## Rates: When Students Ask

**Why should I bother learning this?**

Food and clothing prices, tax rates, electricity rates, gasoline prices, and speed limits — these are but a few of the ways in which we see rates expressed every day. Scientists often use rates to express quantities and to make changes from one unit to another. The ability to find the unit price for a particular object you wish to purchase is often a valuable tool for comparing prices.**What do you mean by “unit price”?**

Unit price is the cost of one of a particular item. You can compare unit prices to help determine which item is a better buy. For example, if a 36-ounce box of soap powder costs $2.49 and a one pound-box costs $1.29, which is the better buy? By dividing $2.49 by 36 and $1.29 by 16, you can arrive at the unit price for each box. In this case, the 36-ounce box is a better buy.**How do you estimate one rate, given another rate?**

It is important that students learn to estimate the answers to rate and ratio problems. Having students estimate answers indicates the depth of their understanding and it gives them a way of checking to see if their answers are reasonable. One way to estimate an answer is to estimate a unit price and then multiply the estimate by the number of units needed. For example, if a set of three pens costs $1.18, how much would 20 pens cost? To solve this problem, you would first round $1.18 to $1.20, since $1.20 is evenly divisible by 3. This would give you a unit price of about $0.40. Twenty pens would cost 20 x $0.40, or about $8.00. Another way to estimate the answer would be to round $1.18 to $1.20 as you did before. Since you want 20 pens and 3 x 7 is 21, you would have to pay about 7 x $1.20, or $8.40. Encourage your students to talk about their strategies.