Base-10 Practice

Today we played a great game to practice place value exchanges when adding. 

I started with a template of ten leaves, each with a digit 0-9.  (You can find it at here)  I cut the leaves out, and then placed them in a pile.  Students drew four digits, and arranged them to create two two-digit numbers. 

Next, students lined the two numbers up to practice double-digit addition.

Differentiation, anyone?My students--even my highest math kids-- are shaky on the concept of regrouping.  Some don't "carry" at all...some do it at random...others do it, but don't have a strong conceptual understanding of what they're really doing when they "carry" a digit. 

To combat the confusion, and to make more visible the need for regrouping, I took a file folder (dual purpose: use for storage afterward), opened it up, and drew a grid with boxes that would the leaves. 

Another support strategy: Draw the grid on your students' personal whiteboards with Sharpie or other permanent markers.  This can be removed later, and quite easily, with either bleach cloths (think Clorox or Lysol) or by simply wiping a regular dry erase marker over your Sharpie lines. 

I did both, using the folder myself for demo and modeling and giving each student a whiteboard and marker to actually write out each problem (since the ultimate goal is for them to be able to line up and correctly add multi-digit numbers independently).  For some of my learners, writing what they know is a critical part of committing it to memory. 

In order to really make the need for regrouping more apparent, I also wrote the digits 0-9 onto post-it notes.  This way, when we added digits to a sum larger than nine, I could say, "whoa! problem!" and demonstrate that I couldn't fit 2 digits into one place value position.  (Eventually one of my students remarked, "Wow, Miss. You got so much problems!")

Enter the base-10 manipulatives:
Once it was obvious that all of the ones we had wouldn't fit into the ones place, I asked my students, "What can we do now?  Is there any way you can get some of those ones exchanged?"  After looking at the 10s-strips and 100s-flats in front of them, eventually each group figured out that I would trade them a 10s-strip for 10 of their ones.  And once that exchange took place, they were able to select which of the two digits from their original answer went in the 1s place, and which went into the 10s place.

One more note of differentiation: I modified the activity even farther so that the addition was one-digit.  Even students who are only adding one digit numbers can practice exchanging ones for tens, which provides them with background experience for adding double-digits later on.

...That's the long version.  The short of it is that this activity was SO effective for practicing all of the skills and concepts necessary for successful double-digit addition!