# What Percentage Problems to Know at Each Grade Level?

Understanding percentages is a fundamental aspect of mathematical education that is used in a wide variety of real-world applications. This is why it’s so important to have a good grasp of percentages from an early age, as each level of education builds on the previous to form a solid foundation to build upon. From kindergarten to high school, students will be expected to learn different percentage concepts, and these are generally dictated by a set of standards that come from the government and/or school district, and should be incorporated into the curriculum as such.

Of course, you may be thinking, “Well, with a calculator, why would you need to know how to do percentages?” A percentage calculator can be a fantastic tool to help solve for percentage equations more easily, but it’s only one aspect of the overall understanding of these functions.

But, as a parent, teacher, or student, how can you be sure that the appropriate concepts of percentages are being taught in school? And, what are some percentage word problems worksheets that students can be provided with in order to help them learn at each level?

## Building a Foundation: Kindergarten and First Grade

In kindergarten and first grade, students are just starting to explore the world of numbers. They may not yet be familiar with the term “percent” or even fractions but they will begin to understand the concept of a part of a whole. For example, they may be asked to identify how many of a group of objects are red, blue, or green in a pile. These are very basic concepts, but important nonetheless. And, some students may be able to start doing this even before kindergarten.

For teachers and parents looking to start to lay that foundation for future percentage calculations in school and at home, some percentage questions you can use examples are:

“If there are ten apples, and three of them are red, what fraction of the apples are red?” or “If there are eight pieces of a puzzle, and you have put two of them together, what fraction of the puzzle have you completed?”

Teach the child to use their knowledge of counting and one-to-one correspondence to understand that these items are part of a whole. Don’t worry if they are not able to yet fully conceptualize the idea, though, as this is something that will be built upon as they go through school and their ability to reason. Just be sure to check for their learning readiness, as you want the child to feel confident in mathematics.

## “Time” for Fractions: Second and Third Grade

Once the student has mastered understanding items as part of a whole, they’ll be prepared for understanding percentage problems at the next grade level: second and third grade.

Now, students will begin to learn about fractions, which are a key component of understanding percentages. They will learn that “fractions” is the actual way in which you represent a part of a whole they learned in the previous grade levels. For example, they may be asked to determine what fraction of an five-slice pizza is left if two slices have already been eaten, and be taught to write that as “⅖”. Note that students may only be exposed to simpler fractions at this point; not complex fractions or how to simplify them.

It is important that teachers and parents use different word problems and visual aids as a way of offering varied approaches to understanding fractions. Students can also be encouraged to come up with their own problems, or start thinking about how to apply these concepts in real-world scenarios. Class pizza party, anybody?

## Transitioning From Fractions to Percentages: Fourth and Fifth Grade

In fourth and fifth grade, students will begin to learn about percentages themselves, first in relation to the fractions they’ve been learning up until this point (though, they will learn to convert fractions to percentages and vice versa later). They will be introduced to the idea of expressing a part of a whole now as a percentage. For example, they may be asked to determine what percentage of a class passed a test. They will also learn about using percentages to compare numbers, like learning about discounts and percentages off.

For homework, students can be asked to go to the store with their parents, and pay attention to price discounts in the store. Then, they can create their own problems and solve them with their parents’ support.

This may be a good time to start introducing to students how to express basic fractions and/or percentages on a calculator.

## Advanced Percentage Calculations: Middle School

In the middle school years, students will continue to build on their understanding of percentages by learning about advanced percentage calculations. This includes learning how to find the percentage increase or decrease from one number to another. For example, they may be asked to determine what percentage faster a runner finished a race compared to their previous time.

In addition to calculating percentage increase or decrease, sixth and seventh-grade students may also be introduced compound interest and tax calculations, though this depends on their abilities as it can be a bit more advanced.

Some specific examples of problems students may solve in these grades include:

“A student scored 80% on a test and then scored 90% on the next test. What was the percentage increase in the student’s score?” or “A pair of shoes costs \$80 without tax. If the tax rate is 8%, what is the total cost of the shoes with tax?”

Again, they may start to learn these concepts by learning how to solve for them on a calculator. It’s also during these grades that students may be separated into different math courses depending on their abilities. It is critical that teachers and parents pay attention to this, so they can differentiate their teaching and succeed based on their understanding of these concepts. Teachers should also find multiple ways to explain concepts so that all students have the ability to understand.

## Complex Percentage Equations: High School and College

By high school and college, students will use calculators more often than not to help solve more complex percentage problems. However, they should still be able to perform percentage calculations by hand and/or in their head to ensure that they understand the formulas and concepts, versus just getting an answer and not understanding how they got there. They should also know how to check their answers mathematically, which is something a calculator can be used for.

Additionally, students will learn more advanced concepts such as calculating percentiles, which are used to understand the distribution of data. For example, the actual U.S. Common Core standard for percentages at the high school level includes, “9-12.HSS-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.”

Students will also learn how to use percentages to calculate probability, a crucial concept in statistics and probability theory.

Finally, students at the high school level may expand into different courses depending on their abilities to understand not just percentages, but other concepts. Many high schools offer AP courses or the equivalent, which allows students who score well in the course to earn college credit. They may also need to take standardized tests (though, many colleges are starting to omit this as a requirement for admissions), and will need to really understand percentages (and, when to use different formulas) in order to solve for the correct answer.

Once in college, students may encounter even more advanced concepts involving percentages, such as using percentages in financial analysis or economics, or learning real-world applications of compound interest on credit cards and/or investment accounts. For example, they may learn how to calculate the compound annual growth rate of a company’s stock or how to calculate the present value of an investment.

This could be in a general math course or depending on their major, in business courses, economics courses, statistics, etc. At this point, students interested in mathematics may go on to study it further, while others may be keen with what they’ve learned up until this point. Regardless, it’s important to always keep up with understanding of percentages, as we use them every day and without practice, it can be easy to forget.

### A Note on Calculators

Calculators have been a controversial topic in the classroom since their introduction. The concern is that calculator can hamper students’ math abilities critical thinking skills by making them too reliant on technology, while others believe that calculators would improve students’ math skills by allowing them to focus on problem-solving rather than computation.

No matter what side of the argument you stand on, today, calculators are used from the early grade levels, and are commonly used in high school and college math classes all around the world. Calculators can be useful tools for learning math concepts and solving complex problems. However, it is still important for students to have a strong foundation in basic math skills (in this case, percentages and the underlying concepts) before relying on a calculator. Yet, when using a calculator, students should understand what formulas and buttons to use to solve the problem in front of them.

And, our percentage calculator can help students solve for more of these complex problems.

## The Bottom Line

Understanding percentages is an imperative part of mathematical education. Students should begin learning about percentages from an early age, building on their understanding of fractions and basic number concepts. As students progress through their schooling, they will encounter increasingly complex percentage problems that will prepare them for real-world scenarios, which may be very important depending on the career path they end up taking.

By developing a strong understanding of percentages at each grade level, students will be well-prepared to tackle more complex math problems in the future. And, if you ever get stuck on a problem, a percentage calculator will do the trick.

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