##
* *Reflection: Real World Applications
Proportional Reasoning and Percent - Can you apply the concepts? (3 Day Lesson) - Section 2: Explore

I decided to do this type of lesson because I have seen how my students perform on multiple choice tests, but what I wasn't able to determine was whether they could take that knowledge and apply it to a real world situation. These performance tasks allowed me to do just that. Since I used the tasks as an assessment of their knowledge, I did not help students at all. I utilized a mixed homogeneous pairing to form my table groups, thus I knew that everyone at the table could do something, and at least one person could explain everything. This allowed for multiple entry points for students, and every child felt like they could contribute.

In terms of presentations, once the two groups formed to a larger group, I chose 3-4 people to present. I made this choice based on the discussions that took place over the two days. For example, in one group a student was adamant that the two men could mow the lawn in 24 minutes, but it took him almost 15 minutes to explain that to his group. However, over time he was able to break down his work enough that his group mates bought in to his solution. I chose him to speak because I knew he would be able to answer questions that arose from the class, if there were any.

See attached videos (Students Working) and Student Work for more insight into how this lesson unfolded.

# Proportional Reasoning and Percent - Can you apply the concepts? (3 Day Lesson)

Lesson 21 of 21

## Objective: Students will apply concepts learned within the proportional reasoning and percent units to solve real world problems.

## Big Idea: What's the point of learning it if you can't apply it in the real world? Students will apply concepts learned in the RP strand of the common core to real world problems.

*60 minutes*

#### Launch

*10 min*

*I will start my lesson this way each day for three days, see my reflection for specifics. *

**Brain Dump:** On a clean sheet of paper, I am going to have students write down all of the information - key terms, rules, procedures, etc that they can recall from the first two units - proportional reasoning and percents. After 5 minutes of working individually, I will ask that tables combine individual lists on one sheet of paper. After another 5 minutes, I will call on one table at random (I will draw a card) to write their dump on the smartboard, and when they finish I will ask other groups to add to the list if they have additional items.

*expand content*

#### Explore

*45 min*

**Day 1: **The first day of this three day lesson I will hand out the packets of the four performance tasks (Cat Food, Lawn Mowing, Sneakers, Yogurt) that I have chosen. I have eight tables in my room, and students will be seated in somewhat homogeneous groups - there will be a pair of higher and lower students at each table. These tasks have multiple parts, and by having different levels at the table, all students will be able to find some part of each task that they can be successful with. During this portion of the lesson, students will work in their table groups to solve each of the four tasks. I will encourage students to make notes on their paper regarding the why and how of their work, as at this point they do not know which task they will present on. This activity is a good use of the mathematical practices. Students are working together and explaining their reasoning to one another to solve problems without giving up (**mathematical practices 1 and 3**). Additionally, they are working with numbers in a variety of ways, both verbally and through computation to solve real world problems (**mathematical practice 4**). Students are also able to use tools strategically - conversion tables, calculators, and notes from class (**mathematical practice 5**). Students also have to pay close attention to precision as the wording of problems changes how the problem should be approached (**mathematical practice 6**). Finally, students are using what they already know to solve new, more complex problems (**mathematical practice 7**).

**Day 2: **The second day of this three day lesson students will once again work to complete the four tasks. Half way through the class period I will assign each table one of the problems to present to the class. Tables with the same problem will now have an opportunity to work together, and I will assign two members of each group to present. I will base my decision on who presents based on comments I overhead during the work time.

**Day 3: **Presentations. On day three of this three day lesson groups will present their problems to the class. Every student in the class has completed each problem, but was asked to be an expert on only one problem. As students present they will be asked to explain the why's and how's of their problem - not just write down their answer. They will also be required to answer any student questions that may arise during or after their presentation.

*expand content*

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- 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: Percent Models - A Visual Approach to Percents
- LESSON 2: Markdown Percent Models - What Percent Are You Paying?
- LESSON 3: Markup Percent Models - Percents Over 100?
- LESSON 4: Percent Models Review - Practice, Practice!!
- LESSON 5: Percent Models Test
- LESSON 6: Finding Percents
- LESSON 7: Finding Percents Fluency - It's a Chain Reaction!
- LESSON 8: Multiple Percents - What happens when you have a discount and tax?
- LESSON 9: Markup and Markdown Review - Are you paying more or less?
- LESSON 10: Markup, Markdown, or Just a Percent? TEST
- LESSON 11: Working Backwards with Percents - What happens when a problem is not straightforward?
- LESSON 12: Working Backward with Percent: Practice Makes Perfect!
- LESSON 13: Performing with Percents - Can you bust some common misconceptions?
- LESSON 14: More Practice with Percents - Practice Makes Perfect!
- LESSON 15: Working Backward and Forward...TEST!
- LESSON 16: Percent Change - By What Percent Did the Value Change?
- LESSON 17: Percent Change - More Practice
- LESSON 18: Simple Interest - Understand Your Money!
- LESSON 19: All Percents Review
- LESSON 20: All Percents Test
- LESSON 21: Proportional Reasoning and Percent - Can you apply the concepts? (3 Day Lesson)