# Lesson 6

Use Strategies and Algorithms to Add

## Warm-up: Number Talk: Little More, Little Less (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding within 1,000. These understandings help students develop fluency and will be helpful later in this lesson when students decide whether to use an algorithm or another strategy to add.

When students notice that a number is close to a multiple of 100 and use this to add, they are looking for and making use of structure (MP7).

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$300 + 156$$
• $$299 + 156$$
• $$303 + 156$$
• $$204 + 376$$

### Activity Synthesis

• “What is it that made these numbers easier to add mentally?” (The first 3 were really close to 300 so we were able to add 300 and make little adjustments. In the last problem, the first number was really close to 200 which made it easy to subtract mentally.)
• “Who can restate _______ 's reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone approach the problem in a different way?”
• “Does anyone want to add on to____’s strategy?”

## Activity 1: Just Ones (15 minutes)

### Narrative

The purpose of this activity is for students to compare two methods to record newly composed tens and hundreds when using the same algorithm. The first method, which students saw in a previous lesson, records the newly composed tens and hundreds as a 10 or 100 at the top of the problem. The second method records the newly composed tens and hundreds as a single digit of 1 at the top of the tens and hundreds column. It is important that students understand that an additional 1 in the tens column represents a newly composed ten and an additional 1 in the hundreds column represents a newly composed hundred. Students interpret the work and thinking shown in the different methods, and discuss the similarities and differences (MP3).

MLR8 Discussion Supports. Synthesis: Revoice student ideas to demonstrate and amplify mathematical language use. For example, revoice the student statement “because when you add 7 and 6, that’s 13, so you have 1 more” as “because when you add 7 and 6, that’s 13, so now we have three ones and one new ten.”

### Launch

• Groups of 2
• “Here are two methods of recording the sum of 657 and 286. Take a minute and think about how the addition is recorded differently in each example.”
• 1 minute: quiet think time

### Activity

• “Discuss with your partner how the newly composed ten and hundred were recorded differently in the two methods.”
• 2-3 minutes: partner discussion
• Share student responses.
• “Now work with your partner to try the second method of recording to find each sum in the second set of problems.”
• 5-7 minutes: partner work time
• Monitor for student work where the second method of recording is used to share during the synthesis.

### Student Facing

Two methods of recording the addition of $$657 + 286$$ are shown.

Method 1

Method 2

1. How is the newly composed ten and hundred recorded differently in each method?
2. Try the second method of recording to add these numbers:

1. $$602 + 179$$
2. $$493 + 161$$
3. $$438 + 364$$
4. $$329 + 381$$

### Activity Synthesis

• Display student work for each problem.
• “Why did we need to put a 1 in the tens (or hundreds) column?”
• “What does the 1 in the tens (or hundreds) column represent?”
• ”A newly composed unit can be recorded with a single digit. What does the single digit represent?” (If it’s in the tens place it stands for 10. If it’s in the hundreds place it stands for 100.)
• ”How does place value help us remember what the additional ones represent?” (If the 1 is in the tens column, it represents 10. If it is in the hundreds column it represents 100.)

## Activity 2: How Would You Add? (20 minutes)

### Narrative

The purpose of this activity is for students to choose an algorithm or other strategy to add within 1,000. Students should attend to the details of numbers in the problems that could indicate whether a particular strategy or algorithm is most useful. The important thing is that students choose an algorithm or strategy that they can use efficiently and accurately for the given problem.

Engagement: Develop Effort and Persistence. Check in and provide each group with feedback that encourages collaboration and community. For example, check that students are staying on task, using math vocabulary, and sharing how they solved the problem.
Supports accessibility for: Social-Emotional Functioning

### Launch

• Groups of 2
• “We’ve been learning about addition algorithms for the last few lessons. Recall that an algorithm is a set of steps that works every time as long as the steps are carried out correctly. But, you know lots of ways to add numbers and lots of representations for showing your work like base-ten diagrams, number lines, and writing words or equations. If it’s not a set of steps that would work every time, we call it a strategy.”
• “In this activity, you’re going to have an opportunity to find the value of each of these sums using an algorithm or other strategy of your choice.”

### Activity

• “Find the value of each sum. Later, you’ll have a chance to share your work.”
• 7-10 minutes: independent work time
• Identify students who used the same strategy to add and those who used different strategies.
• Choose a few problems for students to discuss. Consider selecting $$264 +359$$ (the second expression) and $$399 + 499$$ (the last expression), which lend themselves to be evaluated with an algorithm and another strategy, respectively.
• “Find a partner that added the same way you did. Discuss your reasoning.”
• 1-2 minutes: partner discussion
• “Now find a partner who found the sum in a different way from you. Discuss your reasoning.”
• 2-3 minutes: partner discussion
• Repeat the discussion with 1-2 expressions or as many as time permits.

### Student Facing

Use a strategy of your choice to find the value of each sum. Show your reasoning. Organize it so it can be followed by others.

1. $$199 + 348$$
2. $$264 + 359$$
3. $$203 + 75$$
4. $$316 + 198$$
5. $$399 + 499$$

### Activity Synthesis

• Invite 4-5 students to share a strategy or algorithm that someone they talked to used.
• “What strategies or algorithms do you want to practice more?”

## Lesson Synthesis

### Lesson Synthesis

“Today we saw how we can use algorithms and other strategies to add. After hearing what other students chose to use, what are your thoughts about choosing when to use an algorithm or another strategy?” (I like to use a strategy when both numbers are close to a hundred. If the numbers aren’t both close to a hundred I just use an algorithm. If I see a relationship that makes it easy to use a strategy, then I’ll use one, but if not I'll just use an algorithm.)