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Improve Math Performance (ACT/SAT)


Standardized Test Prep MS/HS/College Strategy

Improve Math Performance (ACT/SAT)

All students taking the ACT or SAT

Identify A Target Number Of Questions

  1. You can often optimize your score by targeting the number of questions you know you can finish to the best of your ability and guess on the remaining questions..Set a realistic goal for the number of questions you think you can answer accurately after taking a few practice tests. Note there are two sections on the Math SAT, one with and one without a calculator. There are multiple choice and fill-in on both sections. Every question is worth the same number of points, so keep that in mind as you decide how you will allocate your time.
  2. Based on your goal, calculate your projected score. Assume your accuracy on the questions you can answer comfortably, typically in the range of 80-90%. Assume you will randomly fill in the remaining questions and get 20-25% correct by guessing. Make sure you are comfortable with this target score.
  3. Given your target number of questions, calculate an average time to spend per question. The ACT Math section is 60 minutes long. Divide 55 minutes by the target number of questions to approximate the average time per question. This allows for you to leave a few minutes at the end to randomly guess on the remaining questions and a few extra seconds on a few questions.
  4. Take a practice Math test using a visual timer and working at the average time per question so you develop a good feel for the pace you will need to work to achieve or exceed your goal. Increase the time per problem/decrease the number of problems if you cannot maintain your accuracy or finish the target number of problems. Decrease the time per problem/increase the number of problems if you find you can meet or exceed your goal.
  5. Monitor your progress with each practice session, and continue to adapt and adjust your targets as you take additional practice tests. If you find that there are specific types of problems that are taking too much time or you have knowledge gaps, try strategies for memorizing terms and formulas. If you find that your accuracy is not as high as you would expect on your completed problems, refer to strategies for checking your work. If you find that you simply cannot maintain the pace you need, consider if mechanical strategies might help.
  6. At least one week before the test, commit to your target numbers and pacing schedule. Know your timing by sub-test and stick to it. Having reliable strategies on test day can lessen anxiety and improve overall performance.

Identify Problem Type Before Solving

  1. The math section assesses a wide range of skills in varied order. It might help you to so first identify the type of problem before you start to solve.
  2. Read the problem and label it. Your label can be by problem type as well as how challenging it is.
  3. Force yourself to pause and switch gears to the appropriate problem type so you can think about your options for strategies and formulas. You might have a strategy to skip problems with a certain label and return to them at the end.
  4. Do not spend too much time with labeling. Labeling is intended to save you time by putting you into the right frame of mind for a specific problem type.
  5. Have a solving strategy for each label you use.

Write It Out

  1. Use the space in your test booklet to write out your steps as you solve each math problem.
  2. Find a good balance between speed and accuracy as you go through the math section. Students often make silly mistakes solving problems in their head when they are nervous, even on the easiest problems.
  3. Create a system for yourself to annotate word problems so you have a structured approach to problem solving. i.e. Underline what you need to find. Circle key words and numbers you will use. Cross out information you do not need.
  4. Writing out your work will help you understand the problem better, avoid careless errors, and allow you to go back to check problems at the end if you have time, so do not erase your work after you answer the question.
  5. You have limited space in the test booklet. Keep your writing neat and organized, so you have the space you need.

Solving Strategies

  1. While it might feel wrong not to solve problems the way you do in school, your goal on standardized tests is to get the right answer in the fastest way possible. While you might solve traditionally for easy problems, it might make more sense to use alternate methods for medium and hard problems. Plan to experiment with a lot of practice problems to identify which approaches work best for you depending on the problem type.
  2. Decide by Difficulty. If you see a problem that you know you can solve quickly and easily, it is usually fastest to solve it. If you find a matching answer choice, fill it in and move on. If you have no idea what to do, skip it. You want to complete the easy and medium questions to the best of your ability first. Return to the hard ones at the end. Keep in mind on the SAT the questions typically go from easier to harder, but everyone has their own opinion on what is easy or hard. On the ACT questions are not intended to progress in difficulty. The remaining strategies are most applicable to medium and difficult questions.
  3. Check the answer choices before you start to solve. Eliminate any impossible answer choices. Do the choices give you clues about the final answer? Are they all in a certain format or within a certain range? Use this to help you get started.
  4. Do a "high level solve" and estimate the answer. Eliminate additional answer options. For example, if you know the answer will be a positive number, cross off any negative answers.
  5. Plug in the remaining answer options. If you're down to two, plug in one and you'll know which of the two is correct. If you have multiple options remaining, be clever about where you start. If you're looking for the "greatest possible..." start with the biggest number, the "least possible" start with the smallest number.
  6. For algebraic expressions, consider plugging in for the unknown. Avoid using "unique numbers" like 0 or 1. Instead, choose simple numbers like 2 or 1/3 that fit the conditions. Make sure to test with all cases (positive and negative numbers, fractions and numbers greater than one, even and odd numbers) since the equation will need to meet ALL conditions. You will need to check all four answers to make sure it is the only match.

Understanding What Is Being Asked

  1. You should generally assume that the test creators are trying to trick you on math problems, so make sure you fully evaluate the problem if you have evaluated it as medium or hard.
  2. Underline the key words and circle numbers in the problem you will need to use. Often the problem includes extra numbers that you do not need -- this is intentional to throw you off track. Don't expect to use all the numbers you are given.
  3. Ask yourself, "What do I need to find?" Guesstimate what your answer should look like. You might be able to quickly eliminate one or more answer choices just by your estimate.
  4. Write down anything important. For example, if they use a phrase such as "cross the x-axis" make sure you stop and write down that y=0 so you do not forget.
  5. Draw it or Re-Draw it. An accurate sketch can help you visualize and organize the information (see next slide).
  6. Assume two steps. Most problems have a second step to get to the final answer, but the test creators will always make the solution to the first step an answer choice. Always ask yourself, "Did I find exactly what they are asking me for? Do I need to keep going?"
  7. If you have trouble with word problems, memorize key terms (in total, of, groups of) that clue you in to which mathematical operations to use. These key words will help you on the test and in math class .

Draw Pictures

  1. Drawing pictures when solving math word problems can help you quickly identify what you know, what information is missing, and what you need to do to solve the problem. This can be particularly important for students with weaker visual reasoning or memory skills.
  2. Read the problem from the beginning one time through. Draw the general shape(s) you need. Next read through the problem and stop each time you get a new piece of information to draw it into the picture.
  3. Keep the picture simple and neat so you can easily find the numbers you need. Use basic shapes such as rectangles, triangles or circles or stick figures for people. Use arrows or words if needed. Include labels so you remember to do conversions if needed.
  4. Draw to scale even without a ruler. If you get to a tricky problem that you really need to see, use what is in front of you to help you draw to scale or draw straight lines. You cannot bring a ruler, but you can use your pencils, erasers, and calculator to draw near straight lines and help you estimate distance. Know the approximate length and relative sizes of what you can bring with you to the test, including your calculator, eraser, pencil. Look at them to help you estimate what is twice as long, 1/4 the size, etc.
  5. Re-draw it. If the test provides you with a figure and it says "not drawn to scale", keep in mind the original picture is intended to throw you off. Decide whether it is worth the time to re-draw. This strategy might be most important on the SAT Math where they intentionally do not draw problems to scale and on the ACT graphs which generally require more interpolation.

Graph & Chart Questions

  1. Read the question before analyzing the graph. There is often extra information on these visuals that you will not need to understand or consider. Remember, your only purpose is to answer the question, so interpret with a focus on what you need to know.
  2. Read the chart title and headings/variables so you are sure you know what data are being presented. Circle any labels in case you might need to make a conversion.
  3. Pause to be sure you fully understand what the graph is presenting. Especially on the ACT, this can be tricky and you might need to interpolate from the data.
  4. Don't assume the scale/axes labels. Always check the names and scale on the X and Y axes. This is particularly true on problems where you are asked to compare graphs. The might look the same, but they might be using different increments or slightly different names of data sets.
  5. Circle the point in the graph or data in the chart that you will use before checking the answers so you do not lose your place. If you have trouble finding it, take a breath. Remind yourself that you will find the answer in the graph/chart. To help with visual interpretation, use your finger as a straight edge to draw straight lines between data points if you need.
  6. Quickly eliminate incorrect answers. If you would need to do math or interpolate, consider if it will be faster to plug in the remaining answers rather than solving. If you are having trouble finding the answer, check your labels to see if you need to do a conversion.

Identify, Prioritize And Study Key Terms, Formulas And Rules

  1. Using math practice problems or a workbook, identify where you have specific gaps in content memory (rather than problem solving). Which terms do you forget? Which formulas do you confuse? Err on the side of caution--if it is something you are not sure if you know, plan to review it and use strategies to memorize it.
  2. Make flashcards. Put the formula/term on one side. On the other side put the definition, when you use it, and an example. Always include an example so you develop a good sense of when to apply it and how. Use color if it helps you group thoughts or types of problems, especially for students with stronger visual memory. Draw a picture or diagram also if it helps you remember the information.
  3. Prioritize your cards. Put must-know terms in one pile, and nice-to-know cards in another. Depending on the number of cards and how you prefer to work, you might decide to break this into three or four priorities rather than two.
  4. Based on the time until test day and how long it takes you to memorize, commit a certain amount of time for daily practice with your cards. Take your cards in your backpack and pull them out for extra practice.
  5. Quiz yourself daily starting with your must-know pile. Mix up your cards so you are not practicing in the same order. If you are struggling to remember a term, say it aloud while you read it. Once you think you know a term, continue to practice it for a few more days to ensure mastery. As you master cards, keep them in a separate pile. The more you practice and review, the better you will know it and be able to apply it on test day. Once a week, go back to your mastered pile and review it. If you forgot any, move these back to your study pile.
  6. Handmade flash cards are most effective for most students, but you can certainly use digital flashcards or any other method that you know works well for you. Whichever method you choose, repeat practice and mixing up the order of the terms are key for ensuring mastery.

Unusual Cases

  1. Math has several "always" and exception cases which you should recognize and be prepared to apply throughout the test.
  2. Here are some examples. You can add these and others to your flashcards as you study.
  3. The square of any number must always be a positive number.
  4. 0, 1 and -1 are often the "exception to the rule". Always substitute these numbers to make sure your final answer is correct.
  5. When you need to consider a range of numbers, always double check the numbers at BOTH endpoints of the range to see if they fit. Consider if the sign is greater than or equal or just greater than to determine if the endpoint should be included in the answer.
  6. When you need to convert between units, pick one unit and make sure all the numbers are converted to proper units before solving.
  7. Right and equilateral triangles are exceptional triangles--triangles don't need to be right. Quadrilaterals are not necessarily squares or rectangles. Know the rules that apply to specific figures.