using base ten blocks lesson 5: Addition with regrouping

Many students begin learning addition with regrouping--also referred to as carrying over-- in a mechanical and almost robotic fashion. Take 17+3: We start adding up in the ones column. 7+3 is 10; bring down the 0 and carry the 1 to the tens column. 1+1 is 2; bring down the 2. The answer is 20. While they get the answer correct, there is little understanding of the process that they went through and even less understanding of the concept of place value.

Using Base 10 blocks for addition with regrouping helps children feel, touch, manipulate and see addition problems. They then begin to develop connections between numbers, quantities, place value, and operations. A child with experience with base 10 blocks will start to physically take apart and recombine numbers-- using the manipulatives--and later, do so mentally; they begin to internalize what they've learned from their experiences.

Before beginning children/students on addition with regrouping, it's important they have had sufficient time to develop familiarity with the blocks as well as some prerequisites including:

1. Recognizing relationships between units, rods and flats, i.e., 10 units make up a rod, 10 rods make up a flat.

2. Used blocks with base 10 chart to represent values. Children should have experience creating quantities using base 10 blocks on a chart and writing down their values. They should recognize that the number 113 is made up of one flat, one rod and three units. They should also create numbers using base ten blocks and write down its value.

3. Addition (no regrouping).

Optional but helpful:

4. Race to 20 (or 100--depending on what is appropriate for the child). The game helps develop the "trade-in"rule, which is an important concept in regrouping. It familiarizes students with the rule but doesn't overteach it. When students move from the game to addition with regrouping, the trade-in rule is already second nature or something that's very familiar to the student.

Using the tips and techniques listed above, students progressively develop important math ideas and build upon experiences, from prior activities, to successfully transition into new concepts. More intriguing is watching students develop a slew of ideas and concepts that we didn't have to teach them; rather they learned from their own exploration and experiences.

Using Base 10 blocks isn't the panacea for all math challenges and ills but it does help children develop a deeper understanding of numbers and the operations they're engaging in.