The purpose of this task is to help students see that when you have a context that can be modeled with a ratio and associated unit rate, there is almost always another ratio with its associated unit rate (the only exception is when one of the quantities is zero), and to encourage students to flexibly choose either unit rate depending on the question at hand.
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This problem is the fifth in a series of seven about ratios. In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates. The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.
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This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally.
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This problem can be solved in more than one way. The choice in solution method may reflect the comfort and mathematical sophistication of the student.
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The purpose of this task is to engage students in Standard for Mathematical Practice 4, Model with mathematics and as such, the question as it is worded cannot be answered without making some assumptions. For example, if the items that are purchased do not have the same value, then the price reduction depends on the cost of the items.
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This is a task where it would be appropriate for students to use technology such as a graphing calculator or GeoGebra, making it a good candidate for students to engage in Standard for Mathematical Practice 5 Use appropriate tools strategically.
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There is a non-mathematical fact that students must know about mixtures in order to answer this question. When salt is dissolved in water, the salt disperses evenly through the mixture, so any sample from the mixture that has the same volume will have the same amount of salt.
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This task requires graphing time and distance.
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This real world word problem requires students to figure out the scale ratio and unit rate.
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This task requires students to solves multistep ratio and percent problem.
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This taks is word problem requires students to calculate distance and speed.
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This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not.
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This real world word problem requires multiple steps.
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There are a couple of ways to solve this real world word problem.
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This real world word problem about calculating a tip in a restaurant requires multiple steps.
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This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.
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This this task about mixing paint requires students to graph ratios on a coordinate plane. It is a standard language in ratio problem.
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This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.
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While the task as written does not explicitly use the term "unit rate," most of the work students will do amounts to finding unit rates. A recipe context works especially well since there are so many different pair-wise ratios to consider.
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This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.
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