The eventual goal of this standard is fluency. I explain to my students that this will not happen all at once; I hope to gradually move them towards having their own procedures and strategies by which they can fluently add and subtract. I invite students to the carpet to discuss place value. I want to make sure my students have a firm understanding of the values of digits in two-digit numbers before I move them into adding and subtracting three-digit numbers.
To do this, I write 56, a two-digit number, on the board. I ask students to tell me what digits are in the ones and tens place. Then I ask a volunteer to come up and illustrate how we would represent 56 using base-tens. The representation should show 5 ten-rods and 6 ones. I ask if there is another way we can represent the value of each digit. I give students a hint; I tell them we have used this chart before when we needed to understand the value of two-digit numbers. Students are quick to say a place value chart. I enter the numbers into a blank place value chart on the board by placing the 5 under the tens place and the 6 under the ones place. Just to make sure students understand the importance of digit value, I ask them to tell me if I have placed the numbers correctly. Some students explain that I placed each number correctly because there were 5 tens and 6 ones in the base-ten model. I continue to work with students using a couple more two-digit numbers just to make sure they fully understand the value of digits before I move forward. MP6- Attending to precision.
Material: Students Work
In this portion of the lesson I want my students use what they know about place value to correctly identify which digits are in the ones, tens, and hundreds place. This will help them correctly align numbers. First, I demonstrate what they should be thinking and saying. For example: 64 + 5 is written in sentence form. In order for you all to add or subtract the two numbers using the standard algorithms, you need to correctly align the numbers. To start, the largest number should always go on top! Which number is the largest? (64) I ask them to explain why 64 is larger than 5. Some students notice that 64 is a two-digit number, and 5 is only a one-digit number. You are correct, but based on the value of the digits, 64 is larger because it has 6 tens and 4 ones, and 5 only has 5 ones. To make sure students fully understand I use my magnetic base-ten blocks to represent 64 and 5. What is the difference between the two numbers? The visual representations confirm students thinking. MP3-Construct viable arguments & critiquing the reasoning of others.
After I have fully demonstrated what they will be doing and how they should be thinking, I ask students to move to their assigned partner. You all are going to work on identifying digits to help practice addition and subtraction through 100. As students are working, I circle the room to see if students can add and subtract accurately, and to see if they can explain their strategies by asking questions. Why did you align your numbers that way? Explain. Can you tell me the correct position of each number? Can you explain the reasoning behind the strategy you used? Can you think of another method that can help you correctly identify the value of digits? MP1- Make sense of problems and persevering in solving them.
Student work samples show how students used place value in order to solve addition and subtraction problems.
Material: Spinner Activity
In this portion of the lesson, I want students to have additional work time. I want them to know there are different ways of thinking about properties of operations to add and subtract. By exposing students to different methods and viewpoints, students can pursue their own purpose. Therefore, many of my students who were struggling are coming up with different approaches, discussing various strategies, and learning from one another.
To see just what students are capable of doing on their own, I ask them to move into their assigned groups and provide them with base-ten materials. I explain that they will take turns spinning two numbers to either add or subtract. However, I ask them to first represent each number with base-ten blocks and to identify identify the value of each digit before aligning the numbers. This assures that they are adding hundreds with hundreds, tens with tens, and ones with ones. As students are working, I circle the room to check for understanding. For instance, I may ask: what digits are in the ones, tens, and hundreds places? Can you explain? Can you represent the number using base-tens? Why is it important to align the numbers according to their place value? How does place value help you solve addition and subtraction problems? Some students discover that place value helps them group digits according to the value. Other students can explain the value of each digit fluently. For example, one girl in my class was able to classify digits by their value, and another used her notepad to enter the digits into the correct places. As students in her group modeled numbers and aligned the digits, she explained why they are wrong or right. I continue monitoring students until their given time is up.
I want to end this lesson with students giving their own account to what was learned. I ask students to join me on the carpet, and I take a seat in the middle of the circle. I ask student volunteers to begin sharing. As students are sharing, I make sure to ask questions to check for understanding. For instance: What number is in the hundreds, tens, and ones places. Can you represent the number using base tens? Can you explain why your illustrations represent your number correctly? Students seem to know what materials to use to represent hundreds, tens, and ones. They also know the value of each digit in isolation. They use this information to help them correctly add and subtract two- and three-digit numbers. I also ask them about moments in their learning where they struggled. This helps me to collect meaningful data for re-teaching strategies. Some students recall just knowing where the numbers should go, but not actually knowing how much each digit was worth. I ask what helps them understand the value. They all agreed that allowing them time to use base-ten materials and place value charts helps them make sense of the worth of each number.
To end I ask students to complete this activity by writing their experiences in their math journals.