I start the lesson off by asking students to move into their assigned groups. I tell them I want them to understand that place value can lead to number sense and efficient strategies for computing with numbers. Even more important I want them all to be able to explain the process using mathematical terms.
Essential Question: How does a digit's position affect its value?
To see what students know about place value, I give each group a set of base-tens and place value mats. Then, I write three two-digit numbers on the board (56, 58, 78). I ask students to illustrate the numbers using the base-ten materials. While students are working I ask, What number is in the tens place? What number is in the ones place? How do you know? Can you use this concept to align numbers correctly in order to add and subtract them?
Some students say how many tens and ones they have, and some students align the numbers according to their value.
I gave students a thumb up for using mathematical terms to explain their reasoning.
Material: Thumbs up sign
The most important piece is to see what students are thinking, and if possible probe them a bit further to see if they can apply it in a newer situation.
I go over a few more two- and three-digit numbers just to make sure students have a good foundation before I move forward!
MP7 -Look for and make use of structure.
In this portion of the lesson, students will get to see how applying place value to adding multiple digits can be used to guide their learning. I tell students to stay in their assigned groups. I post a word problem on the board. I give students some base-tens and a place value mat. I want them to be able to "see" the action of the problem while they are working.
Sophie read her book each day for four days. She read for 30 minutes on Monday, 20 minutes on Tuesday, and 20 minutes on Thursday. She read for 100 minutes in all. For how many minutes did she read on Wednesday?
I ask students to read the problem aloud with me. What do we need to find out? (How many minutes did Sophie read on Wednesday?) What information does the problem give us? (It tells us how many minutes Sophia read on Monday, Tuesday, and Thursday. It tells us she reads 100 minutes in all). One of the students notices that the initial problem did not tell us how many minutes she read on Wednesday. I point at what we need to know, and I ask students to re-read it just to make sure they understand what the problem is asking us to do.
So if Sophia read 100 minutes in all, how can we find out how many minutes she read on Wednesday.
I take a quick pause here, because I want students to notice that this problem is actually two steps. I ask, Who has an idea where to begin? Students suggest adding the minutes for Monday, Tuesday and Thursday. So, you are saying we need to add 30+20+20= 70. Are we finished with the problem yet? (No, because we still do not have the total for Wednesday.) Who can tell me how to do that? (Once you have added all of the minutes, you need to subtract it from 100). So, we subtract it from 100. 100-70= 30.
How many minutes did Sophie travel on Wednesday? (She traveled 30 mins.)
During the actual adding and subtraction portion, I ask students to represent their actions using base-tens, if needed for support. Since we have been working for awhile on this concept, students are pretty comfortable representing with base-tens.
I go over a couple of more questions that are not two-steps, just to see what students are thinking so far. While students are engaged in asking and answering questions about the process, I check for understanding. For instance, once my students have solve two-digit problems I have them to look back at the problem to determine if the solution is reasonable. This allows me to see how well they can explain their reasoning using mathematical terms.
MP6 - Attend to precision.
Material: Word Problems
Now that students have gotten a chance to explore how this skill works, I want to give them a go on their own! I ask students to return to their original seats, so that they can show me exactly what they know.
I tell them they will be working on their own word problems. As they are working, I circle the room to check for understanding! Can you explain how place value was used to help you solve your problem? How do you know? Can you create your own problem? Can you draw an illustration to represent your answer, or to show how you solved it? The method behind these questions is to see how well my students can explain their answers mathematically, and to see if they can detect the repeated pattern used to solve each problem.
Some students explain how they got their answers using natural language - however, I want them to be able to explain using mathematical terms. As students respond, I repeat what they say using math vocabulary. Hopefully, my modeling will allow them to see how it should be stated.
I ask some students to write their responses on the board, and ask student volunteers to read it aloud to the class. As a class we re-write the responses using math vocabulary. Without knowing, students were critiquing the reasoning of others, and they offered different ways to solve the exact same problem! (MP3)
I continue this process until we review both problems.
After we have discussed and worked our way through each problem, I allow student volunteers to share their strengths and weaknesses with the rest of the class. I encourage students to ask questions to check their classmates' understanding. (Some students ask, How do you know that? Can you explain? Can you illustrate? Can anyone think of a different way to solve the problem?)
I use student responses to determine if students need additional time to explore this skill.