I'm a big fan of using open-ended problems in math class. An open-ended problem is one that has a number of different correct answers or several ways of getting to a correct answer. Below is a question from page 140 of the MMS9 textbook that is not an open problem but has lots of potential.
This problem asks students to evaluate four different versions of a nearly identical expression. It tells students exactly what to evaluate... snore. A bit tedious and not very engaging. Lets open this question up by putting students into pairs and giving them the equation with no (parentheses) or [brackets].
Ask students to find out how many different values they can get by putting in one set of brackets. What if they could put in two sets of brackets? What if they could put in as many brackets as they'd like? What is the biggest value they could create? How about the smallest value that they can find? How about the value closest to 0? Once they've created and evaluated a bunch of different expressions, each group could take turns placing their numbers on a clothesline number line. This will get students practicing order operations with a goal and a challenge.
There is a very similar version of this problem in the Grade 9 Mathematics Curriculum Guide for outcome N04. The following problem is in the Assessment Tasks section:
Without the use of a calculator, simplify the expression 1/2 - 1/3 x 1/2 - 1/3 and express your answer as a fraction.
− By inserting one pair of brackets, how many different answers are possible?
− By inserting two pairs of brackets, is it possible to receive a different answer?
Want an even more open version of this problem? Just give students the four numbers and ask them to use the operations of addition, subtraction, multiplication and division and do the same activity. There is an activity from Illustrative Mathematics that describes this problem using the numbers 1, 2, 3 and 4. Perhaps that could be a warm-up for the more complicated question with fractions.
Nova Scotia Mathematics Curriculum Outcomes
Grade 9 N03 - Students will be expected to demonstrate an understanding of rational numbers by comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers.
Grade 9 N04 - Students will be expected to explain and apply the order of operations, including exponents, with and without technology.