The lesson opens with a student turn and talk about what they know about two-digit numbers. Many students come into second grade not knowing exactly what a two-digit number looks like. This is why it is helpful for students to discuss in partners what they know. Sometimes students can teach each other what they know and share those ideas. In hearing their own thinking, students sometimes recognize their own misconceptions or realize that they may not know what they thought they knew.
Now, I explain to the students that, in the United States, we use a base ten number system. This means that we have organized the way our numbers work by tens. Ask the students what they know about counting by tens. Why is this helpful?
The students will need a place value mat, 10 tens rods, and 10 ones cubes. Before we begin, it is important to create the context so that students understand that we are using models that represent quantities.
So, I open with a "tour" of the place value blocks, showing ones, tens, hundreds, and a thousand cube to show how they all work together in our number system. There are ten of these (one cube) in this (ten rod). Since a ten rod is notched, give a students a moment to count the ones in their tens rods. So how much is this? (Show a one.) How much is this? (Ten rod.)
Let's keep right on going with our base ten system. There are ten of these (ten rod) in this (100 flat) and that makes....Do you think we can count by tens to figure out what number that is? Laying each ten rod right on top of the 100 flat, we count together by tens. I have a student at the board making tally marks to create a concrete proof that we have counted by ten, ten times.
So, let's go back for a moment. I return to the one cube and ask the question, "How many?" continuing on through to the 100 flat. Then I use the same model as used in the 100 block to demonstrate the thousand cube.
Show the students one individual ones cube. I ask them what this represents and where they think they should put it on their place value mat. With a place value mat on their desk top, have the students add one cube to the ones place on their place value mat. Keep adding a ones cube to their collection until they reach ten. Once they have reached ten, ask the students if you should continue adding the ones cubes to the ones place. If necessary, explain to the students that when we get to ten cubes in the ones place it becomes overloaded. When this happens it's like a magnet regroups the ten ones into a rod of ten. I have the students place ten ones cubes in a line and then compare them to the tens rods. Can they see the similarity?
It is at this point that I typically have the students think about how we could take tens rods to make 100. Although I've just done this work with them, it is important for students to do the thinking, and the work, themselves. I show them 10 tens rods and ask students to think silently and be ready explain how these would come together into a hundreds flat. Do you notice a pattern? How many hundreds flats do you think would make a thousand? Hopefully at this point they will realize it is ten. Second graders LOVE the big thousand cube!
Next I have the students begin to build two-digit numbers. I explain to the students that this is a way for them to model each number. We spend a great deal of time reviewing how each digit has a value. We begin practicing building together. I have the students build the number 23 on their mats. We talk about which digit is in the tens place, in this case it is 2. I have the students place two tens rods in the tens column on their place value mat. Next I have them look at the ones place in the number 23. In this case it is 3. I have the students place 3 ones cubes in the ones place. Next, I have the students look at the digits in the number 23 and at the model they just built. What is the digit in the tens place? What is the value? I often have to spend time reviewing with the students that the digit and value is not always the same. For instance, the digit in the tens place in this number is 2, but the value is 20. This can be difficult for students to understand.
I continue to have the students build two-digit numbers, turning and talking with a partner about the value and digit of each place, until I feel that all or most students understand.
Now it is time for the students to practice what they have learned. In my class, games seem to be a great way for my students to stay engaged, while I maneuver around the room to check for understanding and clarify misconceptions.
In this lesson I have the class play Place Value Bingo. Each student is given a card and a handful of BINGO chips (They put these on their name tag "bank" to keep them organized.) I print out a class set of cards before the lessons, mounting them on construction paper and laminate them so that I can use them year after year.
I begin calling out two digit numbers that I randomly pull out of an envelope. When the number is called the students need to look at their bingo card, and find the model of ones cubes and tens rods that represent the number I called. I tell the students that there is a free space, directly in the middle of the card and represented by the blue star.
The goal of BINGO, as always, is to get five in a row. As 2nd graders are quite young students, reminding them of the basic rules of BINGO is important.
If I find that getting 5 in a row becomes too easy, I can change the BINGO game to be a "Cover All" game, where students have to cover the whole card instead of getting five in a row.
Once students have five in a row, they call out "BINGO!" When a student gets BINGO, they read the winning row of numbers and I check to make sure that I have them all in my collection. We play a few times, depending on how long I have for the lesson.
Once finished playing the game, students put away their supplies and talk with their group about why they think we learned about building numbers and place value. It is an interesting time for me to listen to student conversation about their understanding. I often spend time listening to students talk about why we learn things. Their second grade perspective on a topic is very informative.
When I close this lesson, I tell students it is important for them to understand why they are learning about base ten. I tell them base ten will be part of their math tomorrow, the rest of second grade, in third grade, and fourth grade...and for the rest of their lives.