Constructing Tens and Ones
Lesson 9 of 13
Objective: SWBAT count large quantities of objects. SWBAT construct tens and ones out of a large quantity of objects.
Setting Up the Learning
We are going to be talking about using tens and some extras today. That makes me think about when we talked about the numbers 10-19 being 10 and some more. Let’s sing our group of 10 song to help us get ready to think about these other numbers today.
We are going to be using big numbers in our story problems one day so we need to understand how to break these numbers into groups. Using those groups will help us as we figure out how to add and subtract these groups later in the year.
Your thinking job today is: How can I show this number in groups of tens and some extras?
I'll start the lesson by presenting a bag of cubes.
Partner Talk: How many do you think are in here?
Let’s count and figure out how many we really have.
I will counts by 1s, students chorally count along with me. I will write the number on the chart paper so we can refer back to it throughout the lesson.
I want to be really explicit about the connection between 10 and some more for numbers 11-19 and the structure of the number today. For students, this pushes them to "Look for and make use of structure", which is one of the CCSS Mathematical Practices (CC.MP.7).
"So I see that we had 32 cubes today. I’m thinking about the other day when we made numbers that were 10 and some more. T refers back to that anchor chart-I see that 13 was 10 and 3 more, 14 was 10 and 4 more. The 4 told us how many ones, and the 1 told us how many tens."
Connecting to the idea of 10 and some more allows me to spiral in 1.NBT.B.2b, "The numbers from 11 to 19 are constructed of 1 ten and 1, 2, 3...or 9 extra ones".
Focus Question: I have 32. How could I group these cubes to make them easier to count?
"I see that _____ told me I could put them into groups of ten. Let’s do that first."
"We counted to 10 3 times. How many tens do you see? (Push kids to say 3 NOT 30). But did that take care of all my cubes? No! I have 3 groups of 10 but I also have these 2 left over."
Again pushing the Mathematical Practice (CC.MP.7) of making use of structure, I want students to connect the way the number is written, or the structure of the number, to the model we created out of tens.
"Let’s look back at our number and compare it to how we made 32 with cubes. To write a 32, we write 3 and a 2. What does the 3 tell us? The number of tens! We have 1, 2, 3 tens. What about the 2? What does it tell us? The 2 tells us that there are 2 extra, we call those 2 ones."
I will present a problem for students to work on in partners.
"I have a few bags here that have different numbers of cubes in them. Your job is to figure out how many cubes in each bag! You and a partner can work on this together. Count how many and show that number in groups of 10."
I will have students work in partners to construct tens and ones. As I float, I'll choose specific students to share out their thinking.
See attached video for an example of how partner work can help with misconception. You can also read more about this interaction in the reflection.
I'll choose 2 student bags to showcase, and I will chart how students created that number using tens and ones.
Guiding Questions during Strategy Share:
- How does your model with tens and ones match what your number says?
- How could we use how the number is written to figure out how many tens and ones there are?
- How do we count the ten sticks? How many ten sticks are there? (Focusing on number of tens)
- Can I count these single cubes by tens? Why not?
- Where is that number in my model?.
Directions: Students get their own bag of cubes to count. Students predict how many are in the bag, count the cubes, record the number, construct tens and ones, and represent their models in drawings.
To differentiate this activity, my students in need of intervention will get bags with numbers under 50. I will also provide them with a ten frame to support their thinking.
For students who need an extension, they will get “trickster” bags. Example-Students might have LESS than 10 in the bag (how many tens are in 7?) or MORE than 100!
I will review the day's objective and have students share their work with a partner to close out the day:
"Today’s thinking job was: How can I show a large number in groups of tens and some extra ones?"
Partner Talk: Show the first number you did. How did you show that number in tens and ones?