Students should be able to identify common shapes and differentiate between measures such as area and perimeter.
THE ACT MATH TEST consists of 60 multiple-choice questions that must be completed in 60 minutes. A portion of those questions involves modeling, which is the process of expressing real-life phenomena via mathematical explanations and drawings. Question 32 on page 27 of the ACT's guide is a great example of an ACT modeling problem.
ACT modeling questions sometimes use images to represent everyday scenarios involving concepts in math, though this is not always the case. They appear across a variety of math topics on the ACT, from algebra and geometry to statistics. In fact, they appear across all subject areas in the Preparing for Higher Mathematics category of questions.
Since students are allotted just one minute per question on the ACT's math section, test-takers who are less comfortable with modeling may find these question types daunting. To better prepare, here's what to know about the modeling questions.
Understanding models. To understand mathematical models, students must be able to recognize and make sense of diagrams and word problems. For an example of a diagram problem that involves modeling, refer to question 35 on page 28 of the guide. For an example of a word problem that involves modeling, refer to question 2 on page 24.
Recognizing models tends to be the easiest step of the problem-solving process, though it may take a degree of practice with word problems.
As a basic modeling requirement, students should be able to identify common shapes, such as circles, rectangles, squares and triangles, and angles, as in acute, obtuse and right. You should also be able to differentiate between measures such as area, diameter, perimeter and so on.
An ACT modeling question may show the floor plan for a cabin, or it may describe a voting scenario. Remember that there are different ways of showing real-life situations vis-a-vis math.
Interpreting and evaluating models. Interpreting a model is the process of translating visual or written components into mathematical elements. Once you fully comprehend the problem before you, you must know which principles and equations to apply.
You should associate the image of a square, for example, with sides of equal length. Likewise, a circle should remind you of terms like circumference and radius.
One of the most important parts of interpreting models is clearly tracking your work. As you apply rules and formulas, number each step and write clearly so you can read your own writing and retrace your steps if necessary.
Improving models. Before improving a model, students must be able to identify any flaws within it. To accomplish such a task, students must train themselves to think and read like editors, with a critical eye.
Listen to your instinct when you feel like an aspect of the question does not seem right or is incomplete. Then, brainstorm possible solutions.
Producing models. To produce a model, students must be able to translate written words into a mathematical or pictorial representation; in other words, you are creating the model.
Consider, for example, a word problem about a car that makes three different linear journeys before arriving at the same starting point. In this instance, you might recognize that the three different linear journeys could be represented by the three legs of a triangle.
Now, assume that you are dealing with a right triangle and that the distance of one of the journeys is unknown. You would also have to know which formula can be applied to such a problem; the correct answer is the Pythagorean theorem.
ACT modeling questions encompass a wide variety of topics and skills. By slowly exposing yourself to this range of problems, you can feel more prepared and confident come test day.
