Last Saturday, three sisters mowed the lawn in their backyard. Solange starts the mower first and completes 1/3 of the lawn. Then Jane takes over and mows exactly 1/4 of the grass. Denise then finishes off the last 700 square feet of the yard.
Your task is to explain the steps you would take, in order, to solve the equation for x. Imagine that you are writing this for someone who is learning about this process for the first time. You should be as specific as possible, and write in complete sentences.
Not long ago, I read an article by Marilyn Burns in which she explained how she used to view math and writing as “oil and water.” She thought that the two subjects had nothing to do with one another, and “writing played no role in [her] math classroom.” But now, she says, she “can no longer imagine teaching math without making writing an integral aspect of students’ learning.” In this article, Burns goes on to offer a number of suggestions for how teachers can incorporate writing into their math classes. This article really stuck with me, and so now, at least once each week, I like to ask my students to write about the math that we have been doing in class.
At a movie theater in Windsor Terrace, the price of a child’s ticket is half the price of an adult’s ticket. Nick and Katie (both adults) took their three children to see a movie yesterday, and the total cost for all the tickets was $43.75. What was the price of each child’s ticket?
I wanted to share some feedback on this problem because it’s so similar to the Goats and Chickens Problem that Daphne Carter-McKnight wrote about recently. You can read her fantastic writeup of the problem here. I like to use the Movie Theater Problem to assess how well students are able to make connections between the two problems and to see if they’re able to try some new approaches that maybe they didn’t try the first time around.
Farmer Montague raises chickens and goats. She is not sure how many she has of each animal, but she does know that she has 22 animals altogether. She also knows that, altogether, her animals have 56 feet.
How many of each type of animal does Farmer Montague have?
I chose to write about this problem because I love it! I love:
the variety of possible solution methods: arithmetic, algebraic, pictorial, mathematical, and representational;
the humor inherent in the problem;
the potential fun for students and their joy in working it out;
the gender switch on Farmer Montague;
seeing the different ways students draw the chickens and goats;
being surprised at who solves the problem and how;
seeing the light come on in students’ eyes when they arrive at the solution.
This problem pushes students to think outside the box. It is non-discriminatory in that I can, have, and did give this and a similar problem to students learning at the most basic level and those taking the HSE exam in the same week.
An ice cream shop offers customers the choice of a cup or a cone. It offers a choice of three different flavors: chocolate, vanilla, or strawberry. It also offers three different toppings: sprinkles, nuts, or hot fudge.
How many different combinations result from choosing a cone or a cup, one kind of ice cream, and one topping?
With this problem, I hope to observe how students will organize data and if they are able to recognize patterns. I also wanted to see what counting techniques the students might use to find all of the possible outcomes. Some of my students have experience developing harts and graphs, while others are new to these concepts. I was interested in seeing which students would figure out different solutions and help others to formulate solutions if they were having difficulty. My class is composed of students with math grade equivalents between 5.0 to 11.0 on the TABE.