# Lesson 2

Find the Unknown Addend

## Warm-up: Choral Count: Count Back by 10 (10 minutes)

### Narrative

The purpose of this Choral Count is to invite students to practice counting by 10 and notice patterns in the count. As students make sense of patterns in the way that this choral count is recorded, they may notice and explain patterns in the way the tens place changes in the numbers arranged in rows (MP7). For example, students may notice that the numbers across each row change by 2 tens and change by 5 tens in each column. The counting practice and conversations in this activity helps students develop fluency and will be helpful later in this lesson when students will need to use or make sense of computation methods based on place value or counting by 10.

### Launch

• “Count back by 10, starting at 97.”
• Record as students count.

97     87     77     67     57

47     37     27     17       7

• Stop counting and recording at 7.

### Activity

• “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Activity Synthesis

• “Who can restate the pattern in different words?”
• “Does anyone want to add an observation on why that pattern is happening here?”
• “Do you agree or disagree? Why?”

## Activity 1: How Did You Find It? (20 minutes)

### Narrative

The purpose of this activity is for students to find the unknown addend in an equation in a way that makes sense to them and compare their methods. In the launch, students are introduced to base-ten blocks and compare them to connecting cubes. During the launch, students should be given time to observe the image and touch the connecting cubes and base-ten blocks.

Students may find the unknown addend using any method that makes sense to them. Monitor and select students with the following methods to share in the synthesis:

• count on or count back using connecting cubes or base-ten blocks
• use base-ten blocks to show combining or separating tens and ones
• use base-ten drawings to show combining or separating tens and ones

Students have the opportunity in the activity and the activity synthesis to consider the available tools and make a choice that best helps them find the unknown addend (MP5). To support student reflection on the utility of each tool, provide each group with towers of ten connecting cubes, but not enough to represent the numbers in the equation without needing to create new towers of ten.

MLR8 Discussion Supports. When groups compare methods, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “I heard you say . . . .” Original speakers can agree or clarify for their partner.

### Required Materials

Materials to Gather

### Required Preparation

• Each group of 2 needs 90–100 connecting cubes, but no more than 35 towers of 10 cubes should be included in their collection. Break apart any extra towers for this activity.

### Launch

• Groups of 2
• Give each group towers of 10, single connecting cubes, and base-ten blocks.
• Display the image.
• “Each group has some connecting cubes and some base-ten blocks.”
• “What is the same and what is different between these tools?” (They both are cubes or towers of cubes. The connecting cubes are in towers of 10, single cubes, and some are in towers of different sizes. The blocks are only in tens and ones. The blocks in tens do not come apart.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses.

### Activity

• “Work together to find the number that makes the equation true. You can use the connecting cubes, base-ten blocks, or other representations to help find the number or show your thinking. Be prepared to explain your thinking.”
• 6 minutes: partner work time
• As students work, consider asking:
• “Why did you choose this tool?”
• “How did you find the number that makes the equation true?”
• “What is another way you could use this tool to find the unknown number?”
• “Now compare your method with another group. How are your methods the same? How are they different?”
• 2 minutes: group discussion

### Student Facing

1. What is the same and what is different between these tools?

2. Find the number that makes the equation true. Show your thinking using the cubes, blocks, or drawings.

$$41 + \underline{\phantom{\hspace{1.05cm}}}=84$$

### Activity Synthesis

• Invite previously identified groups to share their methods in the given order.
• “Why did you choose this tool to help you find the number?”
• “How are the methods the same? How are they different?” (Some methods are the same, they just used different tools to show it. Some methods used the same tool, but are different because one group added tens and ones to find the unknown number, but another group took away tens and ones to find the unknown number.)

## Activity 2: You Go This Way, I’ll Go That Way (15 minutes)

### Narrative

The purpose of this activity is for students to find the unknown addend in an equation using addition and subtraction within 100 without composing or decomposing a ten. The synthesis focuses on which method students prefer and why. They continue to develop their understanding of the relationship between addition and subtraction as they describe and connect different methods that find the same unknown number.

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk. Give feedback on whether or not they are using the tools strategically and the efficiency of their strategies.
Supports accessibility for: Conceptual Processing, Language, Visual-Spatial Processing

### Required Materials

Materials to Gather

### Launch

• Groups of 2
• Give access to towers of 10, single cubes, and base-ten blocks.
• Display $$17 + \underline{\phantom{\hspace{1.05cm}}}=48$$.
• “Han and Mai are using blocks to find the number that makes this equation true. Both use blocks, but they start by showing different numbers.”

### Activity

• “Work together to use the base-ten blocks to show Han’s method and Mai’s method.”
• “After you do Han’s method and Mai’s method together, decide who will start with 21 and who will start with 96. Use the blocks to find the unknown number on your own.”
• 8 minutes: partner work time

### Student Facing

Han and Mai use blocks to find the number that makes the equation true.

$$17 + \underline{\phantom{\hspace{1.05cm}}}=48$$

1. Han starts by using blocks to show 17. Show how he could find the number that makes the equation true.
2. Mai starts by using blocks to show 48. Show how she could find the number that makes the equation true.
3. Try this one on your own. Choose who will start with 21 and who will start with 96.

$$21 + \underline{\phantom{\hspace{1.05cm}}}=96$$

4. Show your partner how you found the number that makes the equation true.

### Activity Synthesis

• “Which method did you like best? Starting with the total and taking away or starting with the addend you know and adding on?” (I like subtracting because it’s easier for me to see what the unknown number is when I use blocks or drawings. I prefer to add on because the equation shows addition.)
• “Why did you and your partner find the same number even though one person added and one person subtracted?” (The amount one partner added was the same as what the other partner subtracted. When you subtract, it’s like finding the unknown addend. Addition and subtraction are related.).

## Lesson Synthesis

### Lesson Synthesis

Display:

• $$67 - 55 = \underline{\phantom{\hspace{1.05cm}}}$$
• $$55 + \underline{\phantom{\hspace{1.05cm}}}=67$$

“How are these equations the same? How are they different?” (They are the same because the unknown number will be the same. Subtraction is like finding an unknown addend. They are different because one equation is subtraction and the other is addition.)

“What tool would you use to find the value that makes each equation true? Explain how you would use it.”