Going Mental over Percents

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Students will be able to explain multiple methods for mental calculation of a percent increase or decrease.

Big Idea

Exposure to multiple methods makes students more flexible and more confident problem solvers, helping them persevere when they get stuck.

Intro & Rationale

This lesson focuses on mental calculations using percents. We will work on calculating a percent of a quantity, as well as percent increases and decreases. Using Multiple methods is a central idea in this lesson. Exposing students to multiple methods helps them develop the mathematical practices necessary to persevere and plan alternative solution paths (MP1).

In this lesson I give students autonomy to choose their own strategy. This approach empowers all students. Some are always uncertain at first, because they are accustomed to being told what steps to perform. I find that it is important to help some students move beyond playing the game of guessing what I want them to do. This lesson is more powerful when students understand that they have permission to solve problems in whatever way makes sense to them. After uncovering and sharing multiple methods, we move towards better problem solving habits by comparing strategies and making mathematical connections among them (MP2, MP3, MP7).

Warm up

30 minutes

Today's Warm up is projected as students enter so they can begin immediately:

Amanda is bringing a total of $20 to spend at the May Fair. Jackie is bringing 60% more than Amanda. How much money is Jackie bringing?

Students are encouraged to find as many ways to solve this problem in their Math Family Group and told to try to draw a diagram or model to represent their method.

As I circulate I am looking for all the different models my students are using. I am also asking students to explain what they are doing. I want them to practice explaining how their model represents their thinking and what it represents mathematically. I ask questions like:

  • What does this ___________ represent?
  • Why did you do _______ next?
  • How does this ___________ help you find the answer?

I try to question in ways that firm up concepts in a student's mind. I want learners to be confident in what they know. I find that this helps students to be clear and complete in their explanations. Included here is One conversation I had with Cristina and Angelina as they worked on a problem. I focused on helping them to understand their strategiesEngaging my students in these conversations about the math they are doing helps them make sense of the math (MP1) and also makes them more capable speakers about math.


Mental Math Number Talk

20 minutes

Number Talks are a mental math routine that puts student thinking at the center. Students are allowed to solve the problems in any way they want and then explain their strategy. The whole point is to expose students to multiple methods so they can make mathematical connections and become more flexible with math. 

I don't often use context in my Number Talk problems, but here I do because the context helps my students make sense of the concept of percent change. In the past many of my students get confused with percent increases and decreases and they would ask whether they were supposed to add or subtract or just find the percent. The context here helps them figure that out for themselves.

I start by writing "60% of 30 monkeys" on the board and asking students to calculate the amount mentally. After I record all the various methods they used I ask them to figure out mentally calculate the following (one at a time):

  1. 60% more than 30 monkeys
  2. 60% less than 30 monkeys
  3. 80% more than $50
  4. 75% less than $20

I give students a couple of minutes think time for each problem and when several are signalling (thumbs up) that they have an answer I ask for solutions and strategies. Not everyone needs to have a "thumbs up" before I call for answers. The important thing is that students are ready to listen to each other explain what they did and why they did it.  After solving each problem mentally students share their various strategies and I record them on the board (see Number talk to share multiple mental methods).

I invite students to try each other's strategies for subsequent problems. As a result, over time, more and more students participate by sharing the strategy that they used to perform a calculation.



Wrap up

4 minutes

To bring closure to today's lesson, I present students with  the following scenario:

Suppose you can save 15% on your car insurance for earning a safe driver discount. Which strategy (from our Number Talk) would you use to mentally calculate your new cost if you currently pay $900 for six months.

I first ask students to do a Quiet Write in which they write their response for 2 minutes and then share with their Math Family Group. 

I expect two things to happen:

  1. I expect my students to compare the strategies for efficiency
  2. I expect they will discuss the process of calculating both the savings amount as well as the discounted cost 

My students often struggle with percent application problems because they involve multiple steps. For example, they will correctly calculate the percent, but forget to add or subtract the value from the starting amount. Today's Wrap Up will help me to assess which students are prone to such issues. When we share as a class, I will underline the importance of specifically identifying what the problem is asking us to find.