In this portion of the lesson I invite students to the carpet. I ask students if they can tell me what materials I have placed on the table. Students notice that I have base-ten material on my table. As I hold up each one starting at the thousands, I ask them to tell me the value of each. I probe a bit more. I write 238 on the board. Can anyone show me how to represent this number using base-ten materials? What number is in the ones, tens, and hundreds place. I go over a couple more numbers just to see where students are in their learning, and to make connections using previously learned skills.
Well today we are going review base-tens a bit to get us ready to go deeper into understanding and explaining math problems. We are going to start by trying this fun interactive activity. This activity will help us better understand the value of numbers. Are you ready? I remind students of my call system. This helps me keep track of students who have already responded to questions, and it is a great way to ensure all students are participating. As students are working, I reinforce place value skills. MP7-Look for and and make use of structure.
In this portion of the lesson I want my students to spend some time locating multi-digit whole numbers on the number line. Before they begin this activity, I want to demonstrate what they will be doing. A fun way to help students become more fluent in any skill is to allow them to explore the concept in multiple ways. MP1-Make Sense of Problems & persevering in solving them.
I draw a number line on the board. I use 235, 245, 255, 265, 275, and 285, to start. Can anyone tell me where I would place my red marker if I wanted to choose a number between 245 and 265? How do you know? If I place the marker on 285, would I be within a good range of the number I am looking for? Why? What number would this number be closer to? How do you know? (e..g.,some students can determine numbers that are too high by locating the place of each number. For instance, 235 is lesser than 245 because the 3 in the tens place is smaller than the 4 in the tens place.) I will repeat these steps using different numbers two or three times more to make sure students get the hang of what they will be doing.
Task 1: students will practice locating numbers within range on a number line.
Task 2: Students will continue to practice locating numbers within range on a number line, but they only have about two estimations to get it right.
As students are working, I will reinforce place value skills, and basic number sense.
Materials: base-ten material, paper, pencil
In this portion of the lesson students are going to practice making multi-digit numbers using base-ten material. I ask students to pair with their assigned partner. I pass out material to to each paired group. Then, I ask students to represent the number 324 using their base-ten material. I give them about three minutes or so to think quietly about how they are going to do it. I notice some students choose to illustrate their base-tens instead of cutting it out. MP4-Model with mathematics.
For the most part, students use what is comfortable to them to represent the given number.
Then I give them about three minutes to make the model and discuss with their partner how they are going to explain it on their task sheet. I give an additional 3 minutes for them to write their response. After that, I ask students to share their responses with the paired group sitting at their table. I walk around the room to monitor students’ responses, and supporting when needed. Some students arrive at the correct answer, but choose to use different ways to represent their number. I ask them to explain how they both got the same answer, but answered in different ways. (Because there are different ways to make numbers..... If I want to show more than one way to make the number 12, I can use (6 + 6= 12, or 10 + 2=12) It works the same way for larger numbers too!) MP7-Look for and make use of structure.
Actually, you guys are making connections between other mathematical ideas and applications to help you understand complex ideas.. Keep up the good work!
After about 3 minutes I call on random students to explain how their partnership responded to the given task and whether or not they agreed.
This activity is great for students who are reluctant to participate, because they can learn how to respond to questions by listening to their peers. I repeat this task using different numbers for about 10 more minutes. I use students’ responses to decided if additional practice should be incorporated.
In this portion of the lesson I want students to take time to reflect on what they have learned.
What students should know:
I explain that they should be explaining how they know the relationship between the digits in a number, How adding a (o) zero to the end of a number can affect the value of the digit, explain how numbers are different in value and why, how do you think place value connects to other math operations.
I take time to write the essential responses on the board, so that students can focus on the importance of this lesson. I given them about 10 minutes or so to write in their math journals. As students are working I circle the room to check for understanding. For instance, I ask how would adding a 0 to the end of a number affect the value of the digit. (e.,g..The number would be greater than the first number because the zero would increase the value of the digit.)
I use their notes to determine if additional practice should be incorporated.