Calculating probability and sales tax, identifying ratios and proportions, and converting fraction values are a few ways a teacher can introduce the concept of a percent to sixth-grade math students. As with all lessons, a student must learn a specific process before he can continue to the next step. The process of converting ratios and fractions to percentages and back is an essential element that people use for solving complex word problems and learning how to graph amounts.
Define the word "percent." Break the word into the prefix, "per," which translates to an amount, and the suffix, "cent," which is a reference to the total, or the whole. Explain to the students that percentages calculate how many or how much of something will be applied, used, lost or gained. Show the students the relationship between halves and quarters to familiarize them with the terminology associated with percentages.
Demonstrate via the whiteboard how one whole can be split into two halves or four quarters. Ask the students how many quarters are in a dollar to build this new skill on previously established knowledge of money. Continue to quiz the class on the value of specific coins to a dollar bill.
Describe to your students the importance of being able to find the percentage of a specific number by introducing the notion of a ratio. Instruct your students to choose any number and to find 43 percent of that number by first multiplying the number by the percentage they need to find. For example, if the chosen number were 22, they would multiply 22 by 43 to equal 946. Next, tell the students to divide the answer by 100, or, to move the decimal place two spaces to the left to obtain the answer of 9.46, which is then rounded to the nearest whole number, 9.
Revisit the dollar bill exercise and remind the students that the term "quarter" is represented by the fraction 1/4 to help the students acknowledge that a dollar can be split into four equal portions, all 1/4 or 25 percent of the dollar. Introduce the ratio in which you cross-multiply two sets of fractions, 1/4 and x/100, and solve for x to determine that 4x = 100, so x = 25. Repeat this exercise with various fractions to show that the denominator of the equivalency will always be 100 to represent the whole or the "cent" suffix mentioned earlier.
Introduce the concept of tax as a percentage you pay in addition to, but based on the price of your meal. Since each state regulates the amount of sales tax, identify what your state’s tax percentage is, and using the ratio described to find the percentage of a number, teach your students to identify what amount of sales tax would be added to a purchase of $9.99. Your formula should look like this: 7 percent x 9.99 = 69.93 \100 = .70. Remind the students that this step alone only calculates what the tax would be, and that they must add this number to the cost of the food to get the answer of $10.69.
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