I am going to write a two-digit addition problem on the board (56 + 98). I want you guys to align the numbers so that the tens and ones are in the same column. Now, turn and tell your neighbor how you aligned your numbers and why. Make sure to use place value when you are telling your neighbor.
As students are discussing, I circulate and ask students questions. What number is in the ones place? What number is in the tens place? How do you know? Which number is greater? What number do you place on top when aligning your numbers?
MP8- Look for repeated reasoning
After students have talked with their partner for 3 minutes or so, I ask student volunteers to stand up and share their answers. As students share I make sure to high-five students who are using place value vocabulary to discuss their numbers. Some students respond by saying, "I know 98 is larger than 56 because one number has 9 tens and the other number only has 5 tens." Another student points out how he aligns his numbers by labeling the value above each number. "I place a T over the 9 and an O over the 8, and I place a T over the 5 and an O over the 6."
I repeat this task using a two-digit subtraction problem without regrouping.
98 - 27 = ?
Subtract the digits in the ones column. 8 - 7 = 1. Now, we need to subtract the digits in the tens column.
90 - 20 = 70. So, 98 - 27 = 71
I encourage students to use their place value mats and base-ten materials to explain their answers.
Material: Addition/Subtraction Problems
In this portion of the lesson I want my students to spend some time working with this concept on their own. I ask students to move to their assigned partner. I give them a set of base ten blocks, a place value chart, and four two-digit addition and subtraction problems. I hope that my students will use this exploration activity to discover place value concepts and learn addition and subtraction. The blocks can be set to represent ones, tens, and hundreds. Hopefully it will help students visualize the numbers with which they are working.
MP2 - Reason abstractly and quantitatively.
As students are working, I circulate the room to check for understanding. For instance, some students organize their base-tens where the numbers in the ones and tens place align. Some students organize one place at a time.
I ask, why did you decide to organize the problem like that? One student explains that he already knows how to align his numbers, so he decided to represent numbers first to show he understood the task. So, I decide to probe him a bit more. Is there a more efficient strategy? He explains it would be easier for him to go ahead and add. However, he did say working with the base ten blocks helps him become more efficient.
On the other hand, the student who represented his work problem by problem needed the visual representation to support his learning. What did you notice? Do you think this may work with other numbers? How can you be sure? He hesitates for a moment, but realizes that the strategy he is using, to add or subtract the digits in each place, can be used to help him solve the other three problems.
After about ten minutes or so, I ask students to turn and discuss their work with their partner. I want to see what my students are thinking, or if they need additional support. Most importantly I want my student talking and speaking mathematically to learn how to communicate better when they are explaining their own problem solving techniques.
See: Student work sample
The purpose of this lesson was to allow my students an opportunity to work with base ten blocks and place value concepts to help them develop mental imagery when adding and subtracting numbers.
In this activity, I want to check students' growth. To do this I invite students to the carpet. I ask a couple of probing questions. How did base-tens help you become better at adding and subtracting two-digit numbers? Some students say they normally get confused when problems are written as number sentences. Applying a visual helped them align their numbers correctly according to place value.
I write 76, 21, and 11 on the board. I ask: What digits are in the ones and tens places in each of these numbers?
In the number 76, 7 is in the tens place and 6 is in the ones place. I go on to ask students to represent the numbers using base-tens. I do this to determine if students know the value of each digit, and not just its place. I continue until we have discussed all three numbers.
I ask students what will happen if we add two of the numbers together. I ask students to choose two numbers. They decide to add 76 + 11. I write the problem in number sentence form to see if my students can align the numbers correctly according to their place value. I encourage students to use base ten blocks.
MP8 - Look for and express regularity in repeated reasoning. This practice helps students to reason mathematically.
Additional questions to support reasoning skills:
I give students about 2-3 minutes to align their numbers, and then I ask them to turn and discuss their work with their neighbor. After about 2 minutes, I ask student volunteers to demonstrate and solve the problem on the board. (They were able to explain the value of each digit and why it was important to add the ones with the ones, and the tens with the tens.) I ask: what do you think will happen if you add a digit in the ones place with a digit in the tens place? My students scream, "You will get the wrong answer!" Great! I continue working with my students until the the bell rings. I encourage students to make a journal entry of "Today's Lesson".
Be sure to mention if you understand the concept, or if you are still having trouble working your way through the concept. This will help me know if you need additional support.