Description
The concept of percentage builds on the student’s understanding of fractions and decimals. Specifically, students should be very familiar with the idea of finding a fractional part of a whole (such as finding 3/4 of $240). Assuming the student has mastered how to find a fractional part a whole, and can easily convert fractions to decimals, then studying the concept of percentage should not be difficult.
The first lesson, Percentage, practices the concept of percentage as a hundredth part and how to write fractions and decimals as percentages. Next, we study how to find a percentage when the part and the whole are given (for example, if 15 out of 25 club members are girls, what percentage of them are girls?).
The following two lessons have to do with finding a certain percentage of a given number or quantity. First, we study how to do that using mental math techniques. For example, students find 10% of $400 by dividing $400 by 10. Next, students find a percentage of a quantity using decimal multiplication, both manually and with a calculator. For example, students find 17% of 45 km by multiplying 0.17 × 45 km.
I prefer teaching students to calculate percentages of quantities using decimals, instead of using percentage proportion or some other method (such as changing 17% into the fraction 17/100 for calculations). That is because using decimals is simpler: we simply change the percentage into a decimal and multiply, instead of having to build a proportion or use fractions. Also, decimals will be so much easier to use later on when solving word problems that require the usage of equations.
Next is a lesson about discounts, which is an important application from everyday life. Then we go on to the lesson Practice with Percentage, which contrasts the two types of problems students have already studied: questions that ask to calculate a given percentage of a number and questions that ask to find the percentage. For example, the first type of question could be “What is 70% of $380?” and the second type could be “What percentage is $70 of $380?”
The last lesson lets students find the total when the percentage and the partial amount are known. For example: “Three-hundred twenty students, which is 40% of all students, take PE. How many students are there in total?” We solve these with the help of bar models.
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This PDF is enabled for annotation.
This means the student can fill it in using a computer or a tablet (distance learning).
The student will need to use either Adobe Reader (on desktop/laptop) or a PDF app that has annotation tools (phones or tablets). Several PDF apps with annotation capabilities exist; see more details here.
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It is recommended that you not share the entire PDF file with students. Instead, it is better to just give the students a few pages at a time. Here is a simple method for extracting a few pages from a PDF file. It is done using Google Chrome.
1. Open the PDF file in Chrome.
2. Go to "Print" (Ctrl+P).
3. Print to PDF, and choose the page range.
4. Click the "Save" button.
Highlights
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Description
The concept of percentage builds on the student’s understanding of fractions and decimals. Specifically, students should be very familiar with the idea of finding a fractional part of a whole (such as finding 3/4 of $240). Assuming the student has mastered how to find a fractional part a whole, and can easily convert fractions to decimals, then studying the concept of percentage should not be difficult.
The first lesson, Percentage, practices the concept of percentage as a hundredth part and how to write fractions and decimals as percentages. Next, we study how to find a percentage when the part and the whole are given (for example, if 15 out of 25 club members are girls, what percentage of them are girls?).
The following two lessons have to do with finding a certain percentage of a given number or quantity. First, we study how to do that using mental math techniques. For example, students find 10% of $400 by dividing $400 by 10. Next, students find a percentage of a quantity using decimal multiplication, both manually and with a calculator. For example, students find 17% of 45 km by multiplying 0.17 × 45 km.
I prefer teaching students to calculate percentages of quantities using decimals, instead of using percentage proportion or some other method (such as changing 17% into the fraction 17/100 for calculations). That is because using decimals is simpler: we simply change the percentage into a decimal and multiply, instead of having to build a proportion or use fractions. Also, decimals will be so much easier to use later on when solving word problems that require the usage of equations.
Next is a lesson about discounts, which is an important application from everyday life. Then we go on to the lesson Practice with Percentage, which contrasts the two types of problems students have already studied: questions that ask to calculate a given percentage of a number and questions that ask to find the percentage. For example, the first type of question could be “What is 70% of $380?” and the second type could be “What percentage is $70 of $380?”
The last lesson lets students find the total when the percentage and the partial amount are known. For example: “Three-hundred twenty students, which is 40% of all students, take PE. How many students are there in total?” We solve these with the help of bar models.
--------------------------------------------
This PDF is enabled for annotation.
This means the student can fill it in using a computer or a tablet (distance learning).
The student will need to use either Adobe Reader (on desktop/laptop) or a PDF app that has annotation tools (phones or tablets). Several PDF apps with annotation capabilities exist; see more details here.
--------------------------------------------
It is recommended that you not share the entire PDF file with students. Instead, it is better to just give the students a few pages at a time. Here is a simple method for extracting a few pages from a PDF file. It is done using Google Chrome.
1. Open the PDF file in Chrome.
2. Go to "Print" (Ctrl+P).
3. Print to PDF, and choose the page range.
4. Click the "Save" button.
