##
* *Reflection: Coherence
Working Backwards with Percents - What happens when a problem is not straightforward? - Section 2: Explore

Students liked my opening statement: "the beauty of math is that the rules never change." From that statement, I had them talk with their groups about the "equation" (I never formally introduced it as the percent equation) that we used to solve the mark up and mark down problems. Students were able to come up with the equation: original x percent = new, with the stipulation that percent had already been compared to 100 (markup of 20% was already changed to 1.20, markdown of 20% was already changed to 0.80). The fact that the kids were able to come up with that equation made my job today much easier.

For the notes, we simply looked at an example problem. Underneath the problem I had written the equation that they came up with, and I instructed them to read the problem and fill in their equation as they saw fit. Students then realized they had the "new" and not the "original." So from there we were able to talk about inverse operations and what they do. I did find that this method, so far, seems easier for the kids than using a proportion (which we have done every year up until now) ever was. I have included the smartboard notes to accompany my explanation (I upload these daily on my school webpage for parents).

The biggest misconception, though at this point I think it is more carelessness, was placing the values in the wrong spots during the table challenge. Students started hastily placing numbers in the "new" place since that was the focus of the day's lesson, instead of really reading the problem through to determine the information that they had. I think this will come with time and practice.

# Working Backwards with Percents - What happens when a problem is not straightforward?

Lesson 11 of 21

## Objective: Students will be able to work backward in a percent problem to find the original price.

## Big Idea: You can apply percents - but can you work backwards to find them? This lesson gives students an opportunity to unravel percent problems.

*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. For today’s lesson, the intended target is, “I can work backward in a percent problem to find the original price.” 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).

**Thoughts from Me! **As students begin to work on problems, they will be looking for patterns and/or repeated reasoning (**mathematical practices 7 and 8**). What types of problems require division? Students will need to be precise when determining the information they are given so that they are able to accurately find the missing value (**mathematical practice 6**).

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#### Explore

*45 min*

**Working Backwards Notes: **Working Backwards Video

**White Board Practice: **During this portion of the lesson I am going to ask that students flip over their notes sheet in order to access their "built in scrap paper." While one group member writes on the board, the others should write on their scrap paper :) The board should rotate around the table so that all students at the table get to write on the board. The questions in this activity are a mix of applying a percent to find a mark up or down, and then undoing a problem to find an original value. Separately, students will not have any trouble. However, as the problems begin to become mixed - students will have to identify what information they have so that they can choose the correct steps for solving it.

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#### Summary + Homework

*5 min*

**Instructional Strategy - Table Discussion: **To summarize this lesson, I am going to ask that students have a table discussion on the operations involved in working backwards. As I mentioned earlier in the lesson, we are using inverse operations to “undo” what has already been done in a problem – this is an application of one step equations, which have been taught previously within the common core. I will have tables share out their thoughts before I summarize the feedback from all tables.

**Homework: **As tables share, I will pass out the homework, as to better be able to hear what they talk about :)

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##### Similar Lessons

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###### The Defining Pi Project, Day 1

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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: 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)