3-Digit Addition with 'Trading'
Lesson 3 of 3
Objective: SWBAT use place value blocks to model adding 3 digit numbers and record their problem using the standard algorithm.
When I think about adding 3 digit numbers, sometimes I get confused about what I’ve added and how to write it all down. I know that I can use my base 10 blocks, and I know that I can draw picture models to represent what I’m adding, but sometimes the numbers are just too big for a picture. Show me with a thumbs up or thumbs down if you’ve ever been confused by these big numbers.
Today, we are going to learn a new trick to adding 3 digit numbers that I know will help you as become better math experts. At this point, have pictures of base 10 blocks (hundreds, tens and ones) and draw a large hundreds, tens and ones column on the board (or chart paper).
Place the pictures of the place value blocks on the board and have students identify which column they belong in and why (ie: the picture of the 100 block belongs in the hundreds column because I know it is a group of 100, or it is worth 100). Review the rules of regrouping and write them out to the side on the chart paper.
Who can tell me why people move that little 1 over to the tens place? Or to the hundreds place? What does that mean? What am I actually moving over to the next column? What is the magic number in every place (10!).
Ensure students can articulate why a group of 10 ones gets “packaged up” and sent to the tens place. I use my hands to model packaging it all up into a group of 10 and say the word “trade” for a 10 stick. Do the same thing for a group of 10 tens, packaging them up and “trading” them for a hundred.
This new trick that we can use to add 3 digit numbers will make it easier for us to keep track of what we have added and will also make it easier for us to record our work with numbers instead of using pictures of base 10 blocks. I don’t know about you, but it gets tiring drawing all of the hundreds, tens and ones pictures! I have my hundreds, tens and ones board right here that I’m going to use it to line up my numbers (the chart paper with the H T O columns) so that a one or a ten doesn’t end up in the wrong place.
I ask a student to roll a foam dice to generate our number (I use the ones that have 1-9 on them, and use them throughout the year for various activities).
I write that number out to the side of my board and ask what number is in the hundreds place and how much it is worth, what number is in the tens place and what it is worth and what number is in the ones place and what it is worth. I think it’s important students continue to discuss what value a number holds in the place that it is in.
Let’s say the number is 343. I then ask students how many hundred cubes I need to draw in the hundreds column, how many groups of 10 I need to draw in the tens place and how many ones to draw in the ones place. I let another student draw another 3 numbers and record them under the original number :
H T O
3 4 3
+ 1 2 8
I repeat the process of asking what to draw in the hundreds, tens and ones place. I ask students to read the problem back to me (3 hundred forty three plus one hundred twenty eight). I think this is also important for helping them understand how to say numbers properly.
Ok, so I’ve got these pictures, do the numbers I have written next to it match? Now the fun starts! Watch carefully, you might miss the trick! Let me see how many ones I have. Let’s count “1, 2….11” Wait, I passed magic number 10! What do I need to do? Package them up (I use my hands) and “trade” for a 10. I cross out the 10 ones and use an arrow pointing to the tens column and add a picture of a base 10 block to the tens column. Then I go to my numbers and show how I can move the group of 10 over to the tens place by placing a 1 in the tens column. We record our leftover 1 on both the picture and the number problem. We then move on the tens column and we add our pictures up. I didn’t get to magic number 10 in this column, so what do I do? We write the total in the picture model and the number problem. We repeat the same step in the hundreds place.
I think you’re ready to practice your new math expert trick. Use your foam dice to roll your numbers and build the numbers with base 10 blocks and write the number problems. Make sure you say “trade” when you get to magic number 10 and package up the group.
Students have a place value board (which can be made from legal sized paper, regular paper, or laminated larger paper to last longer), foam dice, and base 10 blocks. If I run out of base 10 blocks I use other manipulatives to substitute. I expect students to model with mathematics (MP4) their equation and corresponding representation of the problem.
Ok students, today we discovered a new math trick that experts use to show how to add 3 digit numbers. Who can tell me what this new trick helped them do today? Some possible student responses might be, "line up my numbers, keep the numbers in their proper place, package up a group of 10 and trade it in, keep track of what I’ve added, etc".
Review what it means to get to magic number 10 and why we ‘package up’ to send them over to the next place. Ask students why it is important that our picture and our number sentence match.
I know we are getting into large numbers, but when I line up my numbers with a hundreds, tens and ones column I can make sure my numbers stay in their proper place, plus, my place value blocks can show me the same thing that a number sentence can show me! I just have to remember that when I get to magic number 10 I ‘package them up’ and trade them in. Keep this tool in your math tool box, because we are going to need it again!