the whole to solve the subtraction problem and even more so if the numbers are close. Students may remove the subtrahend in parts (decompose number). 


Place Value & Negative Numbers
Students break each number into its place value. Like values are grouped and then subtracted. Students may use negative values. 
Constant Difference
When students begin to understand subtraction is the difference between two numbers, they can begin to change both numbers by the same amount to make the subtraction friendlier. 


Adjusting One Number
Students adjust one number to make the problem more efficient and friendlier. The final answer needs to be adjusted to compensate for the initial change in number. 
Expanded Algorithm 1
Students expanded each number according to place value and subtract. This ensures place value stays at the forefront of subtraction and explicitly shows what is occurring throughout the algorithm. 


Expanded Algorithm 2
Students begin to place numbers vertically but continue to explicitly show place value throughout the algorithm. 
Standard Algorithm
Students may use the standard algorithm once they have built their understanding of what is taking place throughout. 
