Some of my students seem to have a difficult time understanding place value and number sense. In this lesson I want to explore strategies they have already used to assist them with understanding.
To start I invite students to the carpet to brainstorm what material can be used to build a house. Several students say, wood, and other say they would use bricks. I want students to understand that they have to build a house in the same way they build numbers. It is important for students to understand that they are actually building the number 1,000.
I place a large place value chart on the board to demonstrate how the digit values change as they are moved around in large numbers? I write the number 3256 on the board, and ask students to tell me what number is in the hundreds place. (2) I enter the number two under the hundreds column, and write 200 on the board. I explain that the 2 represents two hundred instead of two because it is placed under the hundreds column. I write another number using the same number as before, however, I write 2356. I ask students what number is in the thousands place. (2) I enter the number two under the thousand place. I write 2000 on the board. I explain that the 2 represents two thousand because it is placed under the thousands. Can anyone explain what determines the value of a digit? Students explain that the value of the digit is determined by its place. Great Job!
MP.4. Model with mathematics.
MP.6. Attend to precision.
MP. 8. Look for and express regularity in repeated reasoning.
In this portion of the lesson, I ask students to grab a partner. I explain that I will call out a number, and they will represent that number using base-tens. I say it is the same thing as building guys; you are going to actually see how numbers are build.
To start, I demonstrate how to build 2,459 on the board. First, I enter the number in the place value chart. As I write I explain the value of each digit. For instances, I say, I have 2 thousands, 4 hundreds, 5 tens, and 9 ones. Because my students are going to be using base-tens materials to build their numbers, I point to the material that correctly represents the value of each digit. I repeat this using two more numbers just to make sure students understand what to do. I encourage students to refer back to the chart on the board to help them determine the value of digits. To help them become better thinkers I ask them to explain why and how numbers increase and decrease in value according to where they are placed on a value chart. Students explain that numbers grow in a 10 times a given number when moved one space to the left.
For struggling students, I encourage them to keep their place value chart handy to support their number. For instances, they can enter the number on the chart before they build it using the base-ten material. This will allow students to be more precise in their work. All students are actively engage in their learning. When their time is up, I ask student volunteers to share their learning experiences with the rest of the class.
Material: Students indpendent assessment.docx
In this portion of the lesson I want students to demonstrate what they have learned so far. Each student will explain the value of each digit in a given number. I encourage students to use notes that are on the board to help them determine the value of each digit. As students are working, I circle the room to check for understanding. I am careful not to interrupt students who appear to be working just fine.
But, I want to assist students who seem to struggle with answering the given questions. For instances, I may ask students to represent the value of certain digit using base-tens. Sometimes a visual explanation can help students determine the value a lot better than the number written in standard form. I continue to circle the room assisting as needed. I use students’ work samples and explanation to determine if additional practice is needed.
Some students struggled throughout the lesson. I invited students to a smaller group session and gave each student a copy of their assignment and a pair of scissors. I ask students to cut apart the cards.
I explain that they are going to use these numbers to create large numbers. I ask students to play with the numbers for 1-2 minutes. I ask students what they notice about the numbers. I accept several responses; however, they are not reasonable. I write a number on the board and ask students to use their number cards to create the number. I do this several times. If students are struggling, I model for them how to stack the numbers on top of each other to create the number. I discuss the value of each digit by pulling out the number card to reveal the value. I repeat this process until students are able to explain the process mathematically.