Lesson 1: Understand Percent6.AT.4

I can…

I can explain a percent as a rate per 100, model it on a decimal grid or tape diagram, and interpret percents greater than 100%.

Key words

• Understand Percent — A percent is a ratio that compares a number to 100, so every percent answers the question “how many out of 100?”
• Percent — A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %.
• Per hundred — The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100.
• Decimal grid — A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent.
• Part-to-whole — A comparison of one part against the whole amount. In a percent, the whole is always 100%.
• Greater than 100% — More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to.
• Equivalent ratio — A ratio with the same value, made by multiplying or dividing both terms by the same number.
• Tape diagram — A bar split into equal parts to show a percent.

Steps

1. Students voted on a mascot, and 4 out of every 10 voters chose the tiger. I want to know how many that is out of 100.
2. "4 out of every 10" is a ratio, so I write an equivalent ratio with 100 as the second term. Multiplying both terms by 10 gives 40 out of 100.
3. On a decimal grid of 100 squares, I shade 40 squares — one square for each percent.
4. 40 out of 100 is written 40%. So 40% of the students voted for the tiger.

Try it

Seven out of every ten socks in the laundry basket are white. What percent of the socks are white, and how do you know?

Check your answer

70%, because 7 out of 10 equals 70 out of 100

Percent means per hundred. Multiplying both terms of 7 : 10 by 10 gives the equivalent ratio 70 : 100, which is 70%.

Sentence starter

I know ___ because ___.

Goal: I can explain what a percent means using the words per hundred, part, whole, and equivalent ratio.