Posted by David Wetzel
Playing “War” with a deck of cards now has whole new meaning - helping students understand math operations concepts.
This card game helps students develop the ability to apply math concepts in a way that no 100’s of worksheets or 100’s of extra homework problems could ever help.
The basic procedure of turning up one card to determine which has the largest card wins. In this new version of “War” Ace’s are removed, Jacks = 11, Queens = 12, and Kings = 13.
Variations of War
Addition War—Players turn up two cards and add, player with the highest sum wins.
Subtraction War—Players turn up two cards and subtract the smaller number from the larger, player with the greatest difference wins.
Product War—Players turn up two cards and multiply, player with greatest product wins.
Fraction War—Players turn up two cards and make a fraction, using the smaller card as the numerator, player with greatest fraction wins.
Improper Fraction War—Players turn up two cards and make a fraction, using the larger card as the numerator, player with the greatest fraction wins.
Integer Addition War—(Black cards are positive numbers; red cards are negative) Players turn up two cards, player with greatest sum wins.
Integer Product War—(Black cards are positive numbers; red cards are negative) Players turn up two cards, player with greatest product wins.
PEMDAS War—Players turn up three cards and use what ever math operations they wish, player with the greatest answer wins. (no exponents available)
Reverse PEMDAS War—Players turn up three cards and use what ever math operations they wish, player with the lowest absolute value wins. (no exponents available)
These are only some of the variations the game of “War” can be adapted to help students develop a greater understanding of math.
____________________
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality”
Albert Einstein (1879 - 1955)
Comments:
Filed Under: Math
Posted by David Wetzel
When students develop the ability to solve pr
oblems either in written or picture form, then they truly understand related mathematical concept or concepts.
The best approach that I used as a teacher, was to provide my students with a problem or the day or problem of the week. Problems of the day were not as complex as problems of the week.
Problems of the day dealt with a specific math concept related to the previous day’s class work or homework.
Problems of the week combined several concepts together to help students make connections between concepts, which is critical to long term understanding.
Sample Problems
Problem 1
A loop of rope is lying on the ground in the position show in the figure below: You are too far away to see which section of the rope is above or below at each of the crossovers at A, B and C.
If we assume that it is equally likely that either section is on top at each crossover, what is the probability that the rope is knotted?
Problem 2
Three intelligent women, Alice, Barb and Carol, sit down to try out a test in logical reasoning. They are so arranged that each can see the color of a label which is either red or blue, attached to the hats worn by the other two but no one of them can see the color of the label attached to her own hat. They are told that at least one of the labels is red. If any one of them can logically deduce the color of the label on her hat, she is to declare it. Carol decides to play this game with her eyes closed, knowing that the other two women have their eyes open. After a little time Carol, who has not seen the label on any of the hats declares her label is red. How can she deduce this?
Problem 3
For this tower of nine squares, determine a line passing through point P that will split the area of the nine squares into two equal parts.
Problem 4
How far is the horizon from the top of a 125.7-meter-high lighthouse? (The earth can be considered spherical with a circumference of 40,000 km.)
Submitting Answers
You can submit your answers to me at drwetzel@science-inquiry.org and I will let you know if it is correct or not.
Additional Resources
12 Tips for Solving Word Problems
Math Problem Solving Stories and Case Studies
Math Teaching Strategies that Challenge Students
Comments:
Filed Under: Math
Posted by David Wetzel
Individual students learn in different ways. When manipulatives are used, their senses are peaked for learning since students can touch and move objects to make visual representations of mathematical concepts.
Manipulatives can be used to represent both numbers and operations of these numbers. In addition to meeting the needs of students who learn best in this way, manipulatives afford the teacher strategies for reinforcing a math concept.
Virtual manipulatives are an additional tool for helping students at all levels of ability to make connections within and between math concepts.
For some students mathematics is just too abstract. These students need visual interactive multiple instructional strategies that combine auditory, visual, and mental activities. They benefit from a combination of visual (i.e., pictures and 2D/3D moveable objects) and verbal representations (i.e., numbers, letters, words) of concepts. This is possible with use of virtual manipulatives.
The ability to combine multiple representations in an interactive virtual environment allows students to manipulate and change the representations. This strategy increases exploration possibilities to internalize concepts, making conjectures between math relationships.
Interactive Virtual Math Resources
Interactive Problem Solving
A Website for Math Learning
Wikis in Math Class
