Let's Make A Deal!

 This week's game was also based on a television game show: Let's Make a Deal!  It is a review game that covers unit rate and leads into constant of proportionality. 

Students are given two choices (which eventually evolve to three or four choices) for which is the better deal.  They then use unit rate strategies to calculate which is the better deal based solely on math. This is an important filter. We actively discuss that in real life people think about other factors besides cost - taste, quality, and so on - but for our purposes, the only factor is the cost.

Students then calculate the better unit rate and explain in a sentence, using my model if they are having trouble wording an answer. 

I then wander the room and check work.  Students know I've picked a random student and that student needs to have their work shown as well as a sentence explaining which is the better deal including the unit rate.  

If students are correct, that is if the secretly chosen student is correct, they get the point. If not, teachers get the point. 

Generally students write in cost per item ($3 per pound, $2.29 per gallon.  When they calculate the cookies, they get 0.23, which they generally write as 23 cents per ounce for Oreos. When students calculate the problem above, they get 1.69/250 = .00676.  Students are often confused how to write numbers correctly when values get more precise than two decimal places. How does it get represented? It is a great question since we never (rarely) use this many decimals for money in real life.

What does .00676 mean?  Well, .01 is one cent, so this value is less than a penny per napkin... that seems to make sense; napkins aren't that expensive... so that means it is part of a penny per napkin. So we can write it as $0.00676 per napkin or we can round and say six-one thousandths of a dollar, or six-tenths of a penny per napkin. What we wouldn't write is 6.76 cents per napkin. We then establish a class agreement that the cent sign will no longer be used, and everything will be written in terms of dollars since that is the calculation result we would get. 

I show students this real image and ask, "If you were buying things from this toy bin, how many toys can you get for $5?"  Most answer 5 toys, since the cost is 99 cents each, which is about $1.  We then look at the photo in more detail and notice that it doesn't say 99 cents, but .99 cents.  This is read ninety-nine hundredths of a cent. This means each toy is less than a penny! 

We redo the math: $5 broken into $0.99 each would be 5 parts with a little left over.  But $5 broken into part of a cent each... $5 / .0099 = 505 toys!  What a bargain!  

Not sure who would need 2600 bananas for $5... but if you are looking...