Lesson 8

Ten as a Unit

Warm-up: Which One Doesn’t Belong: Groups of 10 (10 minutes)

Narrative

This warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It provides an opportunity for the teacher to hear how students use mathematical language to describe characteristics of the items in comparison to one another.

Launch

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

Activity

• 2–3 minutes: partner discussion
• Share and record responses.

Student Facing

Which one doesn’t belong?

Student Response

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Activity Synthesis

• “Let’s find at least one reason why each one doesn’t belong.”

Activity 1: Counting Collections: Count and Show How Many (20 minutes)

Narrative

The purpose of this activity is for students to count a collection of objects and show on paper how many there are so that others can understand how they counted. This collection of objects is a teen number of connecting cubes to encourage students to unitize a ten (MP7). In the synthesis, students consider representations that show a group of 10 cubes.

MLR7 Compare and Connect. Synthesis: After students have shared where 10 is in each representation, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “How did 10 show up in each method?” and “Why did the different approaches work?”

Required Materials

Materials to Gather

Materials to Copy

• Counting Collections Stages 1 and 2 Recording Sheet

Required Preparation

• Each group of 2 needs a bag of 16 single connecting cubes.

Launch

• Groups of 2
• Give each group a bag of connecting cubes and access to 10-frames.
• “Your job is to figure out how many cubes are in the bag.”
• “How can we make sure both partners are counting?”
• “What might it look like to count together? What might it sound like?”
• “How can we make decisions together about how we count?”

Activity

• “Work with your partner to count the collection. Each partner will show on paper how many there are and show how you counted them.”
• 10 minutes: partner work time
• “Trade your representation with someone from another group. Can you understand how the other group counted? Explain how they counted.”
• 3 minutes: partner discussion
• Monitor for students who counted and represented their count by:
• ones, in an organized way such as a row or tower of 16
• a group of 10 and some ones
• a tower of 10 and some ones

Student Response

For access, consult one of our IM Certified Partners.

If students leave the objects scattered as they count, consider asking:

• “How did you count the objects?”
• “How can you organize the objects as you count so you know you counted each one?”

Activity Synthesis

• Invite previously identified students to share in the sequence above.
• “How are these representations the same? How are they different?” (They all show there are 16 cubes, some show counting by ones, some are organized in rows, some made a group of 10 and counted on.)
• “Where is 10 in each representation?” (In _____’s representation, you see the 10 when they count up to it by ones, in _____’s representation, they circled 10 ones to show 10, in _____’s representation they connected 10 and wrote 10 before counting on to 16.)

Activity 2: Building Teen Numbers (15 minutes)

Narrative

The purpose of this activity is for students to compose a teen number as one ten and some ones. In the launch, students look at an example of cubes arranged in a tower of 10 and singles. Then students build teen numbers out of connecting cubes using a tower of 10 cubes. As students share their thinking, the teacher draws a tower of 10 units and some ones. For example, a student may say, “I have a tower of ten, and made a line with the 4 other cubes, 11, 12, 13, 14.” The teacher draws: 14

If students do not specifically describe their arrangement, the teacher should ask students, “How did you arrange the ones?” before drawing them.

Some students may connect the cubes that represent ones in their representation, but it is important that the teacher draw and label them as separate units.

Representation: Develop Language and Symbols. Invite students to explain their thinking orally using the cubes, as an alternative to the written explanation.
Supports accessibility for: Conceptual Processing, Language

Required Materials

Materials to Gather

Launch

• Groups of 2
• Display the image of 14 connecting cubes or show actual cubes.
• “Clare was counting her cubes and arranged them like this. What do you notice? What do you wonder?” (She made a tower with 10 cubes and put 4 more off to the side. Altogether there are 14 cubes.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

Activity

• 6 minutes: partner work time
• Monitor for students who represented 15, 16, and 17 to display in the lesson synthesis.

Student Facing

Choose 4 numbers to represent.
Circle them.

10

11

12

13

14

15

16

17

18

19

Use connecting cubes to show each number like Clare did.

What did you notice as you were showing each number?

Student Response

For access, consult one of our IM Certified Partners.

If students make a tower with more or less than 10 cubes, consider asking:

• “How many cubes are in your tower? How do you know?”
• “How many cubes were in Clare's tower? Can you make a tower with the same number of cubes?”

Activity Synthesis

• Invite previously identified students to share their representations.
• Record with a diagram.
• “What did you notice as you were showing these numbers with connecting cubes?” (They all had a tower of 10.)
• “The numbers we made today are called teen numbers. A teen number is a number with one ten and between one and nine ones.”

Lesson Synthesis

Lesson Synthesis

Display a base-ten drawing of 14.

“Today we showed teen numbers with connecting cubes. We can say 14 is a ten and 4 ones. How does this representation show a ten and 4 ones?” (There are 10 cubes in the tower, so that is why it is called a ten. There are 4 single cubes left over. That shows the 4 ones.)

Label the representation with 10 and 4. “We can also say that 14 is 10 and 4. We can write the equation $$10 + 4 = 14$$.”

“If I have a collection with 1 ten and 6 ones, how many are in my collection? What equation represents this?” ($$10 + 6 = 16$$)

“If I have 19 in my collection, how can I show that with cubes?” (1 tower of ten and 9 ones)
“What equation can I write?” ($$10 + 9 = 19$$)

Cool-down: How Many Connecting Cubes? (5 minutes)

Cool-Down

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