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# Percent Increase

Lesson 5 of 17

## Objective: SWBAT determine percent increase.

#### Do Now

*10 min*

Students enter silently according to the Daily Entrance Routine. Their Do Now assignments are already on their desk and they begin working silently. They are turned over to the blank side and as students file in they are asked NOT to turn the papers over. There is a timer displayed on the SmartBoard with 3 minutes set. I ask all students to write their name on the blank side of the paper. This helps me collect papers quickly at the end of the sprint without having to wait for students to write their name on their paper (or wonder if they are adding or correcting answers). Once all students are ready with pencils in hand, I say “ready, set, go!” and students race to complete each percent fluency question on their paper.

Note* These sprints are created from materials on the NY State education site, www.engageny.org

I increased the amount of time on this sprint because many of my students were not able to complete the sprint in previous days. Rather than looking at it as lowering the bar, I am meeting my students where they are and allowing them the time and motivation to complete the sprint.

At the end of 3 minutes, I ask all students to raise their pencils in the air and count the number of problems they completed. If they complete 35 problems or more (80% of the sheet) they may submit their paper for achievement points in a determined basket in the room. I set the timer with 20 seconds letting students know this is when I need everyone back in their seat.

Achievement Points (“Intro to System of Rewards) were introduced at the beginning of the year. They seem to be motivating my students more at this time of year. Many are asking me to continue to use them in class and many are excited to redeem them for homework passes, school supplies, or lunch-time treats. I have also decided that it is far easier to keep track of achievement points on a single sheet of paper than it is on a card. This new resource is included in this section.

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#### C Notes and Guided Practice

*15 min*

Students are given a sheet of paper with the title of the lesson on the front, “Percent Increase” and the rest is blank for “notes”. Students are asked to copy the definition and formula of “percent increase” on the board.

**Percent increase**: the ratio (fraction) of an amount of increase to the original amount, calculated as a percent

Then, they must take a few seconds to think of a situation where the amount of “something” increases or goes up. They are instructed to raise their hand (after a 10 second wait time) to share their example:

Examples range from grades, to amounts of money, or pairs of shoes. I use whatever topic is offered to build a word problem on the spot. Here’s a narrated example that shows how I engage as many students as possible in understanding the details of the problem, **MP6**:

**Me**: “So what are we talking about today guys, what is an example of something that could increase in number?”

**Student 1**: “money!”

**Me**: “ok, let’s talk about money; who wants to be the protagonist in this example?”

[Wait for hands]

**Me**: “Let’s say Aleyah has $10 on Monday and then on Tuesday she has $15. By how much did her amount change?”

[Wait for hands, call on a student]

**Student 2**: “$5”

**Me**: “$5 what? Did the amount increase or decrease by $5”

**Student 2**: “increase”

**Me**: “say the whole thing, by how much did her amount change?”

**Student 2**: “it increased by $5”

[cold call 2 – 3 different students asking the same question and pushing them to answer it completely as stated by “Student 2”, but accepting synonyms for the word “increase”]

Once we go over what happened in the problem, I ask all students to copy this story onto their paper. Then I ask them all to copy the question: “What is the percent increase in her from Monday to Tuesday?” The rest is shown in the video below:

If time allows, I will ask students to work with partners to come up with a different example of percent increase and calculate it on their paper. Though my preferred style of note-taking is “Cornell Notes”, I also like to alternate to a blank page, allowing students the freedom to write their notes and examples in a way they feel comfortable doing. For this particular lesson, I also show students model percent increase using bars. The blank page allows students to choose how they want to organize their models, their definitions and their examples.

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#### Partner Practice

*10 min*

Next, Students are instructed to work with their partners to complete this Percent increase task. They may raise their hands to ask questions during this time. They are forewarned that this part of class will only last 10 minutes and after that time they must be ready to work independently on a separate set of questions to prove they understand the topic on their own.

Most students will not remember how to draw double line graphs of the percent and the number of rings. Based on the number of students I observe struggling with this section of the worksheet, I may call on the attention of the whole class, or only conference with smaller groups of students, to show them the following:

I do provide help for this example, but it is equally important to push students to discuss and complete the rest of the example and questions with their neighbors. This ensures full understanding instead of a dependency on my help setting up proportions or understanding what is being asked. Allowing students the space and time to struggle and do the “heavy lifting” on their own is admittedly one of the skills I am working on myself. It is very tempting to take over and explain it all myself, but it reinforced the dependency and gives students an “out” in pushing themselves to persevere and make sense of the problem (**MP1**).

#### Resources

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#### Independent Practice

*10 min*

Next, students are asked to complete the “task” independently and silently. They may raise their hands to ask questions, but they are warned that I will not be helping them to set up the problem. They will be responsible for most of the work and we will review the answers at the end. Students must be prepared with questions to help them clarify any misunderstanding and must be able to justify all of their answers with appropriate work.

The questions on this task will assess understanding of applying the percent increase formula (proportion) to a word problem, connections to visual models, as well as understanding that percent increase is affected by the original number. In the last question, a card collection increases by 1 card, just like Cassandra’s ring collection is increasing by 1 ring in the last problem on the partner practice. They question asked pushes students to consider that while both collections are increasing by a quantity of 1, the percent increase is NOT the same because the original amount is different. This push for understanding is a use of **MP2** as students make sense of quantities and their relationships in each problem situation.

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#### Closing

*10 min*

Once there are 10 minutes left in class students will be asked to share out their answers. I will be walking around during this time, looking for quality answers to the last question that show the student understands how to apply the formula and the effect the original number can have on the percent increase. At 5 minutes left in class, I will be asking several of these students to share out their answers as well as asking other students to state the answers in their own words.

Homework will be distributed and students will line up for their next class.

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- LESSON 9: Sale Price and Grand Totals including Tax/Tip
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