Students need to keep in mind the difference between a ratio and rate, as well as what they know to be true about them. This type of reasoning will help them to solve. Students will use both quantitative reasoning (which is more/less) and qualitative reasoning (which is better). Both ratios and rates are types of proportional relationships, so those guidelines will apply to these problem situations. Also, students should keep in mind if the solution is in lowest terms or as a unit rate.
Sandra drove 90 miles and used 6 gallons of gas. Ben drove 135 miles and used 9 gallons of gas. Sandra said that they used gas at the same rate, even though they drove different distances. Is she correct?
Proportional Reasoning with Ratio Tables
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6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to: