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* *Reflection: Connection to Prior Knowledge
Unit Rates with Complex Fractions - Section 2: Explore

There was a lot of fear in my district that teaching proportional reasoning first wouldn't work - that kids would not remember fractions, but this lesson could not have gone smoother. I approached the complex fraction as a "nasty tower of numbers that we need to knock down," and my kids were up for the challenge! Once we wrote the complex fraction as division of fractions horizontally, there were lots of "ooohs," "aahs," and "I got this" comments flying around the room. The challenge for the kids was not in the skill work of the problem, but rather the problems like "Arthur paints 30 square feet per half hour, what is his rate in square feet per hour." Several kids wanted to change the half hour to 30 minutes, I continually stressed that writing down units is very important and can keep you from making silly mistakes - once they wrote down their units and compared their units to what the question was asking, they realized that 30 minutes was not the correct value to use. I think the appearance of "half" instead of 1/2 is what threw them off the most. My lower readers try to just pull the numbers out of problems without reading the words, so I think problems like this one are good to get kids in the habit of reading and understanding what is actually taking place in the problem.

*Explore Reflection*

*Connection to Prior Knowledge: Explore Reflection*

# Unit Rates with Complex Fractions

Lesson 2 of 14

## Objective: Students will be able to find unit rates involving complex fractions.

*60 minutes*

#### Launch

*10 min*

**Opener: **As students enter the room, they will immediately pick up and begin working on the opener – **Instructional Strategy - Process for openers.** This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is **mathematical practice 3**.

**Learning Target: **After completion of the opener, I will address the day’s learning targets to the students. In today’s lesson, the intended target is, “I can calculate unit rates using complex fractions.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

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#### Explore

*45 min*

**Instruction: Unit Rates with Complex Fractions Video**

**Table Practice**: Coming off some straightforward examples, I want to give students an opportunity to now grapple with the mathematics – and take these complex fractions to the next level. In these table examples, students are not only asked to find unit rates using complex fractions, but also compare these rates. For fun, I often ask my students to take a guess at which one they think is going to be the “winner” based on what is in the problem, and then I have them work it out and get an answer. The beauty of this is that often times they are wrong, so they see that guessing isn’t such a good idea. These examples model the use of complex fractions in the real world, which is **mathematical practice 4**, and require students to reason abstractly and quantitatively,** mathematical practice 2**. Additionally, students will need to persevere with problem solving, as I am going to be hands off! (**mathematical practice 1**).

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#### Summary + Homework

*5 min*

**Instructional Strategy - Table Discussion: **To summarize this lesson, I want to bring students back to where the lesson started – what are complex fractions. Students will discuss the table question and I will take tables to share out.

**Homework:** After the table discussion I will pass out the day’s homework and let kids look it over and ask any questions they may have.

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##### Similar Lessons

###### Proportional Relationships With Decimals

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*Resources(14)*

Environment: Urban

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Environment: Urban

- UNIT 1: Introduction to Mathematical Practices
- UNIT 2: Proportional Reasoning
- UNIT 3: Percents
- UNIT 4: Operations with Rational Numbers
- UNIT 5: Expressions
- UNIT 6: Equations
- UNIT 7: Geometric Figures
- UNIT 8: Geometric Measurement
- UNIT 9: Probability
- UNIT 10: Statistics
- UNIT 11: Culminating Unit: End of Grade Review

- LESSON 1: Introduction to Unit Rates - Learn to be a smart shopper!
- LESSON 2: Unit Rates with Complex Fractions
- LESSON 3: Unit Rates Fluency - Practice makes Perfect!
- LESSON 4: More Unit Rates Fluency - Practice, Practice!
- LESSON 5: Proportional and Nonproportional Relationships - Can you find the constant?
- LESSON 6: Equations of Proportional Relationships - Who needs a table?
- LESSON 7: Equations of Proportional Relationships - Fluency Practice!
- LESSON 8: Graphs of Proportional Relationships - What are the two important characteristics?
- LESSON 9: Graphing Proportional Relationships - Fluency Practice
- LESSON 10: Problem Solving Connections - Can you apply what you know about proportional reasoning?
- LESSON 11: Proportional Reasoning Review - Remember Hollywood Squares?
- LESSON 12: Proportional Reasoning Test - Time to Put it All Together!
- LESSON 13: Proportional Reasoning Remediation/Enrichment
- LESSON 14: Proportional Reasoning Retest - REWIND and Try Again!