So what’s the problem with place value? Why can students look at the same base ten block manipulatives that the teacher is looking at but not understand how to model quantities with them?
Researcher Constance Kamii says that, while adults have no problem looking at a “stick” and understanding that it is simultaneously one ten and ten ones, many students struggle with this idea. The result is that students come to believe that, for example, the digit 6 in 64 can only be viewed as six groups of ten, instead of understanding that it is also sixty groups of one.
Here is an activity that helps children think about how our base ten number system works. In this activity, students are encouraged to think about groups of doughnuts both as ten individual doughnuts as well as one box of ten doughnuts:
Alex and his dad are buying doughnuts for a party. In the store, the doughnuts are packed into special boxes that each hold ten doughnuts. If they bought 14 doughnuts, how many full boxes did they get? How many doughnuts were left over?
Have students explain their thinking with pictures, numbers, and/or words.
After all the students have solved the problem, have several students present and explain the different strategies they used. Discuss what is the same/different about each strategy. Discuss how the different strategies would work if you changed the number of doughnuts. Have students work out solutions for several different numbers of doughnuts.
Here are two excellent place value games.
Here are place value mats that help students develop the concepts behind regrouping by leaving a ten frame in the ones place.
Here is a virtual manipulative activity that focuses on decomposing for subtraction with regrouping.
Here is a ten frame activity to practice making tens.
Finally, here is a video students can watch that explains subtraction with regrouping.