Your grandparents remember vocational education offered in high school that immediately led to careers. Most boys took some vocational education classes, and built birdhouses or bookends, while girls took home economics and made aprons and apple pandowdy. But, they probably remember the training program as being for students who were academically challenged.

Times have changed. High schools no longer have vocational education programs. These have been replaced with Career Technical Education (CTE). The change has been gradual, and we may have been slow to realize the difference.

As with any significant change, nothing happens all at once in a clear shift. Change is gradual, and people are informed at different levels.

A federal study on Career Technical Education found that although these types of classes used to be for students “without a strong academic orientation,” now students of all kinds take these classes. CTE is no longer a track for low-achievers; it becomes a valid pathway to many lucrative careers. And although the array of students taking these courses has grown, numbers of students concentrating on CTE (taking three or more CTE courses) has been declining since the 1980s (U.S. Department of Education, Office of Planning, Evaluation and Policy Development, 2013, p. vii).

Guided pathways are academic plans that lead to being prepared for careers. These channels can begin in high school in the CTE programs, then continue in the community colleges.

Today, many professional careers do not require four-year degrees. Students can prepare for these beginning in their high schools and continue on a guided pathway through their community colleges. Many students don’t know about these career paths. North Carolina developed a website that provides information about the career paths available.

Some of the more lucrative careers that can be obtained through community colleges include cardiovascular technology, radiation therapy technology, nursing, dental hygiene, medical sonography, and cardiovascular sonography.

Today’s career paths in Community Colleges are not for low-achieving non-academic students. To enroll in credit-bearing courses for many of the career pathways offered at North Carolina’s community colleges, students must either meet the ACT Benchmark scores of 22 on the math subscale and 18 on the English or take developmental courses, not for credit.

Students need to have a good foundation in math and English to meet these benchmarks. CTE students should enroll in rigorous high school courses to prepare for these career opportunities.

Soon, (Section 10.13 of S.L. 2015-241: Career and College Ready Graduates) high schools in North Carolina will provide opportunities for college remediation for students before high school graduation through cooperation with community college partners. This program will be mandatory for high school students in their senior year who have not met benchmarks established by the SBCC in their junior year.

Students and school counselors need to know about the career paths from CTE programs in high school to Community Colleges, and on to careers. There are much higher academic expectations for today’s CTE programs than in your grandmothers’ day. People who don’t understand that may discourage students from this path.

and don’t forget our guider to completing the FAFSA!

U.S. Department of Education, Office of Planning, Evaluation and Policy Development, Policy and Program Studies Service (2013). National Assessment of Career and Technical Education: interim report. Washington D.C. Retrieved from Here

]]>Act Academy is an online personalized learning to help you study the math that is on the ACT.

The US citizenship requirement has been removed from the 2018-2019 fee waiver eligibility form.

High school counselors, Upward Bound programs and some non-profit education organizations may now distribute fee waivers. Call ACT Customer Care to find out if a non-profit is eligible to provide fee waivers (319.337.1320).

Click here for fee waiver eligibility form.

You don’t need to know a lot of advanced math to score a 22 on the Math section of the ACT. The chart at this link

https://www.act.org/content/dam/act/unsecured/documents/CCRS-MathCurriculumWorksheet.pdf shows what is on the ACT. Many of these concepts are covered in kindergarten through 8th grade and basic algebra. Make sure you have a good grasp of K – Algebra 1.

You’ll need to review to help you remember, or maybe even to understand some things for the first time. We’ll help you review, and learn to avoid very common errors. The test-writers know about the common mistakes, and the wrong answers are there for those who make them.

Often, mnemonics, or memory tricks, are taught in beginning math classes to help students get through memorized steps. Many of these tricks expire without warning. And, using some tricks keeps students from actually understanding the concepts. Here are some tricks and beliefs that expire. Poor math students are known to hold onto these tricks past their expiration dates. The test-writers know this, too, so they deliberately include problems to identify these students. Don’t be one of them.

You may have seen posts on Facebook about how expressions like 8 – 8 ÷ 4 x 2 + 2 have many different answers. Well, they don’t. There is one answer, and you get it by following the order of operations. And PEMDAS will give you the wrong answer. PEMDAS is an expiring trick that never really worked in the first place. It might work if the teacher controlled the problems to use it on.

Multiplication and Division are equal to each other. They have to be since one can be changed for the other (e.g., ÷ 2 is the same as x ½). You start left to right and take care of anything in parenthesis, then exponents, then do multiplication and division in the order they appear. Then do addition and subtraction in whatever order they appear.

The expression 8 – 2 x 2 + 2 simplified is 8 – 4 + 2, which can then be simplified to 4 + 2, and finally arriving at the answer: 6.

FOIL is a trick for multiplying things like (x + 3)(2x – 5). FOIL stands for First Outer Inner Last. You then have no way to multiply when you see something with one more term: (x + 3)(2x^{2} – 5x + 1). FOIL doesn’t work, and you’re on your own.

What always works is the Distributive Property. Think of the word distribute. If I ask you to distribute the cookies to the kids, I mean to give one to each kid. When we use the Distribute Property to solve this, we distribute each term in the (x+3) times the second parenthesis: x(2x^{2} – 5x + 1) + 3(2x^{2} – 5x + 1)

This always works. Split up the first part and multiply each term times the second. You are distributing the times (2x^{2} – 5x + 1) to each of the first terms. This always works, no matter how many terms there are.

This is true with whole numbers. Once you start dealing with negative numbers, decimals, and fractions, it is no longer true. This tricks people in Word Problems. They might read a problem, and know that the answer will be larger than the numbers given, so they decide to add or multiply, and then it’s a mess.

Some students learned complicated ways to add integers. It can be very simple.Think like this:

Addition and subtraction are opposites. Instead of subtracting, you can add the opposite (or opposite signed number).

Multiplication and division are opposites. Instead of dividing, you can multiply the opposite (or flipped fraction).

In both cases, don’t change the first number. Here are some examples:

-3 – 7 = -3 + -7

3 ÷ ½ = 3 x 2/1 = 3 x 2

Once you have changed all the subtraction to plus opposite, you can think of negative numbers as money you owe, and positive as money you have. The addition problem is asking for the net worth:

-3 + -2 You owe $3 and you owe $2. So, you owe $5. That is -5

4 + -7 You have $4 and you owe $7. So, your net worth is $3 owed. That is -3.

(It is easier to understand that “If the absolute value of the number is larger, subtract… etc.)

Why would you want to change subtraction to addition and division to multiplication? What difference does it make? You want to do it because addition and multiplication are commutative, and subtraction and division are not. The commutative property of addition or multiplication allows you to move things around in the equation, and still get the right answer. To remember, you commute to school or work, and you’re moving. Here’s an example of the commutative property in addition and multiplication:

4 + 2 = 6 and 2 + 4 = 6

3 x 2 = 6 and 2 x 3 = 6

You can’t do this with division and subtraction:

8 ÷ 4 = 2, but 4 ÷ 8 ≠ 2

6 – 4 = 2, but 4 – 6 ≠ 2

You probably remember learning the properties. Many students learn them for the test, then do a brain dump afterward. But properties can make algebra easy if you understand them.

You may be saying to yourself, “But the problems are given to me. I have to answer the questions on the ACT as they’re given to me. I can’t change them.” Actually, yes, you can.

For example, in the previous subtraction problem, we simply change the minus 4 to a plus negative 4:

6 – 4 = 2 becomes:

6 + -4 = 2

To change division to multiplication, simply invert whatever you were dividing by, that is, flip the fraction. If it’s a whole number, you can make it a fraction simply by using 1 as the denominator, because 4 is the same as 4/1. Then, you invert the numerator and denominator to 1/4. For example, you can change our previous problem:

8 ÷ 4 = 2 to

8 x ¼ = 2

Notice, now it is commutative: 8 x ¼ = 2

Distribute the parenthesis to each term to be multiplied:

(x + 3)(2x + 7) = x(2x + 7) + 3(2x + 7) Everybody in the first parenthesis gets a times (2x + 7).

There are more properties, but these two will get you through the ACT.

Invisible 1s are all over math and are a common source of errors. Write them in, so they don’t get you! Here are examples:

x + 5x is the same as 1x + 5x

x + 3y + 2x = 1x + 3y + 2x

y = 3x + 2 is the same as y = 3/1x + 2, and you need to graph this with using rise over run

7/3 ÷ 4 is the same as 7/3 ÷ 4/1, which we now know is the same as 7/3 x 1/4

(x – 3)(2x + 5)

Change this to (x + -3)(2x + 5) before you distribute. Believe me. I have graded tens of thousands of algebra tests. Dropping negative signs is a common mistake. Make everything addition, and the negative signs will stick with the numbers.

For some reason, many people stop distributing when they get to the last term. (You don’t want to leave one kid without a cookie, now do you?) All you can do is check for this. Here’s a problem to show you what I mean:

3(5x + 6y + 3z + 1)

Some people will mistakenly simplify this as:

15x + 18y + 9z + 1

. . . when it should be this:

15x + 18y + 9z + 3

This is what I am talking about. The 1 did not get multiplied by 3 as it should have. I don’t know why this is so common, but it is. Test-writers know it, too. And remember, they are always looking for ways to trip you up. This wrong answer will be there. Don’t fall for it. Check your work.

If you are a student, keep track of which kind of mistakes you are making on tests. Get to know yourself. Start checking your work for these mistakes. Checking your work means look for these mistakes, not do the problems over.

If you are the teacher or a coach, make up some problems with these mistakes in them and have the students find them. Become aware of these common mistakes.

Some tricks really will help you know how to identify answers. They are based on understanding the underlying concepts. Even if you know how to do all the problems, you don’t have time. They are trying to find the students who understand the underlying concepts.

The graph of y = 3x + 2 will be a line.

- If the number on x is positive, the graph is a forward slash. If negative, it’s a backslash.
- The y-axis is the up-and-down axis. When x is 0, the line is on the y-axis, so it goes through at 2 when:

y = 0x + 2

y = 2

This will be a horizontal line intercepting the y-axis (the up and down one) through the number 2. A line has slope if you could ski on it. Remember, 0 is a number. This line has 0 slope. You could cross-country ski on that, but it wouldn’t be much fun. - If x = 3, this is a vertical line. This line has NO slope. You couldn’t ski on a vertical cliff. Remember folks, 0 is a number.

Play around with this free resource that lets you see how the numbers in an equation affect the graph of a line. Notice what is controlled by each number. Spend some time playing with these.

https://www.desmos.com/calculator/p5tqihi9fq

https://www.desmos.com/calculator/z3wu4xa6aj

The graph of y = 3×2 + 4x + 7 will be a parabola.

- If the number on the x
^{2}is positive, it opens up. If it is negative, it opens down. - When x is 0, y is 7. That means it crosses the y-axis at 7.

Play around with this free resource to see what the numbers tell you about the graph of a parabola.

https://www.desmos.com/calculator/zukjgk9iry

Use what is discussed above to sharpen your math skills. Practice. Look for these super common mistakes. Write in the invisible ones. Change subtraction to plus opposite. Change division to multiply the inverse. Explore the concepts of graphing. Memorize Pythagorean Triples. And do practice tests. Stay calm. You only need to get slightly more than half of the problems correct.

Free practice tests are all over the web. https://www.test-guide.com/free-act-practice-tests.html

**Be sure to know the basic area formulas in geometry and the basic geometry vocabulary!**

Here is the Department of Educations blog about the 2019-2010 FAFSA. It has several helpful links: https://blog.ed.gov/2018/09/7-things-you-need-2019-20-fafsa/

Everyone. Despite its name, FAFSA is one-stop shopping for federal, state, and institutional money–including Pell Grants–and it’s the only pathway to student loans. Many colleges use the information from the FAFSA forms to calculate how much institutional aid they will grant to a student. Even your students whose families are doing well financially may be eligible.

The high school class of 2017 left unclaimed $2.3 billion in federal grant money. Why? Because more than a third of eligible students don’t fill out the FAFSA forms. (In North Carolina, this figure was 39% for the class of 2017.) Almost half of students eligible for Pell Grants didn’t fill out the forms. (In 2017-2018, Pell Grants were as high as $5,920.) FAFSA serves not only as a means to attain grant, scholarship, and work-study funds, but it is a mandatory first step to apply for federal student loans, which are typically easier to repay than private loans.

To see how much money they may be eligible for, families can go to FAFSA*4*caster (https://studentaid.ed.gov/sa/fafsa/estimate), which will forecast their eligibility (with amounts) if they do apply.

To start the actual application process, start here: https://studentaid.ed.gov/sa/fafsa

Source:

Right now. Money is usually passed out on a first-come/first-served basis, so the sooner your students apply, the more money they may be eligible for. The dates for submission for the 2019-2020 school year are October 1, 2019 to June 30, 2021. (Corrections and updates are allowed till September 15, 2020.) These dates vary among states, but are valid in North Carolina. (For other states, see https://fafsa.gov/deadlines.htm). Schools have different deadlines, and you can usually find these on their web sites. If you or your students and their families downloaded the application forms prior to October 1, 2019, they should redo so. Forms were changed for this school year. Also, FAFSA is now available on many mobile devices.

Unless students are at least 23 years old, married,or both, they will need information about their birth or adoptive parents. They may even need information about step-parents. Students will create their own FSA ID and FSA ID password, but if parental information is needed, their parents will need *their own* FSA IDs and passwords. (If students have no information about their parents and no means of attaining it, they may still apply.)

To avoid problems setting up the ID, make sure each ID is associated with a different email address, and check the birthdays and social security numbers. Also, don’t use nicknames. The names used should match the names on the social security cards.

Names (remember–no nicknames!), dates of birth, marital status, etc. For the 2019-2020 form, they will need their 2017 tax information. (This is new. In the past, the previous year was needed, and this often wasn’t available at the time of the application.) Now, because the IRS probably already has the parents’ tax information, it can be imported right into the form using the IRS Data Retrieval Tool (DRT). Parents should have their 2017 tax returns and W-2s, just in case, however.

Tell students and families to mark all options, four-year, community college, private, etc. when completing FAFSA. If they change their mind, and for example, decide to go to a community college instead of a four-year school, they may not be informed about financial aid opportunities.

Helping low-income and first-generation college families with information about FAFSA is critical. Simply providing them with information can be very helpful.

Use the information in this blog to create a newsletter and information handout to provide to parents of your seniors.

If you have problems with FAFSA, call: 1-800-433-3243.

]]>Did you know that, by law (SL 218-32; HB 986), (final version) students who score a level 5 on their End-of-Grade (EOG) or End-of-Course (EOC) tests must be placed in an advanced course the following school year? This is true for all public schools in North Carolina, grades 3-12. (Charter schools are exempt.)

For elementary school, the LEAs can decide what “advanced courses” might be. Some examples are compacted, exploratory, or single-subject acceleration courses. In middle and high school, these include compacted courses, courses designated as “honors,” and college-level courses. Seventh graders who score a 5 must be placed in high school math—not simply a high-level 8th-grade course—but a real high school course (Math 1, 2, 3, or a 4th-level math class).

When advanced courses are offered in mathematics, any student scoring a level five on the end-of-grade or end-of-course test for the mathematics course in which the student was most recently enrolled shall be enrolled in the advanced course for the next mathematics course in which the student is enrolled. A student in seventh grade scoring a level five on the seventh grade mathematics end-of-grade test shall be enrolled in a high school level mathematics course in eighth grade.

’Doesn’t matter. Prior exposure to advanced courses is NOT a prerequisite with this law. Earning a 5 on a standardized math test usually indicates that a student is knowledgeable, motivated, and highly educable. Some students may have gaps in their knowledge for advanced courses, or for the high expectations. School counselors may want to include these students in small groups.

Not without parent or guardian permission.

No student who qualifies under this subsection shall be removed from the advanced or high school mathematics course in which the student is enrolled unless a parent or guardian of the student provides written consent for the student to be excluded or removed from that course.

According to the North Carolina Department of Public Instructions, schools must inform the parents clearly and concisely, in English and in Spanish, if necessary. It is the duty of the school boards within each LEA to put the word out to parents, and it is up to the school boards to determine how they will disseminate the information.

But we don’t offer many honors, AP, or IB courses. What shall we do?

When practicable, local boards of education shall offer advanced courses in mathematics in all grades three and higher.

Make a plan to start offering them, or offer them on line from North Carolina Virtual Public School (NCVPS). They offer all the courses needed, including all of the high school math courses, 1, 2, 3, and the 4th-level courses. They offer AP Math 2 and 3. You might also partner with the NC School of Science and Math.

It’s already in effect. It was in effect for the 2018-2019 school year.

No, they can stay. This bill isn’t about level 4 students. It’s only about level 5. Level 5 students must be placed in these classes. That doesn’t mean other students can’t be.

EOC and EOG data only. That’s according to the law. Students may earn a B or lower as their classroom grade, yet score 5 on the standardized test. If so, this law applies, and they must be put in the advanced classes.

Advanced learning

Beth Cross

Academically or Intellectually Gifted (AIG) & Advanced Programs consultant

bethcross@dpi.nc.gov

Sneha Shah-Coltrane

Division of Advanced Learning Director

sneha.shahcoltrane@dpi.nc.gov

Stephanie Cyrus

AIG & AP Consultant

Stephanie.cyrus@dpi.nc.gov

NC DPI Mathematics Section

Denise Schulz

Elementary Mathematics Consultant

Denise.schulz@dpi.nc.gov

Lisa Ashe

Secondary Mathematics Consultant

Lisa.ashe@dpi.nc.gov

Tammy Lackey

K-8 Mathematics Consultant

Tammy.lackey@dpi.nc.gov

Joseph Reaper

Secondary Mathematics Consultant

Joseph.reaper@dpi.nc.gov

And don’t even get us started on smartphones.

Remember this? “If a tree falls in the forest when no one is there, does it make a sound?” Maybe more relevant today: “If what you say can’t be found online, do you even exist?”

Go ahead, hand out all your flyers and memo’s and forms and directions. Get good at it – because you’ll be doing it over and over. Half of those papers will be lost or tossed before they make it to the bus stop.

School counselors have a tremendous impact on the path students choose in life. The information they have to offer – not just to kids but for parents too – needs to be readily available. Anytime someone wants to find it.

Welcome to the internet, my friends. Here are the top seven reasons every school counselor needs a webpage.

A Free Application for Federal Student Aid (FAFSA) should be low-hanging fruit for families planning for college. But let’s be honest – a lot of parents and students procrastinate on getting the paperwork filled out and submitted.

Your web page becomes your classroom and your soapbox. You can use it to help nudge parents and kids through the process. You’re a trusted source – you know the typical stumbling blocks. Sure, they could just go to the FAFSA website, but your involvement makes the whole thing less intimidating.

You can create an FAQ, highlight the significant benefits of completing the application early on. Parents might not realize that many colleges use FAFSA as criteria for their scholarship programs. And though student loans will always be available, pools of school-specific financial support won’t be.

A link to the forms to the instructions – a list of all supporting documents you’re going to need – your web page becomes a simple to read and credible resource for encouraging college attendance.

The nice thing about your web page is that you can communicate with kids and parents in one spot. Both of them need information on similar topics, but it’s going to be processed differently. Chances are good you’ll want to communicate it creatively.

You can create separate sections for parents and students. With your expertise, you’re the perfect person to know the questions each group has and how to answer them. Your page becomes a resource on priority topics and offering links to resources, forms, and in-depth information.

Parents, in particular, will appreciate the one-stop shop for the information they need. The majority of parents work outside the home and have to catch up in the evening. When they visit your page, they can catch up quick – which makes life a little easier.

The other nice thing about your web page is you might be able to cut down on some of the repetitive tasks that bog down your day. If you get ten phone calls a week asking the same question – answer it on your website.

Chances are good your page is part of the school site. Take advantage of any approved tools or apps. For example, something like Bookio lets people see when you’re available for appointments. Free bulk emailing tools, like MailChimp, can be used to let parents subscribe to a FAFSA newsletter.

Include a calendar (or list) of application deadlines by schools- even if it’s just a spreadsheet. Link to local programs that provide support for college prep or intern opportunities.

And don’t forget the trade or technical schools. For a lot of students, a four-year degree isn’t part of their life plan. Your web page can provide them with the support they need to move forward.

The push to engage on social media is pretty intense. But the downside for educators only gets talked about when something creepy happens. Social media is becoming increasingly unsocial.

It is extremely easy for posts and tweets to be misinterpreted. You can put something up on Facebook and come back two hours later to a whole mess of angry comments about it. Even if people just misunderstood what you were saying – drama spreads like wildfire. And fires can be hard to put out.

The other reality is that kids rarely like sharing their social media experience with parents. So, chances are good you will only get half of your target audience. That brings us to the whole student piece, which has pitfalls of its own.

Maintaining a professional distance can be difficult in social media. Students can’t be your “friends” and interacting in an uncontrolled environment has its risks. For you and the school.

Most school counselors have much larger caseloads than the recommended ratio of 250 kids per counselor. The average is closer to 450. It isn’t always easy to give them face time you wish you could.

But your web page allows you to connect in a controlled environment (unlike social media in which you can’t curate). You can share useful quality information about colleges, financial aid, work-study programs, reports on campus safety.

See if you’re allowed to add videos to make your site more interesting and personal. Always stick to professional topics and please, please, please avoid any joking around. Humor can backfire in a heartbeat, and the last thing you want is to find yourself as a hashtag on social media.

Good news isn’t always easy to find. Kids are under tremendous pressure to achieve. Your website can be a place where their achievements are noticed and applauded.

Work with your colleagues for an ongoing stream of information on academic successes, special events, community projects and volunteer efforts by students. Announce scholarship recipients, awards. Don’t miss art, music and theatre success stories.

Make sure you refresh yourself on privacy rules at the school. If you can’t name individuals, you can push out statistics: “WOW! 33 members of the senior class have been accepted to college during early admissions!” Think about a FAFSA apps submitted section.

One other suggestion – don’t try too hard to be cool. It creeps the kids out and can backfire with parents. And make sure you share achievements across all groups – college bound or not.

School counselors typically have an excellent understanding of what’s going on in their school. Meeting one on one with students, or facilitating groups lets us gain insights into issues that might not be obvious at first glance.

Your page can be helpful in providing inspiration, motivation, support, and encouragement. You can share resources you know are needed to assist specific segments of the school population who are at risk. It doesn’t even have to be unique content – you can use school-sanctioned media to share the message.

Sadly, issues like bullying, suicide, substance abuse are a far too familiar part of student experience. Every opportunity to encourage kids to come forward needs to be taken, but kids hate to snitch. Your web page can reinforce the notion that you’re here to protect them from any harm.

If you’re unfamiliar with how web technology works, you may hesitate when it comes to building your web page. Remember, you are most likely going to be adding your page to the school’s site. There’s going to be some degree of technical support, as well as page templates to help you get started.

Start with what you know. You want to communicate with students and parents for sure, but what about other members of the community? Pull together lists of resources and get them organized by topic.

This is about communication – an area where school counselors typically excel. One suggestion – it’s better to start smaller and grow than to plan some colossal opus that you can’t maintain.

Look realistically at what you have time to do and move forward with that. Ask for feedback too to see if there’s something else people need.

How often do you see a kid walking around engrossed on a piece of paper? Not usually. But those phones – their eyes are glued to the screen. If you’re going to have a web page – you want it to be responsive.

Responsive in the web world means merely the information on your web page responds to the size of the screen it’s viewed. The content you offer – pictures and text – will automatically re-size to fit every device.

You may not have any control over this aspect, but we encourage everyone in school administration should advocate for mobile-friendly websites.

For kids in lower income homes – their phone may be the only access they have to get online. School websites need to make every effort not to leave them behind.

]]>You don’t need to know a lot of advanced math to score a 22 on the Math section of the ACT. The chart at this link

https://www.act.org/content/dam/act/unsecured/documents/CCRS-MathCurriculumWorksheet.pdf shows what is on the ACT. Many of these concepts are covered in kindergarten through 8th grade and basic algebra. Make sure you have a good grasp of K – Algebra 1.

You’ll need to review to help you remember, or maybe even to understand some things for the first time. We’ll help you review, and learn to avoid very common errors. The test-writers know about the common mistakes, and the wrong answers are there for those who make them.

Often, mnemonics, or memory tricks, are taught in beginning math classes to help students get through memorized steps. Many of these tricks expire without warning. And, using some tricks keeps students from actually understanding the concepts. Here are some tricks and beliefs that expire. Poor math students are known to hold onto these tricks past their expiration dates. The test-writers know this, too, so they deliberately include problems to identify these students. Don’t be one of them.

You may have seen posts on Facebook about how expressions like 8 – 8 ÷ 4 x 2 + 2 have many different answers. Well, they don’t. There is one answer, and you get it by following the order of operations. And PEMDAS will give you the wrong answer. PEMDAS is an expiring trick that never really worked in the first place. It might work if the teacher controlled the problems to use it on.

Multiplication and Division are equal to each other. They have to be since one can be changed for the other (e.g., ÷ 2 is the same as x ½). You start left to right and take care of anything in parenthesis, then exponents, then do multiplication and division in the order they appear. Then do addition and subtraction in whatever order they appear.

The expression 8 – 2 x 2 + 2 simplified is 8 – 4 + 2, which can then be simplified to 4 + 2, and finally arriving at the answer: 6.

FOIL is a trick for multiplying things like (x + 3)(2x – 5). FOIL stands for First Outer Inner Last. You then have no way to multiply when you see something with one more term: (x + 3)(2x^{2} – 5x + 1). FOIL doesn’t work, and you’re on your own.

What always works is the Distributive Property. Think of the word distribute. If I ask you to distribute the cookies to the kids, I mean to give one to each kid. When we use the Distribute Property to solve this, we distribute each term in the (x+3) times the second parenthesis: x(2x^{2} – 5x + 1) + 3(2x^{2} – 5x + 1)

This always works. Split up the first part and multiply each term times the second. You are distributing the times (2x^{2} – 5x + 1) to each of the first terms. This always works, no matter how many terms there are.

This is true with whole numbers. Once you start dealing with negative numbers, decimals, and fractions, it is no longer true. This tricks people in Word Problems. They might read a problem, and know that the answer will be larger than the numbers given, so they decide to add or multiply, and then it’s a mess.

Some students learned complicated ways to add integers. It can be very simple.Think like this:

Addition and subtraction are opposites. Instead of subtracting, you can add the opposite (or opposite signed number).

Multiplication and division are opposites. Instead of dividing, you can multiply the opposite (or flipped fraction).

In both cases, don’t change the first number. Here are some examples:

-3 – 7 = -3 + -7

3 ÷ ½ = 3 x 2/1 = 3 x 2

Once you have changed all the subtraction to plus opposite, you can think of negative numbers as money you owe, and positive as money you have. The addition problem is asking for the net worth:

-3 + -2 You owe $3 and you owe $2. So, you owe $5. That is -5

4 + -7 You have $4 and you owe $7. So, your net worth is $3 owed. That is -3.

(It is easier to understand that “If the absolute value of the number is larger, subtract… etc.)

Why would you want to change subtraction to addition and division to multiplication? What difference does it make? You want to do it because addition and multiplication are commutative, and subtraction and division are not. The commutative property of addition or multiplication allows you to move things around in the equation, and still get the right answer. To remember, you commute to school or work, and you’re moving. Here’s an example of the commutative property in addition and multiplication:

4 + 2 = 6 and 2 + 4 = 6

3 x 2 = 6 and 2 x 3 = 6

You can’t do this with division and subtraction:

8 ÷ 4 = 2, but 4 ÷ 8 ≠ 2

6 – 4 = 2, but 4 – 6 ≠ 2

You probably remember learning the properties. Many students learn them for the test, then do a brain dump afterward. But properties can make algebra easy if you understand them.

You may be saying to yourself, “But the problems are given to me. I have to answer the questions on the ACT as they’re given to me. I can’t change them.” Actually, yes, you can.

For example, in the previous subtraction problem, we simply change the minus 4 to a plus negative 4:

6 – 4 = 2 becomes:

6 + -4 = 2

To change division to multiplication, simply invert whatever you were dividing by, that is, flip the fraction. If it’s a whole number, you can make it a fraction simply by using 1 as the denominator, because 4 is the same as 4/1. Then, you invert the numerator and denominator to 1/4. For example, you can change our previous problem:

8 ÷ 4 = 2 to

8 x ¼ = 2

Notice, now it is commutative: 8 x ¼ = 2

Distribute the parenthesis to each term to be multiplied:

(x + 3)(2x + 7) = x(2x + 7) + 3(2x + 7) Everybody in the first parenthesis gets a times (2x + 7).

There are more properties, but these two will get you through the ACT.

Invisible 1s are all over math and are a common source of errors. Write them in, so they don’t get you! Here are examples:

x + 5x is the same as 1x + 5x

x + 3y + 2x = 1x + 3y + 2x

y = 3x + 2 is the same as y = 3/1x + 2, and you need to graph this with using rise over run

7/3 ÷ 4 is the same as 7/3 ÷ 4/1, which we now know is the same as 7/3 x 1/4

(x – 3)(2x + 5)

Change this to (x + -3)(2x + 5) before you distribute. Believe me. I have graded tens of thousands of algebra tests. Dropping negative signs is a common mistake. Make everything addition, and the negative signs will stick with the numbers.

For some reason, many people stop distributing when they get to the last term. (You don’t want to leave one kid without a cookie, now do you?) All you can do is check for this. Here’s a problem to show you what I mean:

3(5x + 6y + 3z + 1)

Some people will mistakenly simplify this as:

15x + 18y + 9z + 1

. . . when it should be this:

15x + 18y + 9z + 3

This is what I am talking about. The 1 did not get multiplied by 3 as it should have. I don’t know why this is so common, but it is. Test-writers know it, too. And remember, they are always looking for ways to trip you up. This wrong answer will be there. Don’t fall for it. Check your work.

If you are a student, keep track of which kind of mistakes you are making on tests. Get to know yourself. Start checking your work for these mistakes. Checking your work means look for these mistakes, not do the problems over.

If you are the teacher or a coach, make up some problems with these mistakes in them and have the students find them. Become aware of these common mistakes.

Some tricks really will help you know how to identify answers. They are based on understanding the underlying concepts. Even if you know how to do all the problems, you don’t have time. They are trying to find the students who understand the underlying concepts.

The graph of y = 3x + 2 will be a line.

- If the number on x is positive, the graph is a forward slash. If negative, it’s a backslash.
- The y-axis is the up-and-down axis. When x is 0, the line is on the y-axis, so it goes through at 2 when:

y = 0x + 2

y = 2

This will be a horizontal line intercepting the y-axis (the up and down one) through the number 2. A line has slope if you could ski on it. Remember, 0 is a number. This line has 0 slope. You could cross-country ski on that, but it wouldn’t be much fun. - If x = 3, this is a vertical line. This line has NO slope. You couldn’t ski on a vertical cliff. Remember folks, 0 is a number.

Play around with this free resource that lets you see how the numbers in an equation affect the graph of a line. Notice what is controlled by each number. Spend some time playing with these.

https://www.desmos.com/calculator/p5tqihi9fq

https://www.desmos.com/calculator/z3wu4xa6aj

The graph of y = 3×2 + 4x + 7 will be a parabola.

- If the number on the x
^{2}is positive, it opens up. If it is negative, it opens down. - When x is 0, y is 7. That means it crosses the y-axis at 7.

Play around with this free resource to see what the numbers tell you about the graph of a parabola.

https://www.desmos.com/calculator/zukjgk9iry

Use what is discussed above to sharpen your math skills. Practice. Look for these super common mistakes. Write in the invisible ones. Change subtraction to plus opposite. Change division to multiply the inverse. Explore the concepts of graphing. Memorize Pythagorean Triples. And do practice tests. Stay calm. You only need to get slightly more than half of the problems correct.

Free practice tests are all over the web. https://www.test-guide.com/free-act-practice-tests.html

**Be sure to know the basic area formulas in geometry and the basic geometry vocabulary!**

Your grandparents remember vocational education offered in high school. Most boys took some vocational education classes, and built birdhouses or bookends, while girls took home economics and made aprons and apple pandowdy. But, they probably remember the training program as being for students who were academically challenged.

Times have changed. High schools no longer have vocational education programs. These have been replaced with Career Technical Education (CTE). The change has been gradual, and we may have been slow to realize the difference.

As with any significant change, nothing happens all at once in a clear shift. Change is gradual, and people are informed at different levels.

A federal study on Career Technical Education found that although these types of classes used to be for students “without a strong academic orientation,” now students of all kinds take these classes. CTE is no longer a track for low-achievers; it becomes a valid pathway to many lucrative careers. And although the array of students taking these courses has grown, numbers of students concentrating on CTE (taking three or more CTE courses) has been declining since the 1980s (U.S. Department of Education, Office of Planning, Evaluation and Policy Development, 2013, p. vii).

Guided pathways are academic plans that lead to being prepared for careers. These channels can begin in high school in the CTE programs, then continue in the community colleges.

Today, many professional careers do not require four-year degrees. Students can prepare for these beginning in their high schools and continue on a guided pathway through their community colleges. Many students don’t know about these career paths. North Carolina developed a website that provides information about the career paths available.

http://nctower.com/

Some of the more lucrative careers that can be obtained through community colleges include cardiovascular technology, radiation therapy technology, nursing, dental hygiene, medical sonography, and cardiovascular sonography.

Today’s career paths in Community Colleges are not for low-achieving non-academic students. To enroll in credit-bearing courses for many of the career pathways offered at North Carolina’s community colleges, students must either meet the ACT Benchmark scores of 22 on the math subscale and 18 on the English or take developmental courses, not for credit.

Students need to have a good foundation in math and English to meet these benchmarks. CTE students should enroll in rigorous high school courses to prepare for these career opportunities.

Beginning in 2018-2019, (Section 10.13 of S.L. 2015-241: Career and College Ready Graduates) high schools in North Carolina will provide opportunities for college remediation for students before high school graduation through cooperation with community college partners. This program will be mandatory for high school students in their senior year who have not met benchmarks established by the SBCC in their junior year.

Students and school counselors need to know about the career paths from CTE programs in high school to Community Colleges, and on to careers. There are much higher academic expectations for today’s CTE programs than in your grandmothers’ day. People who don’t understand that may discourage students from this path.

U.S. Department of Education, Office of Planning, Evaluation and Policy Development, Policy and Program Studies Service (2013). National Assessment of Career and Technical Education: interim report. Washington D.C. Retrieved from https://www2.ed.gov/rschstat/eval/sectech/nacte/career-technical-education/interim-report.pdf

]]>Families need to complete the Free Application for Federal Student Aid (https://fafsa.gov/), known as FASFA, to apply for state or federal financial aid for college in the fall. Many colleges also use the information from the FASFA form to calculate how much institutional aid they will grant to a student. Therefore, all families should fill out the form, even if they don’t expect to get state or federal aid.

Parents and students should get a FASFA ID as soon as possible. Each of them needs a separate ID. They will keep the same ID but will need to change the passwords periodically. They set that up here: https://fsaid.ed.gov/npas/index.htm

To avoid problems with setting up the ID, make sure each ID is associated with a different email address, and check the birthdays and social security numbers. Those are common errors that keep setting up the ID from working.

The government provides a youtube tutorial on setting up the ID: https://www.youtube.com/watch?v=K7ihhGk8mCY&feature=youtu.be. The number to call if having problems is: 1-800-433-3243.

The FASFA form uses tax information from two previous years. Once FASFA opens on October 1, families can use the use the IRS Data Retrieval Tool to transfer income and tax information. https://fafsa.gov/fotw1718/help/irshlp8.htm.

State deadlines for submitting FASFA might be different than federal. Check your state deadlines here: https://fafsa.gov/deadlines.htm

Helping low-income and first-generation college families with information about FASFA is critical. Simply providing them with information can be very helpful.

Use the information in this blog to create a newsletter and information handout to provide to parents of your seniors.

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