Why does a Negative number times a Negative Number Equal a Positive Number?

Have you ever wondered why a negative number times a negative number equals a positive number? As my mathphobic daughter would say, "No, Mom. Math is something I never think about!" Well, for all of us who tend to be left brained people, the question can be answered by using a pattern. After all, all math is based on patterns!

Let's examine 4 x -2 which means four sets of -2. Using the number line above, start at zero and move left by twos, four times. Voila! The answer is -8. Locate -8 on the number line above.

Now try 3 x -2. Again, begin at zero on the number line, but this time move left by twos, three times. Ta-dah! We arrive at -6. Therefore, 3 x -2 = -6.

On the left is what the mathematical sequence looks like. Moving down the sequence, observe that the farthest left hand column decreases by one each time, while the -2 remains constant. Simultaneously, the right hand answer column increases by 2 each time. Therefore, based on this mathematical pattern, we can conclude that a negative number times a negative number equals a positive number!!!!

Isn't Mathematics Amazing?

Using Math Riddles to Reduce Fractions, Recognize Equivalent Fractions, Identify Basic Percents

Do you need something besides a “drill and kill” activity to practice fractions and/or percents? This fraction riddle bundle is my newest bundled resource. It 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.

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; 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 new item.

  

Math Vocabulary Practice

I have discovered teaching the language of math is significant to teaching math concepts and procedures. Students need to use correct mathematics terminology as vocabulary knowledge provides students with a mathematics foundation they can apply and build on whether they are in or out of the classroom. It really is all about the word, the right words! Since mathematical language is used and understood around the world, conventional mathematics vocabulary gives our students the means of communicating those concepts universally.

With that said, I have discovered that my college students hate learning, reviewing or even practicing math vocabulary. I always begin the semester with a Mathematical Language Activity (see below) in which the students write two paragraphs about how they feel about the math language. You'd be surprised at how much I learn!

Even though my students have vocabulary assignments, and we play vocabulary games, especially before a test, many times they do it begrudgingly. Knowing that most of them like word puzzles, I created several math vocabulary crosswords to use in my classroom. The purpose of these puzzles is to have my students practice, review, recognize and use correct geometric vocabulary. I've made all of the crosswords free-form puzzles with the clues written in the form of definitions. 

Often, I create two different puzzles for the same math vocabulary. The first puzzle is easier as it contains a word bank while the second puzzle does not. Since both puzzles are laid out differently, I can use one as a review and the second one as a homework assignment or maybe even as a quiz.

$2.80

My newest crossword is on circles. Both puzzles feature 18 terms associated with circles. The words showcased in both puzzles are arc, area, chord, circle, circumference, degrees, diameter, equidistant, perimeter, pi, radii, radius, secant, semicircle, tangent and two. 

Also available are crosswords on polygons (includes 16 geometric shapes with an emphasis on quadrilaterals and triangles), plain geometry (features 25 different geometry terms with an emphasis on points, lines, and angles), and solid geometry (emphasizes polyhedrons, circles, and formulas for area, surface area, and volume).

To keep my old gray matter working, I do the paper crossword every Sunday. To many of our students, math is like a puzzle, but maybe they can learn to love figuring out the puzzle by doing these crosswords. Why not give one a try in your classroom?