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March 27, 2018
Taking Stock, Taking Action: Addition and Subtraction

In a few months the school year will be over and your current students will be thinking about moving along to the next grade level. Are they ready? Is their additive reasoning where it should be in relation to base 10 understanding, addition and subtraction?
 
This is a good time to take stock of your students' additive reasoning and to take action to strengthen their readiness for the next grade. The table that follows is a reminder of the CCSSM expectations for the use of strategies to solve addition and subtraction problems with numbers of increasing magnitudes and illustrates how procedural fluency is built on conceptual understanding from grades K-3. Students are expected to solve addition and subtraction problems by:

  • Using mental strategies such as counting on, making a ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, or making an equivalent but easier sum (including compensation).
     
  • Using concrete models, drawings or strategies based on place value understanding, properties of operations, and/or the relationship between addition and subtraction.
     

  • Using efficient strategies or algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

     
Note that students are not expected to use standard algorithms (e.g., carrying and borrowing) to solve addition and subtraction problems until 4th grade. Introducing these algorithms too early can lead to procedural use without conceptual understanding. The focus in grades K-2 should be on building strategies based on number sense, base 10 understanding, and properties of operations to set solid foundations for later work with more efficient algorithms and mathematical concepts.

Action Item

Using this information, select some items from the OGAP Item Bank that will provide you evidence of your students' progress in relation to the expectations of magnitude and strategy use for your grade level (See in particular, the Additive Situations and Base 10 Strategies sections). Administer a couple of items. Use the OGAP Quick Sort to analyze the strategies students are using and errors they may be making.
 
Ask the following questions based on the evidence from these items:

1)      Where are my students in relationship to the expectations for               my grade level?
2)      What is evidence that I can build on?
3)      What errors or issues are evidenced in the student work?
4)      How should I focus my instruction based on this evidence?
 
Use other OGAP items, items from your instructional materials, or released items during instruction or as entry or exit cards to help guide your day-to-day instruction. Keep the Number, Addition and Subtraction Progressions front and center.
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