8.N.5: Solve problems that involve rates, ratios and proportional reasoning…

Mix It, Pace It: Ratio, Rate and Percent Grades 6–7

Why doesn't the big batch of paint match? Who walks fastest? Is the bigger pack or the bigger percent off really the better deal? Does twice the time mean twice the distance? Four lessons where students mix, walk, shop and graph their way to ratios, unit rates, percents and proportional relationships.

• Who walks fastest? 50–60 min

  Students time themselves walking 20 m and count their steps, then work out metres per second, steps per second and metres per step. The surprise: the walker who takes the most steps per second is often not the fastest. Students explain rates and unit rates, compare them, and convert metres per second to kilometres per hour.

• Which is the better deal? 45–60 min

  Teams shop from printed store cards, working out the price of one notebook or one litre to find the real best buys, and discover that the bigger package isn't always cheaper and the bigger percent off doesn't always save more money. Students use unit prices, percent as a rate per 100, and find a part, a whole or a percent.

• Does twice the time mean twice the distance? 50–60 min

  A walker moves at a steady pace while teammates mark where they are every 5 seconds, then the class graphs distance against time. A steady walker's points make a straight line through zero, but a walker with a head start doesn't. Students identify proportional relationships from tables and graphs, find the constant of proportionality and write it as an equation.