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A Go Figure Debut for 2022 - A Foreign Language Teacher from New York


Lorraine is also a member of TBOTEMC and has been teaching 32 years. Currently, she teaches Italian 9-12 including AP Italian Language and Culture in a suburban high school on Long Island, New York.  She enjoys teaching her students language and culture. Her certifications include K-12 ENL, French PreK-6, 7-12, Italian PreK-6, 7-12 and Supervision and Administration. (I just had trouble learning French!)

Lorraine describes her classroom as very eclectic. She tries to provide her students with a welcoming environment in which everyone feels comfortable. She also seeks to be consistent regarding structured lessons. Her students enjoy playing Kahoot and bingo games using vocabulary, grammar and culture in the L2.

Lorraine has a daughter in graduate school; so she has time for fun. She likes to swim laps, do yoga or walk on the beach or the beautiful arboretum near her house. She loves to travel but not now since COVID seems to be everywhere.

FREE
Lorraine currently has 904 resources in her Teachers Pay Teachers store called Urbino 12  (Urbino is the renaissance city in Italy where she studied); 47 of them are free for the download. They are of various content for ENL, French, Italian and Spanish K-12. 

Her featured free resource is entitled La Befana Listening. This listening resource has students actively listening to three authentic passages about La Befana in Italy. Students answer specific questions about each passage in English or Italian. Some questions are in English, and others are in Italian so the teacher may pick and choose something suitable for the students in their class. Each passage is approximately three minutes or less in length.

$100.80
Lorraine’s highlighted paid resource is a bundle called AP Italian Bundle. It is essential to help teach your AP students so they will be successful on the exam! The resource contains 35 different resources (that's 201 pages), and you will save 10% by purchasing the bundle instead of the individual resources.

In addition, Lorraine has a blog if you want to check it out.

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This year, My Go Figure Debut will feature TPT sellers that are members of The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC) of which I am a member. TBOTEMC has been in existence since 2014 and is made up of teachers who work together to take their Teachers Pay Teachers stores to the next level. They use the power of cross-promotion to collaborate in their Pinterest, Facebook, and Teacher Talk blog marketing teams. Members advertise their TpT stores, personal blogs, social media sites, or grow their email lists in TBOTEMC’s THREE $100 GIVEAWAYS of TpT Gift Certificates and $100 Amazon & $100 PayPal CA$H Giveaways. The 31+ Back to School, Winter Holiday, Valentine’s Day, End of the Year, and Teacher Talk eBooks continue to promote the members’ TpT stores, TpT products, and social media sites for years to come. For more information on how you can join this group, go to: https://thebestofteacherentrepreneursmarketingcooperative.net/the-best-of-teacher-entrepreneurs-marketing-cooperative-one-year-membership/ 

Never Too Old to Play a Game - Playing Math Games with older students

I currently teach remedial math students on the college level. These are the students who fail to pass the math placement test to enroll in College Algebra - that dreaded class that everyone must pass to graduate. The math curriculum at our community college starts with Basic Math, moves to Fractions, Decimals and Percents, and then to Basic Algebra Concepts. Most of my students are intelligent and want to learn, but they are deeply afraid of math. I refer to them as mathphobics.

We all have this type of student in our classrooms, whether it is middle school, high school, or college. When working with this type of student, it is important to bear in mind how all students learn. I always refer back to the Conceptual Development Model which states that a student must first learn at the concrete stage (use manipulatives) prior to moving to the pictorial stage, and in advance of the abstract level (the book). This means that lessons must include the use of different manipulatives. I use games a great deal because it is an easy way to introduce and use manipulatives without making the student feel like “a little kid.” I can also control the level of mathematical difficulty by varying the rules; thus, customizing the game to meet the instructional objectives my students are learning. However, as with any classroom activity, teachers should monitor and assess the effectiveness of the games.

When using games, other issues to think about are:

1) Excessive competition. The game is to be enjoyable, not a “fight to the death”.

2) Mastery of the mathematical concepts necessary for successful play. Mastery should be at an above average level unless teacher assistance is readily available when needed. A game should not be played if a concept has just been introduced.

3) Difficulty of the rules. If necessary, the rules should be modified or altered in order that the students will do well.

4) Physical requirements (students with special needs). These should be taken into account so that every player has an opportunity to win.

In addition to strengthening content knowledge, math games encourage students to develop such skills as staying on task, cooperating with others, and organization. Games also allow students to review mathematical concepts without the risk of being called “stupid”. Furthermore, students benefit from observing others solve and explain math problems using different strategies.

Games can also….
  1. Pique student interest and participation in math practice and review.
  2. Provide immediate feedback for the teacher. (i.e. Who is still having difficulty with a concept? Who needs verbal assurance? Why is a student continually getting the wrong answer?)
  3. Encourage and engage even the most reluctant student.
  4. Enhance opportunities to respond correctly.
  5. Reinforce or support a positive attitude or viewpoint of mathematics.
  6. Let students test new problem solving strategies without the fear of failing.
  7. Stimulate logical reasoning.
  8. Require critical thinking skills.
  9. Allow the student to use trial and error strategies.
Mathematical games give the learner numerous opportunities to reinforce current knowledge and to try out strategies or techniques without the worry of getting the “wrong” answer. Games provide students of any age with a non-threatening environment for seeing incorrect solutions, not as mistakes, but as steps towards finding the correct mathematical solution.
One math game my students truly enjoy playing is Bug Mania.  It provides motivation for the learner to practice addition, subtraction, and multiplication using positive and negative numbers. The games are simple to individualize since not every pair of students must use the same cubes or have the same objective. Since the goal for each game is determined by the instructor, the time required to play varies. It is always one that my students are anxious to play again and again!

The Beauty of Math Patterns

Some people say mathematics is the science of patterns which I think is a pretty accurate description. Not only do patterns take on many forms, but they occur in every part of mathematics. But then again patterns occur in other disciplines as well. They can be sequential, spatial, temporal, and even linguistic.

Recognizing number patterns is an important problem-solving skill. If you recognize a pattern when looking systematically at specific examples, that pattern can then be used to make things easier when needing a solution to a problem.

Mathematics is especially useful when it helps you to predict or make educated guesses, thus we are able to make many common assumptions based on reoccurring patterns. Let’s look at our first pattern below to see what we can discover.

What can you say about the multiplicand? (the number that is or is to be multiplied by another. In the problem 8 × 32, the multiplicand is 32.) Did you notice it is multiples of 9? What number is missing in the multiplier?
 
Now look at the product or answer. That’s an easy pattern to see! Use a calculator to find out what would happen if you multiplied 12,345,679 by 90, by 99 or by 108? Does another pattern develop or does the pattern end?
 
Here is a similar pattern that uses the multiples of 9. How is the multiplier in this pattern different from the ones in the problems above? Look at the first digit of each answer (it is highlighted). Notice how it increases by 1 each time. Now, observe the last digit of each answer. What pattern do you see there? Using a calculator, determine if the pattern continues or ends.
Recognizing, deciphering and understanding patterns are essential for several reasons. First, it aids in the development of problem solving skills. Secondly, patterns provide a clear understanding of mathematical relationships. Next, the knowledge of patterns is very helpful when transferred into other fields of study such as science or predicting the weather. But more importantly, understanding patterns provides the basis for comprehending Algebra since a major component of solving algebraic problems
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is data analysis which, in turn, is related to the understanding of patterns. Without being able to recognize the development of patterns, the ability to be proficient in Algebra will be limited.

So everywhere you go today, look for patterns. Then think about how that pattern is related to mathematics. Better yet, share the pattern you see by making a comment on this blog posting.

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Check out the resource Pattern Sticks. It might be something you will want to use in your classroom.

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Is Zero An Even or Odd Number?


Is the number zero even or odd?  This was a question asked on the Forum page of Teachers Pay Teachers by an elementary teacher. She stated that Wikipedia had a long page about the parity of zero and that some of the explanation went a little over her head, but basically the gist was that zero is even because it has the properties of an even number. She further stated that before reading this definition, she probably would have said that zero was neither even nor odd.

Here was my reply. Zero is classified as an even number. An integer n is called *even* if there exists an integer m such that n = 2m,  and *odd* if 2m + 1. From this, it is clear that 0 = (2)(0) is even. The reason for this definition is so that we have the property that every integer is either even or odd.

In a simpler format, an even number is a number that is exactly divisible by 2. That means when you divide by two the remainder is zero. You may want your students to review the multiplication facts for 2 and/or other numbers to look for patterns.

2 x 0 =               3 x 0 =
2 x 1 =               3 x 1 =
2 x 2 =               3 x 2 =
2 x 3 =               3 x 3 =

There is always a pattern of the products. Let the students discover these patterns - Even x Even = Even, Even x Odd = Even and vice versa and Odd x Odd = Odd. Since ALL math is based on patterns, seeing patterns in math helps students to understand and remember. Now ask yourself, "Does zero fit this pattern?"

The students can also divide several numbers by 2 (including 0), allowing them to see a second way to conclude that a number is even. (The remainder of the evens is 0, and the remainder of the odds is 1).  Again, "Does zero fit this pattern?"

To demonstrate odds and evens, I like using my hands and fingers since they are always with me. Let's begin with the number two.  I start by having the students make two fists that touch each other. I then have them put one finger up on one hand and one finger up on the other hand. Then the fingers are to make pairs and touch each other. If there are no fingers left over (without a partner), then the number is even.  (See sequence below.)

Let's try the same procedure using the number three. Again, begin with the two fists. (See sequence below.) Alternating the hands, have the students put up one finger on one hand and one finger up on the other hand; then another finger up on the second hand.  Now have the students make pairs of fingers. Oops!  One of the fingers doesn't have a partner, (one is left over); so, the number three is odd. (I like to say, "Odd man out.")   
So, does this work for zero?  If we start with two fists, and put up no fingers then there are no fingers left over.  The fists are the same, making zero even. (see illustration below)

So the next time you are working on odd and even numbers, make it a "hands-on" activity.