Common Core’s advent has inspired math teacher Jessica Hiltabidel to find ways to instigate thinking and encourage “productive struggle” she writes in Educational Leadership.
Pre-Core, Maryland middle-school teachers would guide students through a word problem, such as:
To receive a discount at the Half-a-Dozen Flags Amusement Park, a group of visitors must purchase a minimum of $600 worth of full-day and half-day tickets. Twenty-six tourists in a group purchased full-day tickets at $15 each. Write and solve an inequality to calculate how many more tourists in this group would need to each buy a $9.50 half-day ticket so this group qualifies for the discount.
The “inquiry-based instruction that undergirds the Common Core State Standards” calls for “open-ended questions,” Hiltabidel writes.
One textbook question read, “To go to Disney World costs $50 for each adult ticket and $30 for each child’s tickets. X tickets are bought of each. If the total spent is more than $800, how many tickets were bought?”
She “deconstructed” the problem to read: “You’re taking a trip to Disney World. How many tickets do you buy?”
Students were told to solve the problem any way they wanted as long as they could explain the process.
Some students . . . bought enough tickets for their family and friends. Others bought enough tickets for the Baltimore Ravens football team or all members of their favorite boy band.
After students had presented their ideas and we discussed them as a class, I asked, “How much money would you spend to take all these people to Disney World?”
This time, students were energized and focused on the process of discovery. One group used the Internet to figure out the actual cost of a ticket. . . . By the time we were finished, all my students could identify what key information they would need to solve a word problem like this and what simple operations they could use.
Then she showed them the textbook question. They used “the structure they’d discovered” to “see this complicated question” as a set of steps: Multiply the cost of an adult ticket by how many adults went; multiply the cost of a child ticket by how many children went; add the total, and make sure the sum is larger than $800.
I don’t understand the textbook question. Were an equal number (X) of adult and child tickets purchased? Or is it just an unknown number of both? Is the question asking for the minimum number of tickets purchased that would total more than $800? If it’s not, then there are an infinite number of answers.
Her “reconstructed” question doesn’t involve math. And I’m not sure speculating on who you’d like to invite to Disney World leads to an understanding that you need to multiply the number of adults and kids by the cost of their tickets, add the sum and then . . . What if the total is less than $800?
Am I missing something?