ACT Math in the Classroom

Integrating Assessments, Standards, and Instruction

A-List Education

• Publisher: Routledge
• Year: 2016
• ISBN:
  9781315532837
• Edition: 1
• Topic: Bildung
• Subtopic: Bildung Allgemein

Bring ACT Math and Science prep into the classroom to enhance student learning! In this new copublication from Routledge and test-prep experts A-List Education, you'll learn how the updated ACT exam is closely aligned with the Common Core, making it easy to weave test prep into your curriculum and help students hone the skills they need for college readiness. The book is filled with practical examples of how the Common Core State Standards are connected to specific sections, question types, and strategies applicable to the ACT, so you can simultaneously prepare your students for the test while improving their overall math, science, and reasoning skills.

1
About the ACT

In recent years, the ACT has made an active effort to emphasize college readiness benchmarks to a greater degree than they did before. They have introduced ACT Aspire, a suite of assessment for students starting as early as third grade, using a longitudinal assessment of benchmarks into high school. They are moving past the market of individual students taking the test for college and marketing their tests directly to schools, to be used both for college admissions and for skills assessment.

Is this a good idea? Who knows? There’s certainly a great deal of debate about the value of assessments in general, let alone this particular test. But in the meantime, it’s here, so we must acknowledge it and deal with it. The test has been relatively unchanged for several decades (with a few exceptions we’ll discuss soon), so we do know quite a bit about what’s on the test and have years of experience preparing students for it.

We want to help you incorporate ACT material into your classroom in order to prepare students without running an explicit ACT prep course. To do so, the first and most important thing is simply to know what’s on the test and what the test is like. The best way to do that is firsthand: You should absolutely do some official practice tests yourself. There is a full-length practice test available for free download on the ACT’s website. Go do one and see what you think.

In the meantime, we’re not going to go through our whole prep book (but it is for sale on our website!), but we do want to give you an overview of the structure and content of the test.

Format

The ACT is composed of four sections (called “tests”), plus an optional fifth, always presented in this order:

Table 1.1 ACT Format

Test	Number of Questions	Time	Description
English	75	45 minutes	Multiple-choice grammar and usage questions.
Math	60	60 minutes	Multiple-choice math questions.
Reading	40	35 minutes	Multiple-choice reading comprehension questions.
Science	40	35 minutes	Multiple-choice data interpretation questions.
Writing	1 essay	40 minutes	Optional. One 1-to 4-page essay.
Total	215	2 hours 55 minutes
with essay	215 + essay	3 hours 35 minutes

Most multiple-choice questions have four choices, except for questions on the Math Test, which have five choices. The letters of the answer choices alternate ABCD/FGHJ every other question. On the Math Test, the five choices alternate ABCDE/FGHJK.

The ACT does not take off points for wrong answers. This means that random guessing will not count against you. A wrong answer counts the same as a blank.

Students will get a score from 1 to 36 on each of the four main tests, plus a Composite score, which is the average of the four test scores—English, Math, Reading, and Science—rounded to the nearest whole number.

Everyone will also get a STEM score, which is just the rounded average of your Math and Science scores. This score will not be included in your Composite score.

Students who choose to take the Writing section (the essay) will get additional scores:

• Four subscores from 2 to 12 in different aspects of your essay
• A final Writing score from 2 to 12 that is the rounded average of the four subscores. This is a change, starting with the September 2016 test. In the 2015–2016 school year, students receive a scaled writing score on the 1 to 36 point scale.

When the Writing score was a scaled 36-point score, students who took Writing also received an ELA score on the 36-point scale, which was the rounded average of the English, Reading, and Writing scores. While the Writing score will no longer be on that scale, the ACT said the ELA score will continue to be reported. However, as of this printing, the ACT has not announced how the ELA score will be calculated.

ACT scores are calculated by taking the number of right answers (the “raw score”), and translating that score into a fi nal score using a special scoring table. Each test has its own unique scoring table in order to adjust for slight difficulty differences among tests. The national average Composite score is generally around 21, but average scores can vary by state and by component test.

For a detailed look at test format, ACT, Inc., publishes a book called The Official ACT Prep Guide 2016–2017, which contains three official full-length tests.

Recent Changes

The ACT has not undergone any radical changes like the SAT has. However, in the past few years, there have been a few changes that may be noticeable.

• The essay format and scoring system has radically changed as of September 2015. The old essay featured a different kind of prompt and did not use the 36-point scale (students only got one score from 2 to 12). The STEM and ELA scores are also new additions.
• Starting in 2014, one of the four passages on the Reading Test will now be a double passage, with two different passages on a similar topic and one set of questions about them.
• The distribution of passage types has changed slightly on the Science Tests. Previously the test always contained seven passages, each with five to seven questions, following strict rules about number of questions per passages. As of 2015, some tests have had only six passages with more fluidity in the number of questions per passage, and future tests may have six or seven passages.
• The Math Test had a similar change in the distribution of question types. However, the change in Math is so subtle that no one would notice it unless he or she were looking closely.

If you are using practice tests published before 2015, such as the older book, The Real ACT Prep Guide 3rd Edition, the tests will not reflect these changes. For the most part that’s fine; a seven-passage Science Test isn’t significantly different from a six-passage Science Test. The essay change is significant—you shouldn’t waste time doing essays in the old format—but the essay is optional, so you can always skip it entirely if doing an older test. Their most recent book, The Official ACT Prep Guide 2016–2017, does contain new-format tests, as does the current test that’s available for free download on actstudent.org (form 1572CPRE).

This book will focus on the ACT Math and Science Tests. We will not be discussing the English, Reading, or Writing sections.

Math

Format and Content

The Math Test is composed of one section with 60 questions. The questions are ordered by difficulty such that the early questions are easy and the later questions are difficult. All questions are multiple choice, but this is the only section on the ACT in which the questions have five choices instead of four. Calculators are allowed for the Math Test, but not required.

Questions will cover these content areas:

• Pre-Algebra (20–25%). These questions include any question that deals with only numbers (not variables), word problems that don’t require writing equations, and simple equations with only one variable. Major topics include solving one-variable equations, manipulating fractions and decimals, basic roots and exponents, ratios and percents, statistics and data interpretation.
• Elementary Algebra (15–20%). These questions involve more advanced algebraic manipulation. Major topics include multi-variable equations, linear equations, translating word problems into algebraic expressions, substitution of expressions, polynomials, and factoring expressions.
• Intermediate Algebra (15–20%). These questions involve higher-level algebra questions and more advanced topics. Major topics include: algebraic expressions using exponents and exponent rules, functions and f(x) format, quadratic manipulation, absolute value, arithmetic and geometric sequences, imaginary numbers, matrices, and logarithms.
• Coordinate Geometry (15–20%) These questions include anything and everything related to graphing and the xy-coordinate plane. Major topics include: slope and intercepts, graphing linear equations, circles, ellipses and inequalities, intersection of graphs, midpoint and distance formulas, and transformation of functions.
• Plane Geometry (20–25%). Plane Geometry questions include anything and everything related to geometry and figures, (excluding figures graphed on the coordinate plane, which are classified as Coordinate Geometry). Major topics include: angle rules and properties, properties of triangles, rectangles, parallelograms, trapezoids, circles, and calculating area, perimeter, surface area, and volume.
• Trigonometry (5–10%). Most trigonometry questions require a basic understanding of trigonometric terms, though some questions may involve higher-level formulas. Major topics include: definitions of basic trigonometric ratios, basic identities, graphing trigonometric functions and their transformations, law of sines and law of cosines, and the Unit Circle.

ACT Math Techniques

While much of the test comes down to straightforward knowledge of math, the test isn’t exactly like the kind of tests students see in school. A-List’s ACT book, The Book of Knowledge, has a number of tips and strategies for the special kinds of issues that arise on the ACT.

Error Avoidance

One of the biggest obstacles students face is distractor choices. For the most part, the wrong answers on the question aren’t random. They’re carefully selected to be tempting for students. There are specific reasons why a student may reasonably believe them to be correct. It could be because of a careless math mistake, like not distributing across parentheses or adding instead of subtracting. It could be because they didn’t read the question carefully, like solving for x when the question asks for y.

Techniques

In general, ACT math is not about knowing a lot of content as much it is about knowing a limited amount of content very well. The number of rules students need is small compared with what you actually teach in school, but these rules will be combined in unexpected ways. Therefore, learning multiple methods of problem solving is a crucial part of preparing for the test.

For example, often a question will appear to require complex algebra, but the problem can be solved with simple arithmetic. This can be done by choosing values for the variables (we call this Plug In) or by testing the values in the choices (we call this Backsolve). It takes practice to get comfortable using methods beyond what you’re used to, but these methods are crucial to score improvement. If your students don’t change their methods, they won’t change their scores.

Science

Format

The Science Test is composed of 40 questio...

Table of contents

• Cover
• Title
• Copyright
• Contents
• eResources
• About the Author
• Introduction and Overview
• 1 About the Act
• 2 Alignment with Common Core Math Standards
• 3 ACT Math in the Classroom
• 4 ACT Science in the Classroom
• Appendix: All Math Alignment Tables
• Additional Resources