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.

Using base ten blocks lesson 4: Addition (no regrouping)

Race to 100

Race to 100 is a fun and engaging game for children. The game is simple and straightforward. Two students roll die (or dice) and try to be the first to reach 100.

Place value and regrouping are two concepts that children unknowingly learn through practice and play. The video builds on prior lessons. An important concept we have to share with kids (we can explain it as part of the rules--don't overteach it) is "trading-in". Trading-in is the same as regrouping but we have to explain the rule to kids: when we have ten of any one kind of block (unit, rod or flat), we have to trade in. So if we have ten units, we pick up those ten units, trade in for one rod and place the rod in the rod column. I usually emphasize and exaggerate during trading-in for the first few games with students--or until they picked up the trade in rule. It's also helpful to remind students during play: Wow, you have a lot of units. How many units do you have? Let's count and see if you can trade in for a rod.

Before students play Race to 100, I usually play Race to 10 or 20. This allows students to familiarize themselves with the mechanics of the game as well as with the trading in concept. They learn the basics of rolling the die (or dice), counting pieces and placing them on the board and becoming more automatic with trading in pieces.

Introducing the Base 10 Chart

using base ten blocks lesson 3: How Much is Covered?

using base ten blocks lesson 2: What's Your Number?

using base ten blocks lesson 1: introduction and exploration

using base ten blocks

base ten blocks are great manipulatives and versatile in that they can be used to teach a wide range of concepts--place value, addition, subtraction, number sense, etc.

i first began using base ten blocks while tutoring jason (not his real name)). jason was a second grade student with learning disabilities. math was one of his most dreaded subjects. when i first started tutoring him in multi digit addition and subtaction, i wrote out the problems, divided the columns, gave him visual and verbal cues for regrouping and moving to the next column. at some point i realized that jason never developed certain foundational math concepts and that was the main issue. i could teach him tricks, techniques and short cuts 'til he (and i) were blue but it wouldnt help address the underlying issue--understanding place value.

he had little sense of place value. if i asked him to add 120 and 100, he had to write it out and add it up. there was no sense of "maybe i can group the hundreds and tens values". there was no sense that the two in the tens place represented 2 tens or twenty. so i decided to try base ten blocks and have jason explore place value, addition, and subtraction with base ten blocks. most of the activities in this section are lessons and activities ive used with jason to develop his understanding of foundational math concepts.

-shaun skariah