]]>

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.

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.

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

]]>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, 2018 to June 30, 2020. (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, 2018, 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), 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

Cindy has experience as a business analyst who enjoys discovering the hidden value of data through analysis, trending, charting, and creating data-dashboards to assist in solving problems. She is adept at methodologies that ensure accuracy, integrity, validation, and quality of data while saving time and money. Cindy was recruited from the business analyst world, as EDSTAR Analytics has seen the need for these technical skills in the world of education and social services.

Cindy contributes a valuable blend of broad experience from complex, large-scale system implementations to small-scale projects, providing the ability to see the big picture and still have an understanding of the details. Although relatively new to EDSTAR Analytics, Cindy brings her expertise from her many years analyzing data for large corporations within the Research Triangle.