In this lesson, I want my students to extend their base-ten understanding. We have been working with two-digit numbers, and they understand the value of ones and tens. I ask students to move into their assigned groups. I draw a place value chart on the board. I label it ones, tens, and hundreds. I ask students for an example of a two-digit number. They call out 56, 79, and 34. I ask what digits go in the ones/tens place for all three numbers, and I enter them into the place value chart. As I enter each number, I explain the difference between the values of each digit. For instance: In the number 56, there are 5 tens and 6 ones. I point out that the place value chart helps us understand the value of each digit. Can anyone think of another math manipulative that can represent the value of digits? Students are quick to say base ten blocks. I refer back to the chart and point to 56. How can I represent 56 using base ten blocks? (You can use 5 ten-rods and 6 ones/units.) You guys are exactly right!
I continue calling out a couple more numbers, just to make sure students can correctly represent a two-digit number using a place value chart, and base ten blocks.
For struggling students: I create a correlation chart, so that students can see how the place value chart and the base ten blocks can help make a connection between the written three-digit numbers and their value in hundreds, tens, and ones.
For instance, I write a two-digit number and ask students to enter it into the chart correctly. Some students enter the number just fine; however, some students struggle. If students struggle, I ask them to represent the number first using base-tens.
I point out the digit you represented using the ten-rods should be entered in the tens column, and the digit you represented using the ones should be entered in the ones place.
Students have just worked on MP7 Look for and make use of structure.
Now that my students have practiced using both base ten blocks and place value charts, I want them to use what they know to represent two- and three-digit numbers as hundreds, tens, and ones. I ask students to move to their assigned partners. I give each student a place value chart and a set of base ten blocks.
I start by writing 234 on the board. I ask students to represent this number using their base ten blocks. How many blocks do you have? (2 hundreds, 3 tens, and 4 left over.) Does that help you know what number to enter in hundreds, tens, and ones place on your chart? (Yes!) How many hundreds do you have? (2) How many do you have left over? (If I have 2 hundreds, that means I have 34 left over.) This strategy allows students to group objects into hundreds, tens, and ones. It is my goal for them to use that information to tell how many. I write 345, 567, 98, and 78 on the board. I tell students to continue representing each number using both the base-ten material and the place value chart. As students are working, I circle the room to probe students a bit. I want to see what they are thinking. How do base ten blocks help you understand entering numbers in a place value chart? (I pay attention to the different groups of hundreds, tens, and ones.) What do place value charts and base ten blocks tell you about about the digits in a number? (The placement of digits and the base-ten models help me visually see how much each digit is worth.) Can you give me an example? How does this activity relate to something you might do at home? (I use it when I count money.)
After students are finished, I fill out a questionnaire card, and share their responses with the rest of the class.
Materials: Model Whole Numbers
Equipping the students
In this portion of the lesson, I want my students to recognize that understanding the value of a digit is more than telling the numeral. Most second grade students who can comfortably understand the position and place value of the digits are able to model that number using many types of visual representations. Many students are eager to know a little bit more about visual representations. I take a moment to review several ways to model numbers, such as base ten blocks and real-world items. I ask students the questions to help them interpret the illustrations. How much does each illustration represent? How are they grouped? How many groups of hundreds, tens, and ones?
Students seem to really like using real-world items to represent numbers. However, some students tend to just know the place of the number, and not know what each digit represents.
Since students are still working in groups, I use the same numbers from the last activity: 345, 567, 98 and 78. Ok! I want you guys to give it a go on your own. Do not worry! I will be circling the room to see what you all are thinking, and to provide help as needed. As students are working, I pay close attention to how they are explaining the value of each digit. I ask questions such as the following. What is this number? Make this amount using your base ten blocks. Represent this number on your chart. Can you point to the number that is in the ones, tens, and hundreds place? What number does your illustration represent? Explain?
Work Sample: sample
I always try to make the close of the lesson fun and exciting, yet also a summary of what was learned. During this section, I basically ask students to share what they have learned about place value. As students are sharing, I make sure to ask questions to check for understanding. What digits are in the hundreds, tens, and ones places? Can you represent the number using base tens? Can you explain why your illustrations represent your number correctly? Students seem to know what materials to use to represent hundreds, tens, and ones. They also know the value of each digit in isolation. I also ask them about moments where they struggled in their learning. This helps me collect meaningful data for re-teaching strategies. Some students recall just knowing where the numbers should go, but not actually knowing how much each digit was worth. I ask what helps them understand the value. They all agree that allowing them time to use base-tens and place value help them make sense of the worth of each digit.
As a reward, I found this really unique online resource that allows them to reinforce their learning and have fun at the same time.