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# Music Companies, Variation 1

Alignments to Content Standards: 7.RP.A.2

BeatStreet, TunesTown, and MusicMind are music companies. BeatStreet offers to buy 1.5 million shares of TunesTown for \$561 million. At the same time, MusicMind offers to buy 1.5 million shares of TunesTown at \$373 per share. Who would get the better deal, BeatStreet or MusicMind? What is the total price difference?

## IM Commentary

This problem requires a comparison of rates where one is given in terms of unit rates, and the other is not. See "7.RP Music Companies, Variation 2" for a task with a very similar setup but is much more involved and so illustrates 7.RP.3.

Teachers should be aware that the context of stock purchase may not be familiar to 7th graders. The context should be explained to students if needed.

## Solutions

Solution: Compute the unit rate

One simple way to attack the problem is to compute the unit rate for the BeatStreet offering.

The unit rate that BeatStreet is offering, i.e. the price per share, is $$\frac{561,000,000 \text{ dollars }}{ 1,500,000 \text{ shares }} = 374 \frac{ \text{ dollars }}{\text{ share }}$$

The BeatStreet offer unit rate is thus 374 dollars per share. MusicMind is offering to buy shares at the unit rate of 373 dollars per share and so has the better deal. MusicMind gets the shares at \$1 per share less than BeatStreet. The total difference is $$1.5 \text{ million shares } \times \frac{ 1 \text{ dollar }}{\text{ share}} = 1.5 \text{ million dollars }$$ In summary, MusicMind gets the better deal and would save$1.5 million over what BeatStreet would pay.

Solution: Compute total cost

Since we have to figure out the difference in cost anyway, an alternative way to solve this problem is to just compute how much MusicMind would have to pay altogether.

$$1,500,000 \text{ shares } \times 373 \frac{ \text{ dollars }}{ \text{ share} } = 559,500,000 \text{ dollars}.$$ This is less than BeatStreet offered, so MusicMind gets the better deal. Using this approach not only answers the first question, but the answer to the second is now a simple subtraction problem: $$561,000,000 \text{ dollars } - 559,500,000 \text{ dollars } = 1,500,000 \text{ dollars}.$$

#### jmirabel says:

almost 6 years

I know this is noted in the commentary, but I don't like the context for this age group.

#### Euclid says:

almost 6 years

Many school districts are already teaching grade 7 students about the stock market, so I don't believe the context is inappropriate. I think it may be inappropriate to begin stock market discussions with this problem, though. The daily fluctuations of the market are a great way to demonstrate real world problems that need to be solved using rational numbers. This illustration is just an extension of the stock market into rates and proportions. In my opinion, it is these types of connections that the creators of the common core are looking for.

#### Kristin says:

almost 6 years

Thanks for your comment on this task. We actually had a long debate about whether this context was appropriate for 7th graders, and here is a summary of where we ended up with it:

• Sometimes we use contexts to draw students in or help motivate working on the mathematics--this clearly would not be the case with this task.

• Sometimes we give students problems set in unfamiliar contexts so that they have a chance to work on a task that requires them to learn something about the context in order to be able to solve the problem. This potentially provides an opportunity for students to engage in Standard for Mathematical Practice 1, Make sense of problems and persevere in solving them, as well as develop the necessary skills to Model with mathematics (MP 4).

Obviously, whether this task actually effectively works this way depends on how it is used (and it seems more like an instructional task than an assessment task for this reason). We are hoping that more people will chime in on this conversation since these are important issues to consider and debate.

#### jmirabel says:

almost 6 years

Thank you Kristin. Your response makes sense. I would be curious to see how students respond to this problem in an instructional setting.

#### Kristin says:

almost 6 years

Me too. I hope if anyone uses it they will report back here and let us know.