First, a little background.
The theme of our spring unit is always financial literacy. As teachers of students with varying degrees of need, strength, and interest this means different things for different groups of students. One of my groups is working on selling tickets for our school play, Alice in Wonderland.
We sell tickets at two price points. An adult ticket costs $10 and a child/student ticket costs $8. This is partly my doing, because having two different prices sometimes allows my students to investigate more interesting mathematical questions. Today was one of those days.
Show-goers are also able to purchase play tickets in one of three ways: cash, check, or online with a credit card. My students record the type of ticket and the method of purchase for each order in a table. Students then represent this information visually using graphs. We will use these tables and graphs later on to reflect on the trends and patterns in the ticket sales to make suggestions to our play directors for future ticket sales initiatives. But that’s the bigger picture and I promised you a snapshot. So here it is.
I realized I had been giving my students too much information. As they recorded the total amounts of cash, checks, and credit, I was also telling them the type of ticket. Today we began our routine of using math to figure out the type of tickets using our knowledge of the ticket prices and total amount of money. I gave them this problem as a warm-up:
Yesterday we got two new checks for the play. One is for $36 and the other is for $18. Each adult ticket costs $10 and each student ticket costs $8. How many adult and students were purchased with these two checks?
I also put the two checks on the table in order to scaffold their receptive processing.
Now, before reading on, try to solve the problem yourself. While working try to note the solution pathway you chose while working on the problem…
I gave them a chance to work through the problem on their own. When they were “done,” I asked them to write how they got to their solution in words. My only prompt was, “First I did this, then I did this, and so on…” After every student reflected on how they solved the problem, I asked some to share what they had written and I would model exactly what they said on the board. I had two goals for this. One was for other students to hear and see how their classmates had solved the problem and also for the student who was sharing to analyze the precision of their problem-solving description.
Here are the examples we looked at as a whole-group:
As you can see, all four chose different, but similar pathways to find their solution. What pathway did you use? Was it similar or different to my students? What would your students do? Let me know in the comments!
After we finished the warm-up, one of my students was counting the cash, which had been $88 for several days. Usually the students categorized this as 8 adult tickets and 1 student ticket, but because of our warm-up problem, she asked if she could write 0 adult tickets and 11 student tickets. I was pleasantly surprised and told her that of course she could, but that she should write the answer that made the most sense. She decided since most of the tickets are bought by adults, to write 8 adult tickets and 1 student ticket. I love the smell of sense-making in the morning!
As a class our next steps are to find more generalized ways to represent these types of mathematical ideas. Maybe we can even incorporate that “math with the letters,” who knows?
I noticed your tweet about how to connect this to writing expressions with “letters.” =)
I’ve really worked hard the past two years getting teachers and students to see the power of creating tables as a tool for sense making. I think you could have them create tables of values for all the possible amounts of money that they might bring in for adult tickets and then create a separate table of values for the student tickets. You would have two proportional relationships that they could then compare. Maybe creating the graphs and talking about why one is steeper than the other. Or move them towards writing expressions to represent how much money would be taken in for x number of tickets sold. This all lives in that 6th grade EE and RP sort of territory for me which would be a great scaffold for where you need the students to get to.
Just my thoughts. Love your post and how you had your students sense-making in the morning!