Graphing can be one of the toughest skills for math students to master. In my decade of experience as a high school math teacher I noticed that a good sheet of graph paper can make a big difference. I’d run off a bunch of double-sided copies of this before each unit on graphing so it was available and ready to go.
This graph paper is my favorite design because it fits four to a page and is numbered. I also included a sheet that is specific for Algebra 1, it has space for students to label the slope and y-intercept on the graph. This is perfect for linear equations. Finally, there is one for Algebra 2 students that has space to label the vertex and x-intercepts on a parabola.
Let us know how this resource works out for you. And feel free to share it!
Kathryn Gomes is Debra Bell’s daughter and teaches SAT Math for Aim Academy. She is also offering a self-paced course leading up to the August test. She is a guest blogger for debrabell.com
The Advanced Placement (AP) program, offered by the College Board, allows ambitious high school students to take college-level exams each May that potentially qualify them for college credit at the college of their choice. Each college lists the AP exams and credit they will award for a passing score on their website. Just search for “AP credit” or “equivalency exam credit” on the college’s site.
Our daughter Kayte took 5 AP exams during high school and earned high marks on each. The University of Pittsburgh awarded her 24 credits for her efforts at no cost. Here is the break down of what she did:
Exam
Grade
Score*
Credits Awarded by Pitt
No. of classes eliminated
AP U.S. History
10th
5
6
2
AP European History
11th
5
6
2
AP Psychology
12th
5
3
1
AP French
12th
4
3
1
AP English Literature
12th
5
6
2
*5 is the highest score possible.
Here are five ways the time she invested in preparing for those exams during high school reduced her college costs:
1. The value of those 24 credits at the University of Pittsburgh saved her at least 2/3rd of a year in tuition costs (approx. $12,000 at the time) and all the costs of the required texts for those courses.
2. The 24 credits eliminated almost a full year of the time necessary to complete her degree — time she could then use to earn an income.
3. The credits awarded gave her “sophomore” standing and “junior” standing in French (her second major). This meant she got to register for her classes much earlier than other freshman. This meant she ALWAYS got the required courses she needed the very first semester she was eligible to register for them. (A big reason most students today need 5 years to complete a 4-year degree is they cannot get into required courses when they need them.)
4. Kayte’s high performance on these AP exams qualified her for the honors college at the University of Pittsburgh. This then included many free perks, including preferential housing close to campus and early registration for classes. (Safe, affordable housing is in short supply at Pitt.)
5. Finally, Kayte’s high performance and evidence of a willingness to academically challenge herself with the most rigorous coursework available in high school earned her a full tuition, 5-year scholarship worth approximately $75,000 at the time. (She double majored and finished in 4 years anyway.) High AP scores are often the most decisive factor in a college’s decision to offer merit scholarships to homeschooled students. AP scores are viewed as an objective measure of a student’s achievement, ambition, and readiness for college-level rigor.
Kayte used the AP classes to prepare for these exams. The cost of those classes was money well spent when you think about how much time and money Kayte saved.
Taking AP classes is not required. Anyone can sit for the AP exams in May — students just have to sign up with a local test center (usually a local private or public high school) and pay the fees. But research shows that taking classes aligned with the AP exams substantially improves a student’s success on these exams.
Based on my daughter’s experience, I started Aim Academy Online. We offer coursework beginning in 7th grade that is aligned with AP exams. My rationale is students who have been gradually preparing for these rigorous exams over their entire middle school and high school years will be much better prepared to earn the highest scores possible when they take an AP exam. So far, that rationale appears to be working for the many parents and students who report better than expected success on the exams they have taken. And Kayte — now Kathryn Gomes — is offering her own college-prep coursework in mathematics through Aim to help the next generation of homeschooled students realize the time and savings she did. (See her SAT/ACT test prep course here.)
P.S. I should mention the #1 advantage to all the hard work Kayte put in during high school, according to Kayte: She was able to study abroad for three semesters and one summer at a reasonable cost, and still graduate on time. (Pitt allows students to apply their scholarship monies to these ventures.) Kayte studied in Provence, France; Cairo, Egypt; and sailed around the world withSemester-At-Sea, docking in 10 different countries along the way.
Aim Academy AP Courses
There are now 9 AP courses available through Aim Academy. All of these courses are taught by qualified and passionate teachers with the goal of helping your student earn the best possible score.
If Grit was simply will power or self-control eventually most of us would be exhausted and there would be few of us who would be able to keep up with the work. Although these characteristics are important, for the persistence needed to be gritty we need to develop a different strategy. The strategy of consistently changing our habits.
Will power and self-control are limited resources, and setting ourselves up for success involves doing something that is automatic and doesn’t draw on these limited resources. If every morning I were to exercise only based on my will power, most mornings I would fall back into bed as a dismal failure.
Habits are aspects that we can change with a minimal amount of effort since they require only an understanding of their components. Habits exist because, according to Charles Duhigg the author of The Power of Habit, there is a cue, a routine and a reward.
For example, when you procrastinate it starts with:
A cue – I have so much work to do.
The routine is then that you find something else to do to delay the work
The reward is that you feel better in the moment because you found something else to do that made you uncomfortable.
This behavior creates a “Habit loop”. You feel better in the moment, but you still have the work to do. When you change a habit the cue and the reward stay the same – although it is important that you find out what really is rewarding you with a particular habit.
What needs to change is the routine.
The cue helps you see when you are about to fall into an old habit, and then what you need to do is to find a new routine.
Looking at the same example:
The cue is the stressful feeling you have when you have a lot of work
The new routine could be getting started the minute you experience the cue.
The reward is that you feel better only this time is will be for a longer period of time.
Changing habits is difficult. Our brains are lazy and unless we deliberately create a new routine we will more than likely follow the old habit. The good news is if you work hard at creating new routines, these become as automatic as the old bad habits once were.
Here are some specific tips to building new habits:
Make it easy to engage in a new habit and hard to engage in an old habit. In his book Before Happiness: Five Actionable Strategies to Create a Positive Path to Success, Shawn Achor writes about wanting to develop the habit of running more and watching less television. In order to change his habit he took the batteries out of his remote control and slept in his running clothes. What could you do to help achieve a habit you wanted to create? Move your phone out of the way to keep you from getting distracted, and leave your notes to study on the table beside your bed.
Be specific and don’t try to change more than one habit at a time. When you have identified a behavior you want to change, break it down into small, manageable steps that you can handle.
Write it down and monitor yourself. Science has shown that writing something down that we want to change is more effective than just saying it. Instead of saying I have to get my homework done, make a schedule and write it down.
Stand Firm, No Wavering. Try to create rules for yourself and follow through as though you had no other choice. Commit ahead of time, and state your rules clearly. An example might be, I won’t talk on the phone until I am finished with my work.
Don’t overreact when you mess up. We all fail, but don’t make the failure larger than it should be. Move on and start again. Author Judith Beck uses a great analogy to describe this: “If you fell down one step, would you fall down the rest?” Of course not! Acknowledge the lapse and get back on track.
Anticipate challenges and plan for obstacles. Using the if/then plan we talked about in the first week of class, will help you make the decision in the moment, and not be so easily tempted.
Be informed – Statistics show that approximately 50% of eligible adults don’t vote in many elections. One reason is that it takes work to be informed about the issues and candidates. Take the time to understand how the government works and research some key issues. Visit candidate websites or call them for clarification of their positions.
Ask if you can interview a local official. This can simply be a survey that you type up. Ask about topics that are important to you. Or, just stop by with a paper typed up with your position on an issue. Either way, you may be surprised at how much is accomplished through a face to face meeting. You can use this information to “be informed” (#1) about the candidate.
Attend a legislative session in your town, county, or state. This may take some extra time, but it demystifies the working of government. There are real people meeting and talking about issues that affect our lives. This will help students see that they too can become a legislator in the future.
Attend an event, activity, or protest to raise awareness of an issue. Peacefully protesting is an American tradition and freedom of speech is guaranteed in the First Amendment to the Constitution. Exercising your rights is important in a democratic republic and constructive when done with the right attitude toward others.
Pick an issue that is important to your family and write a letter to the editor of a news source. This is a traditional, but effective, way to share your ideas with others. It’s free, and most local news organizations will gladly print your well thought out ideas. You can try sending your letter to larger media outlets as well; they might just publish it! You could also write a letter to your state or federal representative. They record this data as a way to gauge public opinion.
Remember that apathy is the enemy of good government. As discouraging as government policies might be to us, we shouldn’t give up involvement. Show your children that you are willing to take the time to vote and be engaged. We don’t want to forsake our privilege of shaping the government. Our political future depends on us!
Everyone starts a new school year with high hopes and fresh resolve to make it a year of growth and accomplishment. Over the years I’ve seen many math students excel and others struggle to just get by. I’m a firm believer that habits and attitudes play a much bigger role in our accomplishments in the classroom than innate ability. Here are some concrete ways you can increase your odds of a fruitful and joyous year in math.
Get organized. Have your student set aside a specific shelf for math. It should house their textbook, notebook (not assorted pieces of loose leaf paper), graph paper, calculator, and everything else on those supplies lists. Some of you are thinking really, that’s her first tip? I know, it seems so obvious. Yet, very few high school students take the time to do this. Pick a notebook that can last you for the whole course or at least the semester. I’ve seen students skip over graphing problems because they didn’t want to go searching for graph paper. Print off a nice pile of this graph paper and have it hole punched and ready to go.
Line up help. I’ve done several posts on math tutors here and here. But the important point is if you know math might be a problem devise a plan ahead of time. Don’t wait until your student has struggled through 20 lessons and they finally admit they’re completely lost. A better approach is to pick an objective measurement. For example, any quiz grade below 70% and there’s going to be a one-hour review session with dad or an older sibling. Agreeing to this ahead of time lowers the stress involved with admitting they need help.
Be honest about weaknesses and shortcomings. If math didn’t go well last year it might be best to start with some review. Review helps all of us. In 10th and 11th grade I set aside the first six weeks of school to review for the SATs. My main goal was to get a great score and earn a scholarship. But a secondary benefit was that I reviewed lots of basic concepts before jumping into something new. In the end, I made up those 6 weeks because I was able to learn the new material more quickly.
Try these out and let me know how it goes. And if you want to ask about specific concerns or questions find me on Facebook! I love helping homeschool families figure out high school math.
Kathryn Gomes teaches SAT Math for Aim Academy. This post was originally published on her blog kathryngomes.com.
Greetings, I’m Susan Spivey and I love to talk about good books and great writers. When I’m not reading a book, talking about a book, or writing about a book, I bake! In all seriousness, I view teaching high school literature as not only a personal joy, but a privilege. Sharing the insights I have gained over the years about writers and their works is deeply satisfying. Too often students have been challenged to read stories, poems, and novels without having the tools to make sense of what they find within the pages. I strive to make the reading come alive and help students enjoy their journey through literature, not simply survive it. I structure my classes so students can respond to the reading in a variety of ways. In addition to class discussion, students have the opportunity to write, create art, act, and even sing their response to an assigned piece of writing. Having the ability to give perceptive feedback on literature is a skill all high school students need as they prepare for college. My goal is to help them attain it.
J.S., PA – February 19, 2016
Mrs. Spivey’s literature class challenged and equipped me for college in a way few other high school experiences did. The class, which I took at a homeschool co-op during my senior year, surveyed great Christian literature with a diverse and challenging reading list. Our class meetings were a chance for Mrs. Spivey to push her students to think critically about the material we read; she encouraged us to reevaluate our presuppositions and validated our thoughtful opinions, even when she didn’t share them. This open discussion stood in contrast to many high school classes that shielded authors from critique. Mrs. Spivey’s approach to in-class discussion helped prepare me for college literature and writing classes, where criticism of an author and their worldview is encouraged. Her love of literature was apparent in everything she did; from her enthusiasm in class to her warm invitations to continue discussions and reading outside of it, Mrs. Spivey was a hugely influential teacher who was instrumental in my decision to pursue English and writing as a part of my college and career.
Parent, PA – February 19, 2016
Susan Spivey does an excellent job of instilling the love of learning and literature into her students. I have had two children participate in her English/Literature classes, and even though they enjoyed reading before, Susan was able to unlock areas of interpretation that allowed them both to understand more fully what the authors are attempting to convey. Her writing assignments challenged them to think deeply and put into their own words portions of specific text. Susan also challenges her students by assigning projects that may not be in their particular strength. For example: Not only do the students write, but some assignments may require them to perform a dramatization or an art project. She realizes that not all the students have the same strengths, but she motivates them to branch out and try something new. Susan also wants each of her students to succeed and encourages them to use whatever gifts or abilities they have to do their best. Thank you, Susan, for using Literature to help my children to mature and flourish.
E. C. – May 15, 2017
I enjoyed reading many different kinds of writing from a wide array of authors and eras. I also enjoyed class discussion. Mrs. Spivey always made class time interesting and informative by providing direction where needed but also opening up time for discussion of our own perspectives and interpretations, allowing us to grow further. Mrs. Spivey is very passionate about what she teaches, which makes this course very fun. She asks engaging question and encourages the class to be readers that meditate on the works they read and analyze the contents. Mrs. Spivey is open to new perspectives form her students and never ignores or discounts a persons thoughts. This course taught me how to analyze a work of literature and form an extensive understanding of it. This course also gave many opportunities for practice of creating well-developed and detailed papers about a piece of literature. -American Literature Student
G. Beaumont – May 15, 2017
(Mrs. Spivey) has a vast knowledge of writing, is extremely friendly and kind, and super understanding. Not many teachers WANT their students to learn, they just want them to pass and be done with. I know she genuinely cared about how I did. Mrs. Spivey encouraged class participation and asked us open ended questions, which led to helpful explanations and wonderful discussion. I now have read multiple poems, essays, short stories, plays and understood them. I know how to dissect a poem and how to figure out what the author is trying to convey. I know how to write over ten page papers and keep them interesting! I can see how literature ties into art, science, politics, history and everyday life. I have learned to handle a workload and manage my time better. And lastly, I have learned what it is like to have a deadline (Oh and I had a wonderful teacher, I don’t think I could find a better one).
N.A. ~British Lit student
Mrs. Spivey encouraged class participation and asked us open ended questions, which led to helpful explanations and wonderful discussion. I now have read multiple poems, essays, short stories, plays and understood them. I know how to dissect a poem and how to figure out what the author is trying to convey. I know how to write lastly, I have learned what it is like to have a deadline (Oh and I over ten page papers and keep them interesting! I can see how literature ties into art, science, politics, history and everyday life. I have learned to handle a workload and manage my time better. And had a wonderful teacher, I don’t think I could find a better one).
W.Q. ~American Lit student
Mrs. Spivey explains the reading well in class and helped me to understand many things I wouldn’t have noticed or understood completely from the reading. Her corrections on assignments and essays are also helpful and clear. If I started to fall behind on submissions, she emailed me to ask if anything was wrong (which is helpful in getting me to get back on track). The feedback was great. It was clear and I knew exactly what I had done wrong, or what I had to improve.
