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Percentages in the classroom: examples and strategies to develop understanding and fluency
Summary: discover how percentages are taught in 6th grade. This article explores the connection between percentages, fractions, and decimals, and why the need for these new numbers emerged. It also presents practical strategies for calculating percentages and developing students’ fluency in computation.
Contents
Let’s step into a 6th-grade classroom: Learning percentages
What did you see in the video? Or rather, what is really happening in this classroom?
At a glance, it might seem like just another lesson on percentages. But if we look closely, we’ll see a carefully designed math session that guides students along a path that goesfrom understanding to consolidation, moving through reasoning and decision-making.
To make that happen, the session is divided into three main moments:
- The session begins by working on percentages using known facts and derived facts. This first moment is key. Whole class, students share strategies and connections to use independently later.
- In the second part,the word problems appear. This is when percentages start to make sense, becoming expressions that help students make decisions, interpret reality, and better understand the world around them.
- The session ends with a time forindependent practice.In their logbooks, students consolidate what they have worked on and strengthen the different strategies. The logbook becomes a reflection of their progress and the place where abstraction takes root.
What are percentages? The need for new numbers
Percentages are simply a fraction with a denominator of 100. It’s another way to express it.
For students to internalize this, it is important to place the percentage within the set of rational numbers, along with fractions and decimals. So, when we say 25%, we are really saying “25 out of 100.” This is written as the fraction 25/100, which is equivalent to the decimal number 0.25.
The emergence of percentages, like decimals, responds to a historical need. While natural numbers were created to count, the need to measure exact parts between one number and another soon emerged.
The % symbol itself is the visual representation of saying “divided by 100”. Understanding that 17% and the fraction 17/100 are exactly the same number, just expressed in a different “language,” is the first big step for the student.
How to calculate percentages step by step: practical examples for the classroom
Percentages are expressions commonly used in everyday life (sales, phone battery). Let’s look at different examples of how to work with them in the classroom.
First, keep in mind these basic percentages that students should internalize well, since they will help provide anchor points to work from:
- 50%:means 50 out of 100. That is, half (1/2).
- 25%:means 25 out of 100. That is, one fourth (1/4).
- 10%:means 10 out of 100. That is, one tenth (1/10).
With this in mind, let’s see how to apply the logic with two practical examples.
Example for calculating percentages 1: How do you calculate 75% of 48?
- If 100% of 48 is 48…
- 25% of 48 is 12 (we divided 48 by 4).
- Since 75 is three times 25, we just multiply 12 × 3 = 36.
Example for calculating percentages 2: A bigger challenge… How do you calculate 35% of 70?
To encourage flexible strategies, many times (and as we saw in the video), we encourage students to explore different paths to reach the same result.
Next, we’ll look at two strategies to find 35% of 70.
Strategy A
- 100% of 70 is 70.
- 10% of 70 is 7.
- 30% of 70 is 21.
- And 5% of 70 is half of 10%, that is: 3.5.
Now we just add the result of 30% (21) plus 5% (3.5), which gives us 24.5.
Strategy B
- 50% of 70 is 35.
- 25% is half of that: 17.5.
- 10% is 7.
And with this, we just add 25% (17.5) plus 10% (7), and we also get 24.5.
How to develop fluency in computation
To master calculating percentages, it is essential to develop fluency in computation, with both whole numbers and decimals. But fluency is not just speed without understanding. Being fluent means being efficient, accurate, and flexible in your response.
Deep learning in math combines understanding and practice: build knowledge with meaning and then consolidate it until you gain agility. That’s why, in our program, consolidation is a structural pillar of learning.
Ultimately, the goal is not for students to learn a single method for calculating, but to develop the ability to solve a situation in different ways. They should be able to reason, make connections, justify their thinking, and choose the most efficient strategy thoughtfully and with confidence.
Do you want to explore the concept of fluency in depth?
👉 Don’t miss this blog article.
