Go Figure!

Math Ideas for Parents for Those Long Summer Months

2026-06-03T07:00:00.001-05:00

Success in school starts and continues at home, but many parents feel inadequate when it comes to helping their children with math. While parents can usually find time to read a story to their children, thereby instilling a love for books, they are often at a loss as to how to instill a love and appreciation for mathematics. Like reading, mathematics is a subject that is indeed necessary for functioning adequately in society. Here are some tips to help you as you work with your child this summer.

Recognize that you make an important difference in your child's education. Most children develop a sense of numbers way before the "regular" school years. If you have a young child, take advantage of those early years through activities at home that teach and at the same time are enjoyable. You might take your child on a counting walk in your neighborhood to count how many trees, shrubs, plants, houses, birds, dogs, etc. you see. Look for twigs or pine cones or leaves, etc. and have your child count as many as s/he can. Then lay them side by side to compare the length and ask your child, "Which is the longest, which is the shortest? Are there any that are the same length?"

Provide experiences at home that help your child be successful, and seek ways to let children, even very young children, know that they are needed and important. Cooking is a fun way to do this. Help your child follow the directions on a Kool Aid packet or frozen juice can to make refreshments for the family. Help your child cut a fruit or vegetable into halves, fourths, thirds, etc. Let them help prepare a meal while asking, "What do you do first? Second? Third?" or better yet, allow them to measure the ingredients for a recipe.

Children do not need a lot of motivation when it comes to recognizing and learning the value of coins. You know they are interested when they start bugging you for money. However, it is not sufficient for children to be able to just recognize coins, they must also know the value of these coins. The best way to accomplish this is to use real money. You might show your child two or more coins and have him/her tell you the total value of the coins. Or hold up a coin. After your child identifies it, discuss what the coin would buy at the store. When going to the grocery store, give your child his/her own money to buy something. Have them select an item that costs less than the money you have given them. You can also do a similar activity by asking them to determine what are the fewest number of coins it would take to pay for the item. Give your child a practical math experience by estimating how long it takes to prepare a meal from start to finish.

Parents' attitudes toward mathematics have an impact on children's attitudes; so, be patient with your child. A wrong answer on a math test or a homework assignment is not a time for scolding. It tells you to look further, to ask questions, and to find out what the wrong answer is saying about your child's understanding. Ask your child to explain how they solved the problem. Most importantly, relax! Know that neither you nor the teacher needs to be perfect for your child to learn math. Remember, one bad math assignment/test will not destroy your child's ability to learn math.

But what if you need some assistance? Luckily, in today's world, we can find mathematical help at the click of a button. Below are some great places to go and find outside help if your child is struggling or if you need more information for yourself.

Study Shack is a great place to find or make flashcards, play hangman, do matching activities or crosswords. It has activities for grades 1-6 as well as addition, multiplication, algebra and geometry. Cliff's Notes for Math is site that has notes, examples and quizzes for your older children. The subject areas include Basic Math through Calculus. There are many on-line math dictionaries. My favorite is A Math Dictionary for Kids because it includes animation and interactive activities. Even You Tube is a great resource for students struggling with a concept and needing an alternative way of seeing it.

Finally, talk about people who use math in their jobs, including builders, architects, engineers, computer professionals, and scientists. Point out that even if your child does not plan to pursue a career in which s/he will use math, learning it is still important because math teaches you how to solve problems and how to think logically. AND we use math everyday!

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Here is another resource that may prove useful. It is a ten page, comprehensive, extensive and wide-ranging list of over 200 hyperlinked Educational Website Addresses for ALL subjects.

Organized by a wide range of subject areas
Broken down into subcategories (i.e. science, then earth science, ecology, etc.)
Click on the URL and you are automatically taken to the site.

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

2026-05-27T07:00:00.001-05:00

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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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?!?

2026-05-20T07:00:00.003-05:00

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

2026-05-13T07:00:00.001-05:00

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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…

A Table of Contents
The seven verses with subtitles for easy recall (All in ESV Version)
How to use the Romans Road resource
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?

2026-05-08T07:00:00.001-05:00

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.

Two Mind-Bending May Crossword Puzzles in which all the Answers Start with "May"!

2026-04-29T07:00:00.024-05:00

I love the beautiful month of May. Here in Kansas, the blustery, cold winds are gone, as are the rains of early spring. Thankfully, the days are getting longer and the nights shorter. May is known as the month of transition and holidays like Mother's Day, and Memorial Day. It is also recognized as Military Appreciation Month. Some other dates that hold significance are May 1st and May 5th.

May 1st is May Day, and marks the return of spring by the blossoming branches of the forsythia, or lilacs or daffodils popping their heads out of the ground, or the weather turning warmer. May 5th is Cinco de Mayo (The Fifth of May). This day celebrates the victory of the Mexican army over the French army at The Battle of Puebla in 1862. Did you know that no U.S. president has ever died in the month of May? In every other month of the year, at least one U.S. president has died.

Have you heard about these fun dates in May?

May 1: School Principals’ Day
May 2: World Tuna Day
May 8: No Socks Day
May 14 (second Wednesday in May): Root Canal Appreciation Day
May 14: Dance Like a Chicken Day
May 28: Slugs Return from Capistrano Day

As I thought about May, I discovered that numerous words begin with "MAY". After much research, I compiled a list of 20 different such words to create two May themed crosswords puzzles perfect for students in grades 7-10. One puzzle includes a word bank for easier solving, while the other offers a more challenging experience without it. Although both puzzles use the same vocabulary, they have unique layouts, providing two distinct challenges for your students. And don't worry, I've included answer keys for both puzzles.

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Here are some ideas on how you might use these puzzles.

Try giving the students the crossword with NO word bank to see how much they know.
Use the crossword with the word bank as a review of May and its traditions.
Use either crossword to work in pairs to complete the puzzle. Solving a crossword puzzle together is a great way to connect.
Copy it and make it available for those students who finish their work early.

Happy Puzzling!

The Golden Ratio - Another Math Pattern in Nature

2026-04-22T07:00:00.001-05:00

As stated in a previous blog post, we come across Fibonacci numbers almost every day in real life. For instance, my husband and I were at the Wonders of Wildlife Aquarium in Springfield, Missouri. (If you haven't been, you should go because it is spectacular.) He was noticing how the herrings were swimming counter clockwise and discussing the Coriolis effect with the guide. When we got to the lower levels, where the sharks were, they were all swimming in a counterclockwise direction as well. I asked my rocket scientist husband why this was and again he said, with a straight face, "The Coriolis Effect."

Inside of a Nautilus Shell

I then spied seashells and started talking about Fibonacci numbers and the Golden Ratio. (I know the visitors around us were wondering just who we were!) On the right, you will see a picture of the inside of a Nautilus Shell taken by me! It clearly shows the Golden Ratio. (The Golden Ratio is a special number equal to about 1.6180339887498948482. The Greek letter Phi is used to refer to this ratio. Like Pi, the digits of the Golden Ratio go on forever without repeating.) Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral.

Are you still not sure what I am talking about? Have you ever watched the Disney movie entitled Donald in Mathmagic Land? (It's an old one that

The Golden Ratio

you can find on You Tube.) Well, in the movie they talk about the Golden ratio. This is a proportion that is found in nature and in architecture. The proportion creates beauty. And that proportion is the Fibonacci sequence! If you divide consecutive Fibonacci numbers you will always get the Golden ratio. Try it! Start with the big numbers. If you divide 89 by 55, you get 1.61. If you divide 55 by 34, you get 1.61. If you divide 34 by 21, you get 1.61, and so on. You can look up the Golden Ratio and explore it more. It’s fun!

As I close, think about these two questions and try to answer them.

Where is the Golden Ratio found in the human body?
Why is the golden rectangle important in architecture and art?

How Will Your Students Celebrate Earth Day on April 22nd?

2026-04-15T07:00:00.009-05:00

Earth Day began in 1970, when Gaylord Nelson, a U.S. Senator from Wisconsin, wanted nation-wide teaching on the environment. He brought the idea to state governors, mayors of big cities, editors of college newspapers, and to Scholastic Magazine, which was circulated in U.S. elementary and secondary schools.

Eventually, the idea of Earth Day spread to many people across the country and is now observed each year on April 22nd. The purpose of the day is to encourage awareness of and appreciation for the earth's environment. It is usually celebrated with outdoor shows, where individuals or groups perform acts of service to the earth. Typical ways of observing Earth Day include planting trees, picking up roadside trash, and conducting various programs for recycling and conservation.

Symbols used by people to describe Earth Day include: an image or drawing of planet earth, a tree, a flower or leaves depicting growth or the recycling symbol. Colors used for Earth Day include natural colors such as green, brown or blue.

The universal recycling symbol as seen above is internationally recognized and used to designate recyclable materials. It is composed of three mutually chasing arrows that form a Mobius strip which, in math, is an unending single-sided looped surface. (And you wondered how I would get math in this article!?!) This symbol is found on products like plastics, paper, metals and other materials that can be recycled. It is also seen, in a variety of styles, on recycling containers, at recycling centers, or anywhere there is an emphasis on the smart use of materials and products.

FREE

Inspired by Earth Day, Trash to Treasure is a FREE resource. In it, you will discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom. Because these numerous activities vary in difficulty and complexity, they are appropriate for any PreK-3 classroom, and the visual and/or kinesthetic learners will love them.

To download the free version, just click under the cover page on your left.

What Is the Fibonacci Number Sequence and Why Should I Care?

2026-04-08T07:00:00.001-05:00

Fibonacci

Even if you were taught about the Fibonacci number sequence in school, you probably don’t remember much about it. As with other higher levels of math, many aren’t sure how Fibonacci could possibly be relevant to their real lives; so, why should they even attempt to remember him or his sequence? In reality, Fibonacci numbers are something you come across practically every day. Even so, let’s go back and start at the beginning.

The Fibonacci number sequence is named after Leonardo of Pisa (1175-1240), who was known as Fibonacci. (I love to say that name because it sounds like I know a foreign language.) In mathematics, Fibonacci numbers are this sequence of numbers:

As you can see, it is a pattern, (all math is based on patterns). Can you figure out the number that follows 89? Okay, let's pretend I waited for at least 60 seconds before giving you the answer….144. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. For those who are still having difficulty, it is like this.

The next number is found by adding up the two numbers that precede it.

The 8 is found by adding the two numbers before it (3 + 5)
Similarly, 13 is found by adding the two numbers before it (5 + 8),
And the 21 is (8 + 13), and so on!

It is that simple! For those who just love patterns, here is a longer list:

Can you figure out the next few numbers?

The Fibonacci sequence can be written as a "Rule “which is: xn = xn-1 + xn-2 The terms are numbered from 0 forwards as seen in the chart below. xn is the term number n. xn-1 is the previous term (n-1) and xn-2 is the term before that (n-2)

Sometimes scientists and mathematicians enjoy studying patterns and relationships because they are interesting, but frequently it's because they help to solve practical problems. Number patterns are regularly studied in connection to the world we live in so we can better understand it. As mathematical connections are uncovered, math ideas are developed to help us be aware of the relationship between math and the natural world.
As I close, here are two questions to think about:

How might knowing this number pattern be useful?
What kinds of things can the numbers in the Fibonacci sequence represent?

Dominoes - An Inexpensive Manipulative to Use in Math

2026-04-01T07:00:00.001-05:00

I am always looking for ordinary items that can be used in the classroom as manipulatives. I'm a firm believer in the Conceptual Development Model which advocates teaching the concrete (using manipulatives) prior to moving to the pictorial before even thinking about the abstract. When I was at the Dollar Tree (a great, inexpensive place to purchase school stuff) I saw sets of dominoes for $1.00 each. Since they were inexpensive and readily available, I decided to create several math activities and games to introduce, reinforce, or reteach math concepts.

The Number 52

Think about it; if you lay a domino horizontally, you have a two digit number. Put two dominoes side-by-side, and a four digit number is created. Now you can work with place value, estimation, or rounding. How about lining up dominoes in a column, and working on addition (with or without regrouping) or subtraction (with or without renaming)?

Another perfect domino activity is practicing addition or multiplication facts. How about adding the two sides of the domino or multiplying the two sides together?

The Fraction 1/4

If a domino is placed vertically, you immediately have a fraction. Placed one way it is a proper fraction, but rotated around, it is an improper fraction which can then be reduced. A fraction can also be changed into a division problem, a ratio, a decimal, or a percent.

So think outside that box of dominoes and use them as an inexpensive math manipulative because Dots Lots of Fun!

Check out all my Domino Resources available on Teachers Pay Teachers.

The first two are absolutely FREE!

Dots Fun for Everyone - FREE Three math activities and one game for the intermediate grades.
Dots Fun - FREE Three math activities and one game for the primary grades.
Dots Fun A 24 page resource for grades 1-3 that includes 13 math activities and four games.
Dots Fun for Everyone A 29 page resource that features 15 math activities and three games for grades 3-6.
Dots Lots of Fun Seven math games that use dominoes for grades 2-5.

What is the real purpose of homework?

2026-03-18T07:00:00.026-05:00

Dictionary.com defines homework as "schoolwork assigned to be done outside the classroom (distinguished from classwork)", but is homework beneficial? Teaching on the college level, I see many benefits to those students who have been required to complete real homework in high school. Here are just a few.

1) Homework can improve student achievement. Studies show that homework improves student achievement in terms of better grades, test results, and the likelihood of attending college.

2) Homework helps to reinforce learning and to develop good study habits and life skills. Homework assists students in developing key skills that they will use throughout their lives, such as accountability, self-sufficiency, discipline, time management, self-direction, critical thinking, and independent problem-solving. Homework assignments given to students actually help students prepare for getting a higher education degree. In fact, the more time a student spends honing his skills, the higher his chances are to enter the University of his dreams or later acquire the work he always wanted to do.

3) Homework can make students more responsible. Knowing that each homework assignment has a specific deadline that cannot be postponed makes students more responsible. It requires grit (perseverance), teaches them time management and causes them to prioritize their time for academic lessons.

As you read this list, I know there are many of you, especially those who have small children or teach younger children, who disagree. I am not here to argue about whether homework is appropriate in the lower grades, but I do want to advocate real homework on the high school level. When I say real homework here is what I mean.

In high school, students might finish their homework in the hall right before class and still earn a good grade; that just isn't possible in college. Homework may be due on a certain day, but it is acceptable if it is turned late. This typically doesn’t float on the college level. In high school, a student gets to the end of a semester and needs a few more points to pull up a grade because of missing or incomplete assignments; so, the student asks the teacher for extra credit work. Extra credit does not exist on the college level! You do the work you are given when you are given it!

I teach college freshmen, many who are woefully unprepared for the academic rigors and demands that are expected. For every one hour students take in college, they should expect two hours of outside work. In other words, if a student is taking 12 hours, they should expect to spend 24 hours on homework (12 x 2). Of course this formula doesn't always work perfectly, but it is a good starting point. Usually, college freshmen are in disbelief that they are expected to spend so much time on work outside of class. In reality, they should expect to spend as much time on homework in college as they would at a job because college is a full time job!

Help, we're sinking!

When I hand out my syllabus, many of my freshmen are astonished when they discover the amount of homework I expect and require them to do (readings, papers, on-line research, projects, etc.) AND to compound the problem, many instructors (including me) expect it to be done and handed in on time! Unfortunately, several students have to test the waters to find out that late papers are not accepted.

For those college students who've had little real homework in high school compounded by teachers who have allowed it to be turned in late, those students are aboard a sinking ship that is leaking fast! Sadly, those are the 2-3 students who fail my required class and have to retake it the next semester.

So, as you can see, the decision to agree with or disagree with assignments is really up to the student, but also they need to remember that the learning institution they attend has rules in place regarding assignments. And if homework is assigned, then it will need to be completed and handed in on time, or the impact on the final semester grade will certainly be negative.
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Want a quicker and easier way to grade math homework? Try one of these two math rubrics. I still use them on the college level, and they save me a great deal of time!

Making Perfect Circles by Using Coffee Filters

2026-03-11T07:00:00.020-05:00

When I teach angles or the properties of circles, I find that most children have difficulty cutting out a true circle (even with a blackline). I have resorted to purchasing cheap coffee filters (not the cone shaped ones) and ironing them flat. You can iron several filters at one time, and once they are ironed, they form excellent ready-made circles. Here are some of the ways you can teach angles using these circles.

Writing Formulas on the Coffee Filter Circle

Introduce the fact that each and every circle contains 360 degrees.
Have the students fold their coffee filter in half. Discuss that this is a straight angle. Ask, “How many degrees does it contain if it is one-half of a circle?” (180 degrees)
Have the students fold the coffee filter one more time, into fourths. Talk about this angle being called a right angle and that it contains 90 degrees. Ask, "What fractional part of a circle is this?"
Have the students use this fourth of a circle to locate places in the classroom where it will fit (e.g. the corner of their desk, a corner of a book, a corner of the board).
Explain that these corners are right angles and without right angles, we would live in a crooked world. Nothing would be straight!
With older students, have them write the parts of the circle and the formulas needed for solving problems about circles on the coffee filter circle.

Linking Math and Literature for Older Students

Read Sir Cumference and the First Round Table (A Math Adventure) by Cindy Neuschwander. This is a story about a clever knight of King Arthur’s named Sir Cumference. By using ideas offered by the knight’s wife, Lady Di of Ameter, and his son, Radius, King Arthur finds the perfect shape for his table. Basic geometric vocabulary involving circles (circumference, radius, and diameter) is introduced.

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Want more hands-on ideas for teaching angles? Check out Angles: Hands-On Geometry Activities.

Using Math Humor in Geometry

2026-02-25T07:00:00.004-06:00

I 've been using Pinterest (as well as Tailwind) for as long as I can remember, and I love it. Not only do I post many resources and teaching ideas there, but I learn so-o-o much. For example, I learned how to pack one suitcase with enough stuff for a week. (My husband is thrilled with this one.) I also learned that when you fry bacon, to make a small cup out of aluminum foil; pour the bacon grease into it; let the grease harden; then close up the aluminum cup and toss it into the trash. That is one I use all of the time!

On my Pinterest account I have a board entitled Humor - We Need It! I post many math cartoons or humorous sayings there. My favorite subject to teach my college remedial math students is geometry, and I have plenty of corny jokes that I intersperse into my lessons. Here's one.

What did the little acorn say when it grew up? Gee- I'm - A - Tree! (Geometry)

Or about this one?

What did the Pirate say when his parrot flew away? Polly-Gone (Polygon)

Here are some other geometry funnies from Pinterest.

Try placing a riddle or cartoon in the middle of a test. I often do, and I know exactly where the students are by their laughs. It helps them to relax and maybe get rid of those mathphobic tendencies. I hope these math cartoons brought a smile to your face. Have a great week of teaching!

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You might also like Geometry Parodies, a math handout that includes 20 unusual definitions of geometry terms. Each definition is a play on words or a parody. Twenty-six geometric terms that are possible answers are listed in a word bank, but not all of the words are used in the matching exercise. An answer key is included.

In Math, what is the Difference Between Drill and Practice?

2026-02-18T07:00:00.007-06:00

When I was a kid, one of the things I dreaded most was going to the dentist. Even though we were poor, my Mom took my brother and me every six months for a check-up. Unfortunately, we didn’t have fluoridated water or toothpaste that enhanced our breath, made our teeth whiter, or prevented cavities. I remember sitting in the waiting room hearing the drill buzzing, humming, and droning while the patient whined or moaned. Needless to say, I did not find it a pleasant experience.

I am troubled that, as math teachers, we have carried over this idea of drill into the classroom. Math has become a “drill and kill” activity instead of a “drill and thrill” endeavor. Because of timed tests or practicing math the same way over and over, many students whine and moan when it is math time. So how can we get students to those “necessary” skills without continually resorting to monotonous drill?

First we must understand the difference between drill and practice. In math drill refers to repetitive, non-problematic exercises which are designed to improve skills (memorizing basic math facts) or procedures the student already has acquired. It provides:

1) Increased proficiency with one strategy to a predetermined level of mastery. To be important to learners, the skills built through drill must become the building blocks for more meaningful learning. Used in small doses, drill can be effective and valuable.

2) A focus on a singular procedure executed the same way as opposed to understanding. (i.e. lots of similar problems on many worksheets) I have often wondered why some math teachers assign more than 15 homework problems. For the student who understands the process, they only need 10-15 problems to demonstrate that. For students who have no idea what they are doing, they get to practice incorrectly more than 15 times!

Unfortunately, drill also provides:

3) A false appearance of understanding. Because a student can add 50 problems in one minute does not mean s/he understands the idea of grouping sets.

4) A rule orientated view of math. There is only one way to work a problem, and the reason why is not important! (Just invert and multiply but never ask the reason why.)

5) A fear, avoidance, and a general dislike of mathematics. A constant use of math drills often leaves students uninterested.

On the other hand, practice is a series of different problem-based tasks or experiences, learned over numerous class periods, each addressing the same basic ideas. (ex. different ways to multiply) It provides:

1) Increased opportunity to develop concepts and make connections to other mathematical ideas. (i.e. A fraction is a decimal is a percent is a ratio.)

2) A focus on providing and developing alternative strategies. My philosophy, which hangs in my classroom, is: “It is better to solve one problem five ways than to solve five problems the same way.” (George Polya)

3) A variety of ways to review a math concept. (ex. games, crosswords, puzzles, group work)

4) A chance for all students to understand math and to ask why. (Why do we invert and multiply when dividing fractions?)

5) An opportunity for all students to participate and explain how they arrived at the answer. Some may draw a picture, others may rely on a number line, or a few may use manipulatives. Good practice provides feedback to the students, and explains ways to get the correct answer.

$5.00

Let’s look at it this way. A good baseball coach may have his players swing again and again in the batting cage. This drill will help, but by itself it will not make a strong baseball player whereas practicing hitting a ball with a pitcher requires reacting to the different pitches with thought, flexibility, and skill.

I am of the opinion that drill should not be omitted from the math classroom altogether. Basic math skills should be automatic because being fluent in the basics makes advanced math easier to grasp. There is a place for drill; however, its use should be kept to situations where the teacher is certain that is the most appropriate form of instruction. Even though practice is essential, for math it isn't enough. If understanding doesn't come, practice and drill will only leave a student with disjointed skills. If we want to produce strong mathematicians, we must focus on the BIG conceptual ideas through practice in problem-based lessons. We must present ideas in as many forms as we can so that students will go beyond rote drill to insight.

If you are interested in sharing this with your staff, colleagues or parents, check out the EDITABLE power point entitled: Drill vs. Practice.

In Algebra, Why is any number to the zero power equal to one?

2026-02-18T07:00:00.005-06:00

Sometimes my college students like to ask me what seems to be a difficult question. (In reality, they want to play Stump the Teacher.) I decided to find out what sort of answers other mathematicians give; so, I went to the Internet and typed in the infamous question, "Why is any number to the zero power one?" It was no surprise to find numerous mathematically correct answers, most written in what I call "Mathteese" - the language of intelligent, often gifted math people, who have no idea how to explain their thinking to others. I thought, "Wow! Why is math always presented in such complicated ways?" I don't have a response to that, but I do know how I introduce this topic to my students.

Since all math, and Imean all math, is based on patterns and not opinions or random findings, let's start with the pattern you see on the right. Notice in this sequence, the base number is always 3. The exponent is the small number to the right and written above the base number, and it shows how many times the base number, in this case 3, is to be multiplied by itself.

(Side note: Sometimes I refer to the exponent as the one giving the marching orders similar to a military commander. It tells the base number how many times it must multiply itself by itself. For those students who still seem to be in a math fog and are in danger of making the grave error of multiplying the base number by the exponent, have them write down the base number as many times as the exponent says, and insert the multiplication sign (×) between the numbers. Since this is pretty straight forward, it usually works!)

Notice our sequence starts with 3¹ which means 3 used one time; so, this equals three; 3²means 3 × 3 = 9, 3³ = 3 × 3 × 3 = 27, and so forth. As we move down the column, notice the base number of 3 remains constant, but the exponent increases by one. Therefore, we are multiplying the base number of three by three one additional time.

Now let's reverse this pattern and move up the column. How do we get from 243 to 81? That's right! We divide by three because division is the inverse operation (the opposite) of multiplication. How do we get from 243 to 81? That's right! We divide by three because division is the inverse operation (the opposite) of multiplication. Notice as we divide each time, the exponent by the base number of 3 is reduced by one. Let's continue to divide by three as we move up the column. 27÷ 3 = 9; 9 ÷ 3 = 3. Now we are at 3¹= 3 which means we must divide 3 by 3 which gives us the quotient of 1. Notice, to fit our pattern, the 3 in the left hand column would have to be 3⁰; so, 3⁰must equal one!

This works for any number you wish to put in the left hand column. Try substituting the base number of three with two. Work your way up the sequence dividing by two each time. You will discover that two divided by two equals one (2⁰ = 1). Therefore, we can conclude that any natural number with an exponent of 0 is equal to one. (Zero is not included; it's another mystery to solve.)

What happens if we continue to divide up the column past 3⁰ ? (Refer back to the sequence on the left hand side.) Based on the pattern, the exponent of zero will be one less than 0 which gives us the base number of 3 with a negative exponent of one or 3^-1.To maintain the pattern on the right hand side, we must divide 1 by 3 which looks like what you see on the left. Continuing up the column and keeping with our pattern, 3 must now have a negative exponent of 2 or 3^-2and we must divide 1/3 by 3 which looks like what is written on the left.

Each time, the exponent by the base number of 3 is reduced by one. Let's continue to divide by three as we move up the column. 27÷ 3 = 9; 9 ÷ 3 = 3. Now we are at 3¹ = 3 which means we must divide 3 by 3 which gives us the quotient of 1. Notice, to fit our pattern, the 3 in the left hand column would have to be 3⁰; so, 3⁰must equal one! This works for any number you wish to put in the left hand column. Try substituting the base number of three with two. Work your way up the sequence dividing by two each time. You will discover that two divided by two equals one (2⁰ = 1). Therefore, we can conclude that any natural number with an exponent of 0 is equal to one. (Zero is not included; it's another mystery to solve.)

As a result, the next two numbers in our pattern are..............??

Isn't it amazing how a pattern not only answers the question: "Why is any number to the zero power one?" But it also demonstrates why a negative exponent gives you a fraction as the answer. (By the way math detectives, do you see a pattern with the denominators?)

Mystery Solved! Case Closed!

This lesson is available on a video entitled: Why Does "X" to the Power of 0 Equal 1?

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$4.25

Want simple, visual answers to other difficult math questions? Try this resource entitled Six Challenging Math Questions with Illustrated Answers. Many of the answers feature a supplementary video for a more detailed explanation.

In Algebra, FOIL is NOT the Only Way to Multiply Polynomials.

2026-02-11T07:00:00.004-06:00

Using FOIL

In more advanced math classes, many instructors happen to hate "FOIL" (including me) because it only provides confusion for the students. Unfortunately, FOIL (an acronym for first, outer, inner and last) tends to be taught as THE way to multiply all polynomials, which is certainly not true. As soon as either one of the polynomials has more than a "first" and "last" term in its parentheses, the students are puzzled as well as off course if they attempt to use FOIL. If students want to use FOIL, they need to be forewarned: You can ONLY use it for the specific case of multiplying two binomials. You can NOT use it at ANY other time!

When multiplying larger polynomials, most students switch

to vertical multiplication, because it is much easier to use, but there is another way. It is called the clam method. (An instructor at the college where I teach says that each set of arcs reminds her of a clam. She’s even named the clam Clarence; so, at our college, this is the Clarence the Clam method.)

Let’s say we have the following problem:

(x + 2) (2x² + 3x – 4)

Simply multiply each term in the second parenthesis by the first term in the first parenthesis. Then multiply each term in the second parenthesis by the second term in the first parenthesis.

I have my students draw arcs as they multiply. Notice below that the arcs are drawn so they connect to one another to designate that this is a continuous process. Begin with the first term and times each term in the second parenthesis by that first term until each term has been multiplied.

When they are ready to work with the second term, I have the students use a different color. This time they multiply each term in the second parenthesis by the second term in the first while drawing an arc below each term just as they did before. The different colors help to distinguish which terms have been multiplied, and they serve as a check point to make sure no term has been missed in the process.

As they multiply, I have my students write the answers horizontally, lining up the like terms and placing them one under the other as seen below. This makes it so much easier for them to add the like terms:

This "clam" method works every time a student multiplies polynomials, no matter how many terms are involved.

Let me restate what I said at the start of this post: "FOIL" only works for the special case of a two-term polynomial multiplied by another two-term polynomial. It does NOT apply to in ANY other case; therefore, students should not depend on FOIL for general multiplication. In addition, they should never assume it will "work" for every multiplication of polynomials or even for most multiplications. If math students only know FOIL, they have not learned all they need to know, and this will cause them great difficulties and heartaches as they move up in math.

Personally, I have observed too many students who are greatly hindered in mathematics by an over reliance on the FOIL method. Often their instructors have been guilty of never teaching or introducing any other method other than FOIL for multiplying polynomials. Take the time to show your students how to multiply polynomials properly, avoid FOIL, if possible, and consider Clarence the Clam as one of the methods to teach.

A New Approach to the Order of Operations (PEMDAS)

2026-02-04T07:00:00.015-06:00

Any math teacher who teaches the Order of Operations is familiar with the phrase, "Please Excuse My Dear Aunt Sally". For the life of me, I don't know who Aunt Sally is or what she has done, but apparently we are to excuse her for the offense. In my math classes, I use "Pale Elvis Meets Dracula After School". Of course both of these examples are mnemonics or acronyms; so, the first letter of each word stands for something. P = Parenthesis, E = Exponents, M = Multiplication, D = Division, A = Addition, and S = Subtraction.

I have always taught the Order of Operations by just listing which procedures should be done first and in the order they were to be done. But after viewing a different way on Pinterest, I have changed my approach. Here is a chart with the details and the steps to "success" listed on the right.

Since multiplication and division as well as addition and subtraction equally rank in order, they are written side by side. What I like about this chart is that it clearly indicates to the student what they are to do and when. To sum it up:

When expressions have more than one operation, follow the rules for the Order of Operations:

First do all operations that lie inside parentheses.
Next, do any work with exponents or radicals.
Working from left to right, do all the multiplication and division.
Finally, working from left to right, do all the addition and subtraction.

Failure to use the Order of Operations can result in a wrong answer to a problem. This happened to me when I taught 3rd grade. On the Test That Counts, the following problem was given.

The correct answer is 11 because you multiply the 4 x 2 and then add the 3, but can you guess which answer most of my students chose? That's right - 14! From that year on, the Order of Operations became a priority in my classroom. Is it a priority in yours? Should it be?

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$3.75

I have a product in my store entitled: Order of Operations - PEMDAS, A New Approach. This ten page resource includes a lesson plan outline for introducing PEMDAS, an easy to understand chart for the students, an explanation of PEMDAS for the student as well as ten practice problems. It is aligned with the fifth grade common core standard of 5.OA.1. Just click on the price under the cover page if it is something you might like.

Adding and Subtracting Positive and Negative Numbers Using a Hands-On Approach

2026-01-28T07:00:00.000-06:00

When it comes to adding and subtracting positive and negative numbers, many students have great difficulty. In reality, it is a very confusing and abstract idea; so, it is important to give the students a concrete visual to assist them in seeing the solution. This idea is based on the Conceptual Development Model which is important to use when introducing new math concepts. As a result, when teaching the concept of adding and subtracting positive and negative numbers, what would fall into each category?

When using the two-sided colored beans, the concrete stage of the Model would be where two-sided colored beans are used as an actual manipulative that can be moved around or manipulated by the students. There are a few rules to remember when using the beans.

The RED beans represent negative numbers.
The WHITE beans represent positive numbers.
One RED bean can eliminate one WHITE bean, and one WHITE bean can cancel out one RED bean.
All problems must be rewritten so that there is only one sign (+ or -) in front of each number.

Sample Problem

1) The student is given the problem - 5 + 2.

2) Since -5 is negative, the student gets out five red beans, and then two white beans because the 2 is positive.

3) Since some of the beans are red and two are white, the student must match one red bean with one white bean. (I tell my students that this is barbaric because the red beans eat the white beans. They love it!)

4) Because three red beans have no partner (they're left over) the answer to – 5 + 2 = - 3. (See example above.)

After mastering the concrete stage of the Conceptual Development Model, the students would move on to the pictorial stage. Sketching a picture of the beans would be considered pictorial. Have students draw circles to represent the beans, leaving the circles that denote positive numbers white and coloring the circles that represent negative numbers red.

As an example, let’s do the problem 3 - +5. First, rewrite the problem as 3 - 5. Now draw three white beans. Draw five more beans and color them red to represent -5. Match one white bean to one red bean. Two red beans are left over; therefore, the answer to 3 - +5 is -2.

3 - +5 = 3 – 5 = -2

When students understand the pictorial stage, then abstract problems such as the ones in textbooks can be presented. (Notice, the textbook is the last place we go for an introduction.) I have found that most of my remedial college students move straight from the concrete stage (beans) to the abstract stage without any problem. Many put away the beans after two or three lessons. What works best for your students as they master this algebraic concept is something you will have to determine.

$5.40

If you would like a resource that gradually goes through these lessons, you can purchase it on Teachers Pay Teachers. It introduces the algebraic concept of adding and subtracting positive and negative numbers and contains several integrated hands-on activities. They include short math lessons with step-by-step instructions on how to use the beans, visual aids and illustrations, four separate and different practice student worksheets with complete answers in addition to detailed explanations for the instructor.

Factoring Polynomials Using a "Sure Fire" Method

2026-01-21T07:00:00.001-06:00

I spent the summer months tutoring a high school girl who was getting ready to take Algebra II. She didn't do very well in Algebra I and with geometry between the two classes, she was lost. Since she is a very concrete, visual person, I knew I needed to come up with different algebraic methods so she could succeed.

When we got to to factoring trinomials, she really needed help as most of the methods were too abstract for her. For those of you who have forgotten, a trinomial is a polynomial that has three terms. Most likely, students start learning how to factor trinomials written in the form ax² + bx + c.

There are several different methods that can be used to factor trinomials. The first is guess and check using ac and grouping. Find two numbers that ADD up to b and MULTIPLY to get ac in ax² + bx + c. The second approach is the box method. You write the equation in a two-by-two box. This method is more thoroughly explained on You Tube. Look up factoring trinomials using the box method. There is also the method of slide and divide which again you can look up on You Tube to see exactly how that works. Grouping is another method. Students need to choose which method they understand and which one works best for them. With continual practice, they will get better and faster at using it.

My favorite method is the one most students understand and grasp. It builds on the ac method, but takes it takes it one step further. It made sense to my student, and she was easily factoring trinomials after only two tutoring sessions.

Because it worked so well, I developed a new math resource. It is a step-by-step guide that teaches how to factor quadratic equations in a straightforward and uncomplicated way. It includes polynomials with common monomial factors, and trinomials with and without 1 as the leading coefficient. Some answers are prime. This simple method does not treat trinomials when a =1 differently since those problems are incorporated with “when a is greater than 1” problems.

Following each explanation (five total) are a set of six practice problems that replicate the method introduced. You might familiarize the students with the method, then assign the problems to practice, OR you might present all four explanations, and then assign the practice problems to review. Some students will catch on rapidly and will not need to go through all of the steps while others will need more repetition and practice. Differentiate your instruction accordingly. Try working in pairs or small groups since students tend to learn from each other.

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$5.25

Included in this resource are the following:

A detailed explanation of this factoring method.
Five variations when using this method
Five sets of practice problems – 30 in total
Two sets of review problems – 12 total
Answers Keys with the complete problem-solving process

Measuring Snow Using a Homemade Math Tool

2026-01-07T07:00:00.011-06:00

I am not a very crafty person; so, I am always looking for items that are easy to make that I can give to my grandchildren. One year, I gave them a snowman making kit that included buttons, a carrot, six rocks and two sticks. This year, I am giving them a Snow Measuring Tool. Not only was it fun to use, but it also helped them to practice using a ruler. Here is how you can make one!

Here is the list of supplies you will need:

1) A paint stick - free at most paint stores
2) A permanent marking pen
3) Something to glue at the top of the stick (You can make it, or be like me and purchase one from a craft store.)

First, using a ruler, mark off every inch along the paint stick. I was able to make nine marks. (Notice I used the plain side of the paint stick and not the side with all of the advertising.) Now write the inches beside each corresponding mark.

When that is completed, glue the item you have chosen at the top of the stick. I really wanted to use a snowflake, but my local craft store didn't have any; so, I settled on using one of Santa's reindeer. Which one, I'm not sure since it didn't come with a name.(Hint: My husband used Gorilla Glue so the reindeer wouldn't fall off.)

When it snows, venture outside and stick the Snow Measuring Tool into the snow and read the number of inches that have fallen. If it isn't exactly on an inch mark, then have your child estimate using fractional parts.

While you are measuring the snow, think about this saying: "Ten inches of snow equals one inch of rain." I am sure you have heard that claim as it is a commonly shared belief that seems to be repeated every time it snows a few feet. But, is the saying true? The immediate answer is: Sometimes.

When the temperature is around 30 degrees, one inch of liquid precipitation (rain) would fall as 10 inches of snow, presuming the storm is all snow. But, the amount of moisture in each snowflake differs depending on the temperature which in turn changes the snow to rain ratio.

For example, if a big January snowstorm occurred with colder temperatures (such as 25 degrees), the snow ratio would be closer to 15 inches of snow to one inch of rain. In fact, weathermen take this into account when forecasting how much snow a location will receive. There have been storms with snow closer to 20 degrees, moving the snow ratio closer to 20 to one. And, when it's warmer, say 35-40 degrees, the ratio moves to 5" of snow to 1" of rain.

So, after your children measure the snow in your yard with their Snow Measuring Tool, try converting the inches of snow into inches of rain based on the 10":1" ratio. By doing so, you may become your neighborhood's weather forecaster or even better, a first rate mathematician!

$3.00

Your children might enjoy this snowman glyph. It's is an excellent winter activity for reading and following directions, and requires problem solving, communication, and data organization.

Reducing Fractions, Finding Fractional Parts and Recognizing Equivalent Fractions with Fraction Riddles

2025-12-17T07:00:00.016-06:00

$14.75

Do you need something besides a “drill and kill” activity to practice fractions and/or percents? This fraction riddle bundle is a 33 page resource that is a fun and engaging way to utilize math concepts while keeping the students actively involved.

Specific words are provided. The students are instructed to figure out the correct fractional part of each particular word. (Example: The first ½ of WENT would be WE. Notice that WE is also 2/4 or 50% of WENT.) If each fractional part is correctly identified, when the students write the fractional parts on the lines provided, a new word is created. Each group of new words becomes a riddle or the answer to a riddle.

It is important that students understand that a fraction and a percent represent the same thing; so, in the Snow Riddles handout, 25%, 50%, 75% and 100% are introduced.

In March Riddles, specific questions are asked to acquaint the students with fun facts about the month of March. April Riddles introduces the students to several interesting historical facts that occurred during this month. There's also Holiday Riddles for December and/or the Christmas season.

For each month, there are between 7-11 word fraction riddles; so, there are numerous ways to practice recognizing fractional parts, understanding equivalent fractions, identifying basic percents (25%, 50%, 75% 100%), and reducing fractions to lowest terms.

Instead of completing all of the monthly riddles in one day, the puzzles may be divided up and used as a focus activity, when a student finishes early, or when there is a short amount of time left before the next class or activity. An individual puzzle may be given each day, or the riddles can be interspersed throughout the week or month. Answers are included at the end of each month’s activities. The complete resource features six months (January, February, March, April, October, December) and contains a total of 49 fraction riddles.

If you prefer, each month of fraction riddles may be purchased separately for $3.00 - $3.25; however, this resource bundles all six months for a discounted price. Just click the title under the cover page shown above, and download the preview to take a quick look at this bundle.

Two Crosswords About Santa and His Reindeer

2025-12-10T07:00:00.001-06:00

The legend of Santa Claus is based on the real-life St. Nicholas, a 4th century bishop in Myra, Turkey. St. Nicholas was known for his love for children and the poor. He has many names, but Santa Claus is his most famous name, and that comes from the Dutch "Sinterklaas" (based on "Saint Nicholas"). He's also known as Father Christmas, Kris Kringle, Christmas Man (in German) and Grandfather Frost (in Russian).

Since he has to cover the whole planet in 31 hours (thanks to time differences) that means Santa's sleigh must go at about 1,800 miles per second. I hope he wears a seatbelt! No one knows for sure exactly where he lives. We know he lives at the North Pole, but that covers a lot of ground. In Nordic legends, he is said to live in a small hill in Lapland, Finland. Quite far from the United States, then!

Here are some interesting numbers (this is a math blog.) If Santa delivered presents to every child on Earth, he would be carrying at least 400,000 tons of presents. Nine reindeer can't pull that much weight (not to mention the sleigh and Santa himself)! In fact, he would need at least 360,000 reindeer. Good luck remembering all those reindeer names!

On Christmas Eve, do you ever wonder where Santa is? Don't worry, you can keep an eye on Santa's progress with GPS! The North American Aerospace Defence Command (NORAD) is the biggest program for this and will show you Santa's progress in several languages.

$2.85

In honor of Santa and his reindeer, I've created two crossword puzzles for the holiday season. The 18 words used in both puzzles are: bed, Blitzen, Christmas Eve, Claus, Comet, Cupid, Dancer, Dasher, Donner, eight, Nicholas, North Pole, Prancer, Rudolph, sleigh, snow, stockings and Vixen. One crossword includes a word bank which makes it easier to solve while the other puzzle does not. Answer keys for both puzzles are included.

These might be fun for the kids to do while they are waiting for Santa to arrive!

Two Bible Crossword Puzzles to Learn About the Birth of Jesus

2025-12-03T07:00:00.003-06:00

$2.85

We may consider the Christmas tradition of reading the Nativity story a given, but after hearing others talk, it often gets overlooked in the hustle and bustle of opening gifts and preparing a big meal. The Christmas Story helps children discover one of the most important stories of all time. Through this story, children come to understand the events leading up to Jesus' birth and this special miracle. It introduces children to the reason why we celebrate this special day, and shares with them the wonderful gift from God.

I am aware there are numerous Christmas activities to choose from and many times, it is difficult to separate the "secular" Christmas activities from the Biblical ones. Maybe you are wondering, "What activity can I use to tell the Christmas Story in a different way?" Try using a crossword puzzle!

I have created two Bible crossword puzzles for Christmas that are specifically designed to review and study the birth of Christ as recorded in the Bible. Both are free form crossword puzzles that feature 25 words with Scripture references. If an answer is unknown, the Bible reference provides a way to find the answer while encouraging the use of the Bible. The words included in both puzzles are Bethlehem, Caesar Augustus, December, east, Egypt, Elizabeth, frankincense, Gabriel, glory, gold, Jesus, Joseph, King Herod, magi, manger, Mary, Merry Christmas, Messiah, myrrh, Nazareth, Quirinius, save, shepherds, star, and terrified.

One crossword includes a word bank which makes it easier to solve while the more challenging one does not. Even though the same words are used for each crossword, each grid is laid out in a different way; so, you have two distinct puzzles. Here are some ways you might use these crosswords.

Pass them out while the children are waiting to open presents. It might change their focus!
Include the adults in the puzzle solving by giving them the crossword without the word bank.
Work with a sibling or cousin or friend to learn the characters of the Christmas story.
Use the crossword with the word bank as a review; then hand out the second puzzle to solve as a way to reflect on what facts about Christmas have been learned.
Offer a small prize to the teams or individuals that get all off the answers correct.

Answers keys for both puzzles are included; so, you don't have to search them out yourself.

Teaching Fractions to Students Who Have No Idea How to Do Them!

2025-11-12T07:00:00.008-06:00

I wish I understood this!

I teach remedial math on the college level, and I find that numerous students are left behind in the mathematical dust if only one strategy is used or introduced when learning fractions. Finding the lowest common denominator, changing denominators, not changing denominators, finding a reciprocal, and reducing to lowest terms are complex issues and often very difficult for many of my students.

I classify my students as mathphobics whose mathematical anxiety is hard to hide. One of my classes entitled, Fractions, Decimals and Percents, is geared for these undergraduates who have never grasped fractions. This article encompasses how I use a different method to teach adding fractions so these students can be successful. Specifically, let's look at adding fractions using the Cross Over Method.

Below is a typical fraction addition problem. After writing the problem on the board, rewrite it with the common denominator of 6.

Procedure:

1) Ask the students if they see any way to multiply and make a 3 using only the numbers in this problem.

2) Now ask if there is a way to multiply and make 2 using just the numbers in the problem.

3) Finally, ask them to find a way to multiply the numbers in the problem to make 6 the denominator.

4) Instruct the students to cross their arms. This is the cross of cross over and means we do this by cross multiplying in the problem.

5) Multiply the 3 and 1, then write the answer in the numerator. *Note: Always start with the right denominator or subtraction will not work.

6) Next multiply the 2 and 1 and write the answer in the numerator. Don’t forget to write the + sign. *Note: One line is drawn under both numbers. This is to prevent the students from adding the denominators (a very common mistake).

7) Now have the students uncross their arms and point to the right using their right hand. This is the over part of cross over. It means to multiply the two denominators and write the product as the new denominator.

8) Add the numerators only to find the correct answer.

9) Reduce to lowest terms when necessary.

$4.75

It is important that students know the divisibility rules for 2, 3, 5, 6, 9 and 10. In this way, they can readily reduce any problem. In addition, it is extremely important that the students physically do the motions while they learn. This not only targets the kinesthetic learner but also gives the students something physical that makes the process easier to remember. The pictures or illustrations for each technique also benefit the visual/spatial learner. Of course, the auditory student listens and learns as you teach each method.

I have found these unconventional techniques are very effective for most of my students. If you find this strategy something you might want to use in your classroom, a resource on how to add, subtract, multiply, and divide fractions is available by clicking the link under the resource cover. A video lesson is included to help you.

Why Doesn't the U.S. Convert to the Metric System?

2025-11-05T07:00:00.004-06:00

Did you know that there are only three nations which do not use the metric system: Myanmar, Liberia and the United States? The U.S. uses two systems of measurement, the customary and the metric. Yes, since our country does use the metric system, we have "given more than an inch, but we haven't gone the whole nine yards".

Today, when we shop for groceries, soda is sold in liters. Medicine is sold in milligrams, food nutrition labels are metric, and what about a 100-meter sprint or a 5K race? Still, we are the only industrialized nation in the world that does not conduct business in metric weights and measures. To be or not to be a metric nation has been a question of great consternation for our country for many years.

Here are some reasons why I think our nation should go to the metric system.

It's the measurement system 96% of the world uses.
It is much easier to do conversions since it is based on units of ten. Water freezes at zero, not 32°, and it boils at 100, not 212°.
Teaching two measurement systems to children is time consuming and confusing.
It is the "official" language of science and medicine.
Its use is necessary when you travel outside of the United States.
Conversion from customary to metric is often fraught with errors. Because the metric system is a decimal system of weights and measures, it is easy to convert between units.
There are fewer measures to learn. Once you learn the meaning of the prefixes, you can easily convert mass, volume and distance measurements. No further conversion factors need to be memorized except the specific power of 10. For the Customary System you have to remember 5280 feet = 1 mile, 4 quarts = 1 gallon, 3 feet = 1 yard, 16 oz. = 1 pound, etc.
And just think, I would have less clutter in my kitchen since I wouldn’t need liquid and dry measuring cups or teaspoons and tablespoons! All I would need is a scale and liquid measuring cups!

So, while most nations use the metric system, the United States still clings to pounds, inches, and feet. Why do you think Americans refuse to convert? I’d be interested in your perspective and ideas.

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$3.00

Get ready to gauge your students' proficiency and equip them for success in all things metric using this pre-assessment metric test. This math test is designed to assess your students' pre-existing knowledge of the metric system. Not only will your students gain a deeper understanding of the differences between metric and customary units of measurement, but with the help of visual examples, they will be able to remember those pesky measurements.