Thursday, February 13, 2014

Working Toward Conceptual Understanding of Double Digit Subtraction Part 2

Several weeks ago, I posted about an intervention group of third graders who need some major conceptual development around double digit subtraction.  Today I want to show you how we moved forward from there.  The following shows some of the steps I took with this same group of students to move them toward three digit subtraction.

Place Value to 1000

I used several things to make sure students had an understanding of place value of three digit numbers as well as the ability to read and write these numbers.  I used my arrow cards along with my place value to 1000 deck for most of these activities.
 Here students use arrow cards and sketches to represent the number 850

 Here you can see that a student has written the number 480 as 804.  Using the visual images on the place value deck along with hands on activities with base 10 pieces and group discussion helps correct this problem.
 When students are comfortable with numbers up to 1000, I use the larger arrow cards to push to even larger numbers.  Here students build a number using arrow cards to read to the rest of their group.
 Here students write numbers to match the pictures on the place value deck cards

Playing 10 more/10 less and 100 more/100 less

The next step was to make sure kids were comfortable adding and subtracting 10 and 100.  We play this simple game using the place value deck to practice this important skill.  The visual images of the base 10 pieces really support this skill as it is developing.

 Students create their own record sheet.  The number of the card they flip goes in the middle.  To the left they find 10 less (or 100 less) and to the right they find 10 more (or 100 more)
 This game is simple, effective and requires no teacher prep.  My favorite kind!

Moving into subtracting other numbers

We then moved into doing some problems and problem strings as a group.  This is when kids are shown the problem, get some think time and then we share answers and strategies with the whole group or with a partner and then with the whole group.

 Here is how one student used previous knowledge about 100 - 78 to get himself started with 1000 - 781
 Here is another student's process for finding the answer to 1000 - 781
 Here is how another student thinks about 1000 - 781.  Notice how they use addition to add up to 1000.
This group has come a long way in a few short weeks.  I am hoping to be able to say they are all caught up with their peers (at least in this area!)

It takes some time, but this conceptual development of big ideas of mathematics is always worth it!