Teaching Place Value the CRA Way!

Place value comes up every year throughout elementary school. But what makes it so difficult for our students to understand and what can we do to make place value instruction more clear for our most struggling students.

Quick and simple place value games can help your students to build understanding and gain fluency with place value concepts. But before I get to the games...

Where do we start and where are we going? 

  • In Kindergarten, students are building a foundation by noticing that when they have ten ones and some more ones they create a teen number. 
  • In first grade, place value explodes with students understanding that ten ones can be put together to create a unit called a "ten" and that two digit numbers are really telling the number of "tens" and "ones". 
  • In second grade this understanding is extended as students work their way up to 1,000 noticing that this pattern of grouping ten of a unit together yields a new type of unit. 
  • In third grade students round and continue adding and subtracting multi-digit numbers... not a big place value year in terms of developing new ideas around the base ten system :) 
  • In fourth grade students resume the extension of units all the way up to 1,000,000 and begin to notice that instead of just saying "ten of a unit yields a new unit" that they can describe the relationship of units next door do one another by saying 10 times more or 10 times less. 
  • In fifth grade students tie together each of these previous understandings and apply them not only to whole numbers but to decimal numbers as well! 
It is clear that mastering the standard at each grade level is critical to moving on to the next grade level because each of these understandings is so closely related and builds so specifically on previous understandings. 

What does this mean for my instruction? 

It means that your students can not leave your grade level with an emerging understanding of place value concepts! I would go as far as to say that in the world of "Concrete-Representative-Abstract" that students need to have moved as far down this continuum as possible before moving to the next grade level. 

That being said, I am a staunch advocate of letting students stay in the concrete and representative stages as long as is needed because it will help your students to be more solid in their abstract understandings and your students will be more efficient at mental math involving place value in general!

What will this look like on a daily basis?

  1. Use SO MANY manipulatives when your students are learning about place value. 
  2. Use a variety of manipulatives- don't just get stuck using base ten blocks daily! When your students use a variety of manipulatives they are deepening their understanding and building connections between these models. 
  3. Be thoughtful about using pre-grouped, non-grouped, proportional and non-proportional models when choosing manipulatives and representations. 
  4. Link manipulatives, representative models and abstract equations together. For example, if you can show your understanding using place value disks, that's great! Can you write an equation that matches what you just did with your disks? 
  5. Repetition, repetition, repetition. My third grade teacher used to say "Practice doesn't make perfect, practices makes permanent!" That means that when our students are practicing these skills it is important that they are practicing correctly and that they are practicing in great volume. What they do well and often will become permanent! 

So, What About The Games? 

Play games that promote repetition with linking of hands on tools to abstract ideas. The game "One or Bust" is an example of this type of game. Students choose a card and add that block to their game board. Students link their understanding between the concrete and the abstract as they play by stating aloud the change in their numbers as they progress through the game. In this 5th grade version of the game students would say something like "I have sixty-three hundredths. One more hundredth is sixty-four hundredths." 

If you are interested in games like "One or Bust", I have created a version of the game for numbers to 100, 1000 and 1 (decimals). Click the pictures to check them out! 








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