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.

$3.50

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!

Why Do Christians Celebrate Easter?

For most schools in Kansas, there is no school on Good Friday.  Good Friday is always two days before Easter and commemorates the crucifixion of Jesus Christ and His cruel death on Calvary. Christian theology teaches that Christ's death is the perfect atonement for sins, and as a result, the crucifix, or cross, is one of the fundamental symbols of Christianity.

On Easter, our family will gather at church to celebrate Jesus Christ's resurrection from the dead. The New Testament teaches that the resurrection of Jesus is the foundation of Christianity. It establishes Jesus as the powerful Son of God and as a living Savior because He conquered death through His resurrection. It is a day of joyous celebration when many hymns as well as arrangements of special music and songs of the faith are sung.

In our current culture, I'm not sure what people really know or understand about Easter, especially children. Is it just Easter egg hunts, Easter candy and chocolate Easter bunnies? To find out what my group of girls at church knew, I created an Easter Crossword Puzzle based on the Gospels of Matthew, Mark, Luke and John. 

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The purpose of these two crosswords is to practice, review, and study the true story of Easter. Both feature 25 clues with corresponding Bible references where the answers can be found. The clues are: Judas, darkness, angel, feet, thirty, Peter, Barabbas, two, Jews, Joseph, tomb, stone, Mary Magdalene, thorns, purple, Thomas, resurrection, bread, blood, Gethsemane, three, crucify, Simon, Golgotha and risen. One crossword includes a word bank which makes it easier to solve while the more challenging one does not. Even though the same 25 clues 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 puzzles with your children:

• Use as a review or as an introduction to the true Biblical Easter story.
  
• Work in groups to complete the crossword, using the Bible references to look up the verses.
  
• Use the puzzle with the word bank as a review; then hand out the second puzzle to solve.

Thankful for this holiday and for the grace of Jesus Christ.

Happy Easter!

Let's Celebrate Earth Day on April 22nd.

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.

Is FOIL to difficult for your students? Try Using the Box Method.

I tutored a student this summer who was getting ready to take Algebra II. He is a very visual, concrete person that needs many visuals to help him to succeed in math. We worked quite a bit on multiplying two binomials.

There are three different techniques you can use for multiplying polynomials. You can use the FOIL method, Box Method and the distributive property. The best part about it is that they are all the same, and if done correctly, will render the same answer!

Because most math teachers start with FOIL, I started there. The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product. Inner is for "inside" so those two terms are multiplied—second term of the first binomial and first term of the second). Last is multiplying the last terms of each binomial. My student could keep FOIL in his head, but couldn't quite remember what the letters represented, let alone which numbers to multiply; so, that method was quickly laid aside. 

I next tried the Box Method. Immediately, it made sense to him, and we were off to the races, so to speak. He continually got the right answer, and his confidence level continued to increase. Here is how the Box Method works.

First, you draw a 2 x 2 box. Second, write the binomials, one along the top of the box, and one binomial down the left hand side of the box. Let's assume the binomials are 2x + 4 and x + 3.

          (2x + 4) (x + 3)

Now multiply the top row by x; that is x times 2x and x times +4., writing the answers in the top row of the box, each in its own square.  After that, multiply  everything in the top row by +3, and write those answers in the second row of the box, each in its own square.

Looking at the box, circle the coefficients that have an x. They are located on the diagonal of the box.

To find the answer, write the term in the first square on the top row, add the terms on the diagonal, and write the number in the last square on the bottom row. Voila! You have your answer!

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Terrible at factoring trinomials (polynomials) in algebra? Then try this method which never fails! It is the one most students understand and grasp. This step-by-step guide 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.