I am going to write two numbers down. I want you to decide which is greater. I also want you to be able to explain which number is greater.
Write : 341 339
Turn and talk: Which number is greater and WHY?
Students should be able to explain why using place value vocabulary (i.e: four tens are greater than three tens so I know 341 is larger OR even though 339 has more ones than 341, a ten is larger than a one and 341 has more tens)
At this point in the year, most of my students have an understanding of tens and ones. I chose this problem because it allows students to explore the relationship between tens and ones (i.e: some students might immediately think that 339 is greater because it has more ones--this problem encourages students to consider the tens place). I want my students to be able to understand and internalize the difference between the tens and ones place (i.e: even though 339 has more ones, it has fewer tens and tens are greater than ones). For students who do not have a clear idea of tens and ones, I set this problem up as a turn and talk so that they can listen to their peers' ideas and verbalize their current level of understanding.
Now, we’re going to do another practice problem. I want you to decide which of the following number sentences are correct.
I post this problem on the board or on a piece of chart paper.
Which of the following number sentences are correct?
Turn and talk: Which problems are correct? How do you know?
During the turn and talk, I allow students to use a number line or hundreds, tens, and ones blocks if need be. I leave these resources in the middle of the carpet and allow students to access the manipulatives if need be (we have worked on using these manipulatives in past lessons.) Students also have familiarity with the >, < , and = signs from the past lessons. If these symbols are new for your students, take time to familiarize them before giving them the problem of the day.
I have two or three students share out what they discussed during the turn and talk.which number. I make sure that students are using mathematical/ place value language to discuss which number is correct.
If necessary, I go through 1-3 more practice problems as a group to solidify student understanding and to give students practice explaining their reasoning.
I start guided practice by handing out white boards and writing the words TRUE and FALSE on the board.
I am going to show you some number sentences. I want you to write whether they are true or false on your white board. You need to be able to explain whether they are true or false using your place value vocabulary!
Using a PowerPoint,I flash various comparison sentences on the board and allow students time to write TRUE or FALSE on their white boards. Then, I have them hold their white boards up and call on at least one student to EXPLAIN why their answer is true or false.
The comparison sentences on these slides use both standard and expanded form. I include both varieties of comparison sentences because I want my students to be able to reason both quantitatively (using standard form) and abstractly (using written or expanded form). These problems push students' thinking and challenge students who have a firm number sense when comparing three digit numbers.
I allow students who are struggling with comparing numbers to use a number line or place value blocks (hundreds, tens, and ones) so that they can more concretely envision the numbers they are comparing. I also encourage these students to draw the numbers they are comparing using place value blocks which enables them to visualize the comparison. It is also very important for students who are struggling with these number sense concepts to hear explanations for WHY one number is greater or less than the other and to be pushed to explain their own thinking. Being able to explain these concepts verbally pushes students to internalize the concepts and develop a greater mathematical vocabulary.
Now that we have practiced as a group, you are going to practice on your own.
I hand out the mixed practice packet (three pages).
At this point, I pull any students who have been struggling to work with me on the rug while the other students work independently at their desks. In this small group, I model a problem using place value blocks, allowing students to discuss and reason whether the statement is true or false. Modeling and giving students a concrete representation of the problem enables them to visualize the problem more clearly. After doing one or two of the problems as a group, I give each student in my small group a bag of place value blocks and have them work independently nearby me to build the problem using their place value blocks and then reason to solve the problem.
Today we reviewed how to compare two numbers. In your math journal please answer the following question:
Is the following statement true or false?
314 > 310
Explain how you know.
When students finish writing, I have them share their journal entry with their thinking partner. If time permits, I ask a student or two to share their work with the class.