There's a Vinculum in Math? What Is It?

When writing division problems, we can use three different forms, a fraction, the division symbol (÷) or the division house. Why it has been called the division "house" has always been a mystery to me since most math symbols are named something that sounds important. I tried looking it up on-line, but never found a formal mathematical word. Well the mystery has been partially solved thanks to SamizdatMath on Teachers Pay Teachers who mentioned the word vinculum.

I decided to research "vinculum", and here is what I discovered. It is a Latin word that means to ‘bond’ or ‘tie’, and was first used by Michael Stifel in 1544 in Arithmetica integra. It is the horizontal line used to separate the numerator and denominator in a fraction. We also see it above the digital pattern that repeats in a repeating decimal or in geometry above two letters that represent a line segment.

Originally the line was placed under the items to be grouped. What today might be written 7(3x + 4) the early users of the vinculum would write 3x + 4. Today that line is placed over the items to be grouped. The line of a radical sign or the long division house is also called a vinculum.

The symbol is utilized to separate the dividend from the divisor, and is drawn as a right parenthesis with an attached vinculum (see illustration above) extending to the right. The vinculum shows that the digits of the dividend are to be kept together as they represent one whole number.

But when it is all said and done, the entire division "house" symbol seems to have no established name of its own. How mathematically sad! Consequently, it has simply be termed the "long division symbol," or sometimes the division "bracket" or division "house". So the next time you draw the symbol on the board, impress your students with the math word "vinculum"!

Can you find the vinculums in this cartoon?

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$3.00

Since many students do not know their multiplication tables, working with fractions can be an impossible task, but the divisibility rules, if learned and understood, can be an excellent math tool. This math resource makes it easier to divide numbers, reduce fractions, and determine factors. It contains four easy to understand divisibility rules and includes the rules for 1, 5, and 10 as well as the digital root rules for 3, 6, and 9. A clarification of what digital root is and how to find it is explained.

It's NOT on the Test?!?

Not on the Test

While watching my granddaughter at her tennis lesson, I was visiting with two teachers.  One was a retired fourth grade teacher and the other currently taught Algebra in middle school.  Both we decrying the fact that each year the students come with knowledge that is more narrow than broad.  They both felt this was because more and more time is now spent on testing or getting ready for testing.  As I stated in a previous posting, The Pros and Cons of Testing, "High stakes tests have become the “Big Brother” of education, always there watching, waiting, and demanding our time. As preparing for tests, taking pre-tests, reliably filling in bubbles, and then taking the actual assessments skulk into our classroom, something else of value is replaced since there are only so many hours in a day.  In my opinion, tests are replacing high quality teaching and much needed programs such as music and art."

A long time ago, a friend sent me a song written by Tom Chapin with John Forster called Not on the Test. I saved it, and I listen to it often, especially when I am having a "down" day.  Tom and John wrote the song to express their disappointment in the lack of arts education in many public schools.  Even though the song refers to No Child Left Behind and Common Core, I think you might get a much needed laugh from the song.  Just click on the link under the picture, and let me know what you think!

Bible Activities to Learn and Review the Romans Road to Salvation

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Memorizing Scripture is a crucial aspect of the Christian faith, but there is one particular set of verses that holds great value for witnessing. The Romans Road is a powerful tool that leads individuals through the essential steps of salvation, from understanding the need for it to receiving it through Jesus Christ. Its straightforward format makes it especially effective in sharing the message of Christianity with others. 

The Romans Road is a powerful Bible tool that leads individuals through the essential steps of salvation, from understanding the need for it to receiving it through Jesus Christ. It is a collection of seven verses from the ESV Version (Romans 3:10, 3:23, 5:8, 6:23, 10:9-10 and 10:13) that serve as a Bible roadmap to the core principles of the Christian faith. With this Romans Road Bible resource, it’s even easier for you to commit these verses to memory by incorporating interactive activities like utilizing pictures, filling in the blanks, and using a word bank to reinforce your learning. In addition, road signs are incorporated to guide you on your spiritual journey.

Included in this resource is…

1. A Table of Contents
2. The seven verses with subtitles for easy recall (All in ESV Version)
3. How to use the Romans Road resource
4. Five different and engaging activities

• Using Pictures Instead of Words (Romans 3:10, 3:23)
• Missing Words (Romans 3:10,3:23, 5:8)
• Road Signs (Romans 3:10, 3:23, 5:8, 6:23)
• Word Bank Activity (Romans 10:9-10)
• Guiding Arrows – All Verses

Master one verse at a time: Instead of trying to memorize a whole passage at once, focus o perfecting one verse before moving on to the next. This will help you retain the information more effectively.

Review, review, review: Before starting a new verse, take a moment to refresh your memory of the previous one. This will help you make connections between the verses and solidify your understanding.

Utilize subtitles: Subtitles can serve as helpful cues to jog your memory about the verse and its placement within the larger passage. Use them to your advantage during the memorization process.

Are Calculators a Crutch or a Useful Math Tool for Students?

Once upon a time, two mathematicians, Cal Q. Late and Tommy Go Figure, were having a discussion...an argument, really.

"Calculators are terrific math tools," said one of the mathematicians.

"I agree, but they shouldn't be used in the classroom" said the other.

"But?" asked Tommy Go Figure, and this is when the argument started. "That is just crazy!  I agree that having a calculator to use is a convenience, but it does not replace knowing how to do something on your own with your own brain."

"Why should kids have to learn how to do something that they don't have to do, something that a calculator can always be used for?" Cal Q. Late argued.

Tommy retorted,  "Why should kids not have the advantage of knowing how to do math?  To me, a calculator is like having to carry an extra brain around in their pockets.  What if they had to do some figuring and did not have their calculators with them?  Or what if the batteries were dead? (Here's a good reason for solar calculators.) What about that?"

Cal reminded Tommy, "No one is ever in that much of a rush. Doing math computation is rarely an emergency situation. Having to wait to get a new battery would seem to take less time than all the time it would take to learn and practice how to do math. That takes years to do, years that kids could spend doing much more interesting things in math."

"Look," Tommy went on, exasperated, "kids need to depend on themselves to do jobs. Using a calculator is not bad, but it should not be the only way kids can do computation. It just doesn't make sense."

Cal would not budge in the argument. "The calculator is an important math tool. When you do a job, it makes sense to use the best tool there is to to that job. If you have a pencil sharpener, you don't use a knife to sharpen a pencil. If you are in a hurry, you don't walk; you go by car. You don't walk just because it is the way people used to travel long ago."

"Aha!" answered Tommy. "Walking is still useful. Just because we have cars, we don't discourage kids from learning how to walk. That is a ridiculous argument."

This argument went on and one and on...and to this day, it has not been resolved. So kids are still learning how to compute and do math with their brains, while some are also learning how to use calculators.  What about you?  Which mathematician, Cal Q. Late or Tommy Go Figure, do you agree with?

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Of course, this argument was made up, but it is very much like the argument schools and teachers are having about what to do with kids and calculators. What do you think?  Leave your comment for others to read.