Today I will be talking a lot about place value (hundreds, tens and ones) as I introduce the traditional addition algorithm and its derivations. I will use the warm ups today to review place value terms so students are ready for work with the algorithm.
I ask students to write the number 369 in their math journals. I ask them to circle the digit in the hundreds place. What digit did you circle? (3). What is the value of that 3? What does it stand for? (3 hundred). Do the 3, 6 and 9 all mean the same thing, stand for the same thing? (I hope that students are able to tell that the 3 is 3 hundred, the 6 is 60 and the 9 is 9 ones. If not, I ask further questions to bring this out, such as how many tens in the number? (6) What does that mean? (6 tens or 60).
I ask students to write the number 790 in their math journals. I ask them to circle the digit in the tens place. What did you circle? (9) What does the 9 stand for? What is its value? (9 tens or 90). What does the 7 in the number stand for? What is its value? (7 hundreds or 700). How many ones in this number? (0)
I repeat the process with the numbers 603 and 814.
I watch for students who are still struggling with the concepts of hundreds, tens and ones and what the digits mean. I will work with this group separately later in the independent practice part of the lesson to support this concept understanding.
For this part of the lesson I gather students on the rug. I have a small box of 9 tens rods and 20 ones cubes in each box. I hand each group of 2 students a box and a drawing of a house on a large piece of paper. The house is divided into 2 sides and 3 floors (as seen in the videos below). The left of the house is the ten's apartment and the right is the ones. Each "family" has an upstairs, a middle floor and a basement in their apartment.
I point out the tens side and the ones side. Next I ask each team to build the number 43 in the upstairs of the house. I have one person in each pair build the ones and one build the tens part of the number. Next I ask them to build 25 in the downstairs of the house. I put the equation 43 +25 on the board vertically with a house around it. I ask students to slide everything to the basement of the house and count it. What do they have? (68). I put the 68 for the answer for the problem on the board.
We repeat the process for 32 + 25 and 71 + 12 (use any numbers that do not require regrouping here). If I think students understand the process I now ask them to build 27 + 35, which I write vertically on the board. We repeat the process of bringing the blocks to the basement to count them. For the first time we have more than 9 ones. I ask students to count how many blocks in the basement. Most will count on and say they have 62. I ask students how many ones they have (12). I write the twelve below the line. I ask students how many tens they have? (5 tens or 50). I write the 50 below the 12. Now I ask students how much 12 + 50 is? I draw a new equals line and write 62 below it. Is this what they have for blocks? 12 ones and 5 tens? And together they add up to? (62).
I repeat this with the children with different equations where the ones total more than 9. I do enough problems that I feel that children are demonstrating an understanding of the process. I note those who are still struggling.
I break the students into 3 groups to work at practice centers today. Students only visit one of the centers. This allows students to work on the things that they are having trouble with, or to move ahead and be challenged.
Center 1: One group of students is struggling with place value. They work to identify the value of digits in 3 digit numbers. They read a number and then one of the digits is pointed to by an adult at that center. Each student takes the correct number of base 10 blocks (hundreds, tens or ones) for just that digit. If the number is 245 and the 4 is pointed to, students take 4 tens blocks and when asked what the value is say 40.
Center 2: Here students work with an adult (if there is a second adult in your classroom) to build 2 2-digit numbers with base ten blocks, using the houses, and then add the numbers.
Center 3: Students work independently to complete 2 digit addition problems using the algorithm and/or base 10 blocks.