##
* *Reflection: Perseverance
Factors and Multiples in the Real World - Section 4: Independent Practice

One way I am supporting my students this year with MP 1 (make sense of problems and persevere in solving them) is by insisting on problem annotations as a sense making tool.

You can see in this sample what my expectations look like this early on in the year (this lesson was taught during my first week of classes). Students are boxing off the important numerical information, underlining any other key information, and underlining the question(s) they are being asked. Students also then must make a note of the important numerical information underneath the problem.

Next week, I'll add the expectation of making what I'll call 'additional annotations.' Students will need to note how any other key information helps them to determine what they need to do. For example, if a problem talks of sharing apples fairly between friends, students will write a small division symbol near these words. Or, if a problem asks when both chicken nuggets and french fries are being served on the same day again, students will write 'LCM' near this part of the problem.

I model annotations whenever I am working out a problem on the doc cam. I'm also asking students to give feedback on annotations we see on anyone's shared work. I give real-time feedback as I circulate during student work time. And, I provide written feedback on exit tickets, homework, assessments, and the like.

# Factors and Multiples in the Real World

Lesson 7 of 19

## Objective: SWBAT solve real-world problems in context involving factors and multiples.

*60 minutes*

#### Think About It

*7 min*

Students work in partners on the Think About It problem (part a, above the line). After 2-3 minutes of work time, I ask students to identify what the problem is asking us to find.

I then have students share out the different ways that Jane can make snack packs. As an engagement strategy, I have students call on a peer after they've given their response. This continues until all possibilities are shared.

I frame the lesson by telling students that they're going to have to use what they know about factors and multiples, and decide which of these concepts to apply while solving real-world problems.

#### Resources

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#### Guided Practice

*10 min*

This lesson doesn't contain new material. Rather, students are applying what they know about GCF and LCM, and will need to decide which concept to use in each situation.

We continue the problem about Jane and her snack packs in the Guided Practice section. Because of their work on the Think About It problem, students are quickly able to share that Jane can make 4 snack packs. I extend student thinking by asking what would be in each snack pack.

I ask everyone to write a response to part c, to summarize how finding factors helped them to answer the questions on this page. Student responses may look like: "We knew that the factors of number divide into a number with no remainder. We also knew that the common factors of two numbers divide evenly into both numbers, which told us how many snack packs we could make."

I use cold call to question students about the second problem in this set.

#### Resources

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#### Partner Practice

*20 min*

Students work in pairs on the Partner Practice problem set. For each question in this set, I've asked students to decide if they need to use factors and multiples, and I expect them to write a justification for their choices before solving the problems. I want students thinking: To solve problems involving events happening in cycles, it may be helpful to find multiples and common multiples. To solve problems involving dividing groups evenly, it may be helpful to find factors and common factors.

As students are working , I circulate around the room and check in with each pair. I am looking for:

- Are students explaining their thinking to their partner?
- Are students writing their work in the work space?
- Are students using factors and multiples to help them solve?
- Are students annotating the problem?
- Are students answering in full sentences?

I'm asking:

- How did you know to use multiples/factors?
- Explain how you determined this answer.
- How did you use common factors (or common multiples) to help you solve?
- Why did you choose this method (ex - if student used prime factorization or t charts)?

After 15 minutes of partner practice, students work independently on the Check for Understanding problem. I have students vote on whether this problem requires factors or multiples. Seeing this data from kids allows me to make a list of students to support at the start of independent practice. I have one student present his/her work to the class under the document camera.

#### Resources

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#### Independent Practice

*15 min*

Students work on the Independent Practice problem set.

In this problem set, I decided to not to have students explicitly write whether or not they're using factors or multiples to solve each problem. I want students to go through this thought process on their own, without the scaffold of me asking.

As I circulate, I keep an eye out for student answers to problem 2. Students should be able to quickly determine the LCM of 6 and 15. However, to correctly respond to the question, students need to recontextualize the 30, and write that the two events will both happen again at 12:30. If I see students writing simply 30, I'll ask them if the number 30 makes sense, given what the problem is asking them.

#### Resources

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#### Closing and Exit Ticket

*8 min*

After independent practice time, I have students share with their partners the strategies they used to solve Problem 5. Students get really excited about chicken nugget problems. As a class, we discuss problem 1. I have students show me on their fingers how many possibilities there are for Part A.

Students then work independently on the Exit Ticket to close the lesson. Prior to teaching, I create my Criteria for Success, so I know exactly what I am looking for in student work.

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##### Similar Lessons

Environment: Urban

Environment: Urban

Environment: Urban

- UNIT 1: Number Sense
- UNIT 2: Division with Fractions
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Coordinate Plane
- UNIT 5: Rates and Ratios
- UNIT 6: Unit Rate Applications and Percents
- UNIT 7: Expressions
- UNIT 8: Equations
- UNIT 9: Inequalities
- UNIT 10: Area of Two Dimensional Figures
- UNIT 11: Analyzing Data

- LESSON 1: Performance Task Lesson - GCF
- LESSON 2: Finding Factors
- LESSON 3: Finding Greatest Common Factors (GCF) Using T-Charts
- LESSON 4: Finding Greatest Common Factors (GCF) Using Prime Factorization
- LESSON 5: Performance Task Lesson - LCM
- LESSON 6: Multiples and Least Common Multiples (LCM)
- LESSON 7: Factors and Multiples in the Real World
- LESSON 8: Distributive Property
- LESSON 9: Division Bar Models
- LESSON 10: Estimating Quotients Using Compatible Numbers
- LESSON 11: Division: One-digit Divisors
- LESSON 12: Division: Two-Digit Divisors, Part 1
- LESSON 13: Division: Two-Digit Divisors, Part 2
- LESSON 14: Solve and Interpret Division Problems
- LESSON 15: Adding and Subtracting Decimals
- LESSON 16: Multiplying Decimals
- LESSON 17: Decimal Quotients
- LESSON 18: Dividing by Decimals
- LESSON 19: Performance Task Lesson - Decimal Operations