Despite our current standards placing an emphasis on place value strategies for addition and subtraction of multi-digit numbers, there continue to be many teachers who “teach” the standard algorithm as early as second grade. Why? Is it because many of us cling to the way we were taught? Is it because we struggle to understand the place value strategies? Is it because we believe the standard algorithm to be most efficient and are striving for efficiency rather than understanding? Is it because we misinterpret our standards thinking that when they mention multi-digit addition and subtraction they simply mean teaching the standard algorithm?
By quickly teaching students a series of steps to be memorized, we are robbing them of the time they need to fully understand the processes of addition and subtraction. We are skipping important lessons, discussions, and insights about place value that would bolster their number sense and help them better understand these operations.
What can we do?
- Pose simple investigations in which students count a quantity by ones and then bundle into tens or hundreds to explore place value concepts.
- Explore numbers through visual models that place an emphasis on seeing numbers as tens and ones (and then hundreds, tens, and ones).
- Spend time exploring and justifying different ways that numbers can be expressed (e.g., 48 might be 4 tens and 8 ones or 3 tens and 18 ones), providing the foundation for regrouping.
- Move from concrete experiences to drawings using squares, sticks, and dots to allow students to visualize numbers even when they are not handed concrete materials. Make connections between these drawings and the concrete materials used in prior investigations.
- Make connections between expanded form (100 + 20 + 5) and students’ concrete and pictorial place value representations.
- Help students connect their addition or subtraction methods (e.g., How is using base-ten blocks to combine two quantities the same/different from using expanded form to add two quantities?)
- Continue to revisit place value as students use various models to add/subtract (e.g., How did thinking about place value help you add on this open number line?).
- When students have developed place-value strategies and understanding, introduce and compare the standard algorithm to the place-value strategies they have been using so they discover how/why it works. Place two strategies side by side. How are they alike? How are they different?
Building a deep understanding of place value concepts leads to a deeper understanding of multi-digit addition and subtraction, as well as greater number sense. Let’s give our students this strong foundation!
You will find lots of specific ideas in the place value modules in Math in Practice. For more information about Math in Practice, visit https://www.heinemann.com/mathinpractice/