Rate pie lesson June 11, 2008
Posted by Jason McDonald in : Video Lessons , 1 comment so farAverage pie lesson
Posted by Jason McDonald in : Video Lessons , 6 commentsThis lesson covers how to use average pies on SAT questions.
SAT math pacing plan examples June 2, 2008
Posted by Jason McDonald in : SAT tips , add a commentIf you haven’t already taken an SAT practice test, take one before reading this section. Use the score from your practice test or from an official SAT as a baseline. Add 50 points to this score in each section — this is your target score. This target score should be realistic and attainable.
As you may already know (if not, be sure to take my free five-day e-course), you should not answer all the questions if you want to maximize your math score. You’ll only have to answer nearly all of the questions if you’re realistically shooting for 750-800. If that’s the case, you’re pacing is great; go study some time-saving math strategies!
So, how long should you spend on each problem? Long enough so that you get 75 to 90 percent of the ones you spend time on correct. At what point should you circle a question in your booklet and move on? The actual time cap per problem depends on your target score. Let’s do a couple examples:
Pacing Plan Example 1:
Jimmy Dean took the SAT and scored 410 in math. His target score for the next practice test should be 460 (410 + 50). How many questions should Jimmy omit in the 20-question section? On average, how long should he spend on each problem? What should his time cap be per problem?
Let’s start with a few relevant rows pulled from the pacing table in Day 1 of the five-day e-course:
| Target Score (800 possible) |
Attempt this many questions (54 possible) |
Accuracy on attempted questions | Omit this fraction of section |
| 400 | 17 | 75 % | 2/3 |
| 450 | 28 | 75 % | 3/5 |
| 500 | 29 | 90 % | 1/2 |
How many questions should Jimmy omit in the 20-question section? From the middle row above, Jimmy should omit 3/5 of problems in each section. For the 20-question section he should omit 12 questions (3/5 of 20) and focus on 8. Notice he would NOT omit three questions, do two, omit three, do two, etc. It would be better for him to omit 12 trickier and time-consuming questions. In other words, he should pick his eight problems to focus on from the first half or two-thirds of the test.
On average, how long should he spend on each problem? There are 70 minutes to complete 28 problems. This gives an average of 2.5 minutes per problem (70 ÷ 28).
What should his time cap be per problem? Jimmy doesn’t have to limit himself to the average time on every problem. Many problems will take less than half the average, so it’s ok if several problems take 1.5 times the average, or about 3.5 minutes in Jimmy’s case.
Pacing Plan Example 2:
Jimmy’s sister Jane took the PSAT and scored 59 in math (projected to 590 for the SAT). Her target score for the next practice test should be 640 (590 + 50). How many questions should Jane omit in the 16-question section? On average, how long should she spend on each problem? What should her time cap be per problem?
Again, we’ll start with a few relevant rows pulled from the pacing table:
| Target Score (800 possible) |
Attempt this many questions (54 possible) |
Accuracy on attempted questions | Omit this fraction of section |
| 600 | 43 | 90 % | 1/5 |
| 650 | 48 | 92 % | 1/10 |
| 700 | 51 | 95 % | 1/20 |
How many questions should Jane omit in the 16-question section? From the middle row above, Jane should omit 1/10 of problems in each section. For a 16-question section she would omit one or two questions (1/10 of 16 = 1.6). It would be better for her to omit the trickier and time-consuming questions. In other words, she should skip one or two of the questions towards the end of the section.
On average, how long should she spend on each problem? There are 70 minutes to complete 48 problems. This gives an average of 1.5 minutes per problem (70 ÷ 48).
What should her time cap be per problem? Jane doesn’t have to limit herself to the average time on every problem. Many problems will take less than half the average, so it’s ok if several problems take 1.5 times the average, or a little more than 2 minutes (1.5 × 1.5 = 2.25).
Summary
The number of problems you attempt as well as the time you allow for each problem depends on your target score. From the above examples, Jane needs to omit 1/10 problems while Jimmy needs to omit 6/10! Jane can’t afford to spend 2.5 minutes on any problem, while Jimmy should spend 2.5 minutes on most problems he attempts or else he’ll bomb them!
Some Common Pacing Questions
So, will I actually have time on the test to do the above calculations?
ABSOLUTELY NOT! You need to develop your pacing plan now on practice tests so it’s second nature when you take the “real deal.”
While I’m taking my test should I glance at my watch before every problem so I know when it’s been 2 minutes?
For your next practice test, the answer is yes. But after that, you’ll have a sense of when it’s time to circle a question and move on without looking at your watch for each problem.
Why only add 50 points to my most recent score? If Jimmy’s last test score was 410, why shouldn’t he shoot for 600?
It’s not realistic for him to score 600 by pacing alone. This entire pacing topic is based on how to increase your score without even learning any new math concepts or strategies! Once Jimmy maximizes his score through pacing (the easiest, quickest way to improve his score), then he can review some essential SAT math skills and learn some SAT math strategies to increase his score even further. It’s possible for Jimmy to improve to 600, but only by learning new strategies, skills and adjusting his pacing as his score improves.
Don’t stop now
Now that you know how to figure out your optimal pacing plan, take a few minutes to answer the following questions for your next math practice SAT exam:
What is YOUR target math score? (add 50 points to your last math score)
How many questions should you omit in the 8-question, 10-question, 16-question, and 20-question sections? Reminder: the 8 and 10-question sections are the multiple-choice and grid-in subsections of the 18-question section. Each has it’s own order of difficulty even though the numbering doesn’t start over!
On average, how long should you spend on each problem?
What should your time cap be per problem?
If you figure out the answers the above four questions, and more importantly, follow that pacing plan, you’re sure to score higher than your last test.
SAT math strategy prerequisite
Posted by Jason McDonald in : SAT tips , 10 commentsThink with your pencil!
No matter how rusty students’ math skills are, they could benefit first from learning SAT math strategies to increase their score. When I tutor students for the SAT, they often start our tutoring session with “I had NO idea how to do lots of those problems.” I can often tell which problems they couldn’t get right before they even ask me a question.
I simply look at their test booklet and over 80% of the time, if a problem has no writing near it, they didn’t get it. I don’t ask them which of the six essential strategies they tried because I know they didn’t. Why didn’t they? They were like a deer in headlights.
Whether you know the essential six math strategies or not, you need to know where to begin when you’re stuck. The saying in whitewater kayaking is, “When in doubt, move your paddle.” This helps someone struck with fear and not sure which way to go.
Heading in any direction is better than not moving at all, even if it’s the wrong direction! Simply recognizing you’re moving in the wrong direction is enough to tell you to change course! Physical movement keeps the brain involved and doesn’t allow you to “freeze up.”
The SAT question writers have an amazing ability to write questions that lead you to think, “I have no idea what to do here.” The saying that applies to the SAT is, “When in doubt, move your pencil.” If you’re stumped on a geometry problem with a diagram, create a crude protractor or ruler and start measuring! Sketch your own diagram if it doesn’t have one! If a problem is “wordy” or confusing, display the information differently. Make a table or a chart. Draw a tree diagram or a simple picture.
If you’re stuck on a problem with variables, make up numbers or plug in answer choices; and more importantly – write them down and work them through (think with your pencil)! Do anything that gets your pencil moving! If your pencil is moving, your brain is engaged. If your brain is engaged, you are one step closer to a solution; even if that solution is, “I’ll come back to this problem later if I have time.”
The most important fact you need to experiment with is it takes little to no more time to write stuff down than it does to do it in your head. The points you gain by avoiding errors and sparking ideas when stumped, by far, outweigh the time it takes to move your pencil. If you review your practice test and find yourself saying, “I should have got that right,” or “that was a stupid mistake,” you need to write more stuff down and let your pencil do the thinking.
Don’t let the limited blank space intimidate you – use scratch paper. Ask for it before the test begins.
#1 SAT math strategy May 31, 2008
Posted by Jason McDonald in : SAT tips , add a commentMAKE A VISUAL
SAT problems rarely provide information or ask questions in a straightforward fashion. One of the most useful ways to cut through the confusion the test writers provide is to display the information your own way. Forming this habit serves three purposes:
1. It wakes you up from the SAT trance that zaps your time.
2. It often displays the key relationship to solve the problem.
3. It helps you avoid or even catch mistakes that are most common when doing work in your head.
This can be done through a table, ratio box, average pie, rate pie, Venn diagram, tree diagram, list of numbers, graph, or a sketch. It doesn’t have to be pretty, just do it fast.
Here are a couple video mini lessons you should view as you probably haven’t seen them in school (They’re just a couple minutes each).
Average pie video lesson.
Rate pie video lesson.
Example 1 (easy):
If the average (arithmetic mean) of the below six numbers is 2x, what is the value of x?
5, x, x, 20, 35 and 40
After trying the problem on your own (hint: make an average pie), watch the video solution on how to get the right answer in 30 seconds.
Example 2 (medium difficulty):
Machine A makes 1500 newspapers per hour and works for 6 hours. If Machine B makes 1000 newspapers per hour, how many hours would it take Machine B to make the same amount of newspapers Machine A made in 6 hours?
(A) 1.5
(B) 5
(C) 6.7
(D) 7.5
(E) 9
After trying the problem (hint: make a rate pie), watch the video solution on how to get the right answer in 30 seconds.
Example 3 (medium difficulty):
A stock rose 60 points in a year. It gained one-third of those points in the first quarter, one-fifth in the second quarter, one-fourth in the third quarter and the rest in the fourth quarter. How many points were gained in the second half of the year?
(A) 12
(B) 13
(C) 15
(D) 20
(E) 28
After trying the problem (hint: make a table), watch the video solution on how to get the right answer in about 30 seconds.
Could you have done the above problem without a table?
Of course you could. Most people would do this problem without a table. In fact, many people would try to do this problem without even writing anything down. Keep in mind though most people score around average on the SAT. You don’t want to be “most people.”
Contrary to popular belief, making a table actually saves time. You won’t spend a second thinking about what to do. You’ll just do it. As you can see in the video solution, it only takes 30 seconds to get the answer!
Using a table also keeps you from doing unnecessary math like adding the fractions in this case.
Example 4 (more difficult):
The least integer in a set of consecutive even integers is
-100. What is the greatest integer in this set if the sum of these integers is 206?(A) 52
(B) 54
(C) 104
(D) 106
(E) 108
After trying the problem, watch the video solution on how to get the right answer in less than 30 seconds.
REAL SAT PROBLEMS – MAKE A VISUAL
As you can see, making a visual doesn’t take long. It leads you to the right answer in less than 30 seconds even on “difficult” problems. Now it’s your turn. Prove to yourself this strategy works on real SAT problems from The Official SAT Study Guide.
Video solutions to all of the below problems are posted in the members forum.
Easy
pg. 670, #6 (average pie)
pg. 716, #2 (sketch)
Medium
pg. 842, #11 (rate pie)
pg. 793, #7 (average pie)
pg. 671, #8 (table)
pg. 489, #10 (sketch)
pg. 735, #7 (Venn diagram)
More difficult
pg. 843, #16 (ratio box)
pg. 807, #14 (sketch)
pg. 412, #18 (rate pie)
What is a good SAT score?
Posted by Jason McDonald in : College Related , 113 commentsFor years past, many dynamics have played a part in the admission process . . . essays, interviews, community involvement (i.e., extra curricular activities), recommendations written by teachers or community leaders, your high school GPA, and your SAT scores. More and more colleges in the last decade or two are questioning the validity of SAT scores. Do good SAT scores really predict success in college? Do bad SAT scores predict failure? Of course not.
So who cares about your SAT scores? Colleges. Most do, anyway. There are three sections on the SAT: Writing, Math and Critical Reading worth a possible 800 points each. An average SAT score is around 1540 out of 2400 points. Students with an average SAT score have many options, but a score above 2100 would place you in the 90th percentile (meaning you scored better than 90% of the test takers) and might cause the “name brand” schools to take a closer look at your admission application.
Listed below are some colleges that require SAT scores and “rough, unofficial estimates” of the SAT scores for those admitted at each school.
Iowa State – 1825
Ohio State – 1800
DePaul – 1750
Arizona – 1700
Indiana University- 1650
Brown University – 1380
Harvard – 2200
Williams – 2125
University of Virginia – 2000
UCLA – 1900
There are many colleges that are “SAT optional.” In fact, some of the administrators at these SAT-optional schools claim that the test is not a good predictor of success in college. They also argue that the SAT exaggerates the difference between wealthy students whose families can afford expensive SAT prep courses and poorer students who see the exam for the first time on test day. If this is true, then the SAT isn’t serving the purpose for which it was designed, which is to give equal opportunity to all students.
Robert Schaeffer, the public education director of FairTest (a research center that is opposed to standardized tests) says, “SAT-optional, it seems, is no longer a euphemism for ’second-rate.’ Many of the most selective campuses in the country are concluding that they can make better admissions decisions without the SAT.” Students who don’t necessarily score well on standardized tests would be relieved to know that their admission to certain colleges could be based on other strengths, such as personal interviews and serving in their community.
Many colleges and universities have gone the way of SAT optional in their admissions process. For a complete list visit SAT optional schools. The schools listed below are just a few who consider the SAT scores only if the minimum GPA or class rank requirements are not met. As you’ll see if you visit the above link, there are hundreds and hundreds of schools that are SAT optional.
University of Texas
George Mason University in Virginia
Black Hills State University (SD)
Iowa State University
University of Wisconsin-Stout (Menomonie, WI)
Sarah Lawrence College (NY)
Texas A&M University (Galveston, TX)
Tennessee Temple University (TN)
University of Michigan (Flint, MI)
East Tennessee State University
Remember, just because a school is SAT optional does not mean it is easier to be admitted there. It simply means they rely more heavily on the other factors for your admission (essays, interviews, extra curricular activities, recommendations & GPA).
So, what is a good SAT score? We can conclude that a good SAT score is different for each student and college. Many schools often accept students with average SAT scores while others rarely do. We can also conclude that, depending on which colleges are candidates, SAT scores may not even be necessary for admission!
If you ARE looking into schools that require SAT scores, be sure to maximize your score by preparing for the test. A good SAT score for you is about 200-300 points higher than your score the first time you take the test.
Guessing on the SAT
Posted by Jason McDonald in : SAT tips , 1 comment so far
Not everyone should guess on the SAT. In fact, most people shouldn’t. Decide for yourself before test day if you should guess or not.
The majority of test takers have heard there’s a “guessing penalty” on the SAT. This is a partial truth. While the computer grading system has no way of knowing which answers were guesses, it does subtract a fraction of a point for wrong answers.
Many major test prep companies encourage guessing on SAT questions if one or more answers can be ruled out. See table below for a sample of this oversimplified logic. Their logic states that statistically, in the long run, scores will increase with “educated guessing” because the points received for correct guesses are greater than the fractions lost for those missed. This logic is flawed for most guessers for three reasons:
- It assumes the ruled out answers are, in fact, incorrect. If test takers fall for one of the many SAT traps to determine an answer looks wrong, they’re out of luck no matter how much guessing karma they have! Read myth #6 to see an example of how uninformed test takers can rule out the correct answer.
- If the guesser correctly rules out one or more answers, (s)he is likely to choose the final answer based on what looks right (This is not random guessing!) That’s right, the test writers have laid traps with answers that look right and they’ve included questions with correct answers that look wrong.
- Even if the guesser correctly rules out one or more answers,
and randomly chooses one of the remaining answers, (s)he is not likely to do this enough on a single test for the statistics to reliably play out (ever heard of too small a sample size?). Everyone knows that landing heads on a fair toss has a probability of 50%. Does that mean it will definitely land heads 2 out of 4 times? 5 out of 10? No way! It’s not unusual to land heads (or tails) more than 7 out of 10 times. This same principle applies to your guessing on a handful of questions. You may not have only wasted valuable time coming up with those guesses, but you may very well have lost points on the five or ten questions in which you guessed.
| Rule out before guessing | Likely correct answer points | Likely incorrect answer points | Likely net increase |
| 0/5 | 20 | ¼ of 80 = -20 | 0 |
| 1/5 | 25 | ¼ of 75 = -18.75 | 6.25 |
| 2/5 | 33 | ¼ of 66 = -16.5 | 16.5 |
| 3/5 | 50 | ¼ of 50 = -12.5 | 37.5 |
NOTE — for the above table to have any significance, the following three conditions must be met:
1. Correct answer is never ruled out
2. Guessing is truly random
3. Guesses are made for a significant number of questions (the above table was based on 100 guesses! There are only 54 in the entire math section!)
MORAL OF THE STORY
If you think you can increase your SAT score through guessing, do yourself a favor. Learn how to recognize SAT traps and where they frequently occur, as well as common mistakes made in ruling out answers. Then guess randomly from the remaining choices. I suggest choosing the same letter all the time, such as (A) or if that was ruled out, then (B) or if that was ruled out, then (C), etc.
Some people benefit from guessing in the verbal section but not the math, while others gain points from guessing in the easy portion but not the medium or difficult ones. Most test takers consistently lower their score altogether from guessing!
Don’t believe the major test prep companies, your guidance counselor or even your math teacher when it comes to guessing on the SAT. Heck, don’t even believe me and my ten years of SAT tutoring experience! Next time you take a practice test, put a mark by questions where you guessed. Score your test with and without those guesses and you tell me, should you guess on SAT math questions? I bet not.
Resume May 25, 2008
Posted by Jason McDonald in : Background , add a commentJason McDonald: professional life
PROFESSIONAL SUMMARY
Worked as private tutor at primary, secondary and college levels. Worked with youth and special populations teaching skills focusing on experiential learning, discovering strengths, and empowering individuals. Worked in various corporate environments as an engineer.
EDUCATION
University of California, Santa Barbara: Bachelor of Science, Mechanical Engineering. Graduated with High Honors and distinction in the major: June 1997
TEACHING EXPERIENCE
Academic Tutor, 1999-current
Tutor middle school, high school, and college students in physics and mathematics, including arithmetic, algebra, geometry, calculus and SAT prep.
Math Teacher, New Vista High school, Boulder, CO. 2001-2002.
Taught SAT prep classes and math workshops.
Tutorial Leader, Hewlett-Packard, Colorado Springs, CO. Summer, 1994. Taught middle school students how to program calculators. Worked with small groups troubleshooting and problem solving.
Field Instructor, Highland Outdoor Science School. Beaumont, CA. Spring ‘99. Taught archaeology, aquatics, astronomy, environmental science, archery, canoeing, and rock climbing. Facilitated ropes courses, new games and team-building initiatives.
Adaptive Ski Instructor, Breckenridge Outdoor Education Center. Breckenridge, CO. Winter 1998/99. Provided outdoor experiences for people with disabilities. Assessed individual needs, designed personalized lesson plans, and adapted lessons based on performance and ability levels.
Environmental Educator, Colorado Youth Program. Boulder, CO. Summer 1998. Guided 11-16 year old adolescents through 10-day outdoor sessions focusing on nature, ecology and teamwork. Designed and taught sustainable educational curriculum, hands-on learning activities, environmental service projects, and evening activities.
Engineering Coach, Magnet Middle School, Palo Alto, CA. 1998. Worked as a mentor with small groups on a weekly basis to create a science project. Taught visualization skills, model making, and prototype testing.
Wilderness Guide, Institute of Cultural Affairs. Bethel, WA. Summer 1999. Mentored youth on three-week self-discovery backpacking journey through the Olympic Peninsula. Focused on problem solving, conflict resolution, communication and personal accountability.
TECHNICAL EXPERIENCE
Mechanical Engineer, IDEO Product Development. Palo Alto, CA. 1997-1998. Worked with designers and engineers providing support on numerous innovative products. Work included research, design, building prototypes, quality control, and testing.
Design Engineer, Microsoft Corporation. Redmond, WA. Summers 1995-96. Worked with Engineers, Industrial Designers, service and component vendors, tooling engineers, and prototyping shop to design, test, and develop next generation joy stick.
Test Engineer, Hewlett-Packard. Colorado Springs, CO. Summer 1994. Worked with Engineers, assembly line workers, and machinists to verify tolerances and reconcile CAD drawings. Trained employees and led seminars on use of test and measurement equipment.
INTERESTS AND STRENGTHS
Enthusiastic about learning and enjoy making problem solving experiential. Through creativity and compassion, I integrate other curricula into the learning process to increase learning skills for all subjects.
FAMILY
I live with my wife and son in the Greater Portland area of Maine and tutor math, science, and SAT prep. My brother owns Benchmark Realty and Automated Homefinder. My parents are retired after returning from Bulgaria where they taught English as Peace Corps volunteers.
HOBBIES
Meditation and hanging out with my son are a couple of my favorite weekly activities in Southern Maine. I enjoy playing ultimate frisbee when I have the energy. Surfing, snowboarding, camping, and bicycling are a few of my favorite outdoor activities. I am a private pilot and LOVE to fly as often as I am able. I can be found on the beaches in Cape Elizabeth and Scarborough as well as walking the streets of Portland in my free time. We enjoy visiting friends and family in Colorado and California when we get the chance.