Math Games – Part II

You probably already incorporate games in your teaching. Games are a great way to focus students’ attention as few other teaching strategies can. The ones selected here deal directly with the math content covered in the middle grades. Each has a learning objective; each could be embedded in a lesson plan. Here are a few more games that you can add to your store of games that teach.

Fraction Game
For work on fractions, this applet is a winner! It allows students to individually practice working with relationships among fractions and ways of combining fractions. It helps them visualize what is meant by equivalence of fractions. A link to an applet for two-person play is also given here.

Polygon Capture
This excellent lesson uses a game to review and stimulate conversation about properties of polygons. A player draws two cards, one about the sides of a polygon, such as “All sides are equal,” and one about the angles, such as “Two angles are acute.” The player then captures all the polygons on the table that fit both of the properties. Provided here are handouts of the game cards, the polygons, and the rules of the game.

The Factor Game
A two-player game that immerses students in factors! To play, one person circles a number from 1 to 30 on a gameboard. The second person circles (in a different color) all the proper factors of that number. The roles are switched and play continues until there are no numbers remaining with uncircled factors. The person with the largest total wins. A lesson plan outlines how to help students analyze the best first move in the game, which leads to class discussion of primes and squares as well as abundant and deficient numbers.

Planet Hop
In this online one-person computer game, four planets are shown on a coordinate grid. A player must pass through each on a journey through space. The player must find the coordinates of the four planets and, finally, the equation of the line connecting them. Three levels of difficulty are available. This is one of 12 interactive games created by the Maths File Games Show.

Towers of Hanoi: Algebra (Grades 6-8)
This online version of the Towers of Hanoi puzzle features three spindles and a graduated stack of two to eight discs, a number decided by the player, with the largest disc on the bottom. The player must move all discs from the original spindle to a new spindle in the smallest number of moves possible, while never placing a larger disc on a smaller one. The algebra learning occurs as the player observes the pattern of number of discs to number of moves needed. Generalizing from this pattern, students can answer the question: What if you had 100 discs? The final step is expressing the pattern as a function.

Traffic Jam Activity
Why the jam? There are seven stepping stones and six people. Three stand on the left-hand stones and three on the right-hand; all face center. Everyone must move so that the people on the right and the people on the left pass each other, eventually standing on the side opposite from where they started. But no two people may stand on the same stone at the same time! This problem requires reasoning, but its solution also reveals a pattern that leads to an algebraic expression. A lesson plan is provided.

We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/05/2012.

Fractions: Multiplying and Dividing

Is there anything more difficult to explain at 5th and 6th grade level than the rules for multiplying and dividing fractions? These resources offer support in explaining the concepts that underlie the rules. Visual, interactive models are provided where possible. You will also find opportunities for your students to practice their skills in this area of arithmetic. If you have other approaches to teaching this topic, please share! Just use the comment box below!

Multiplication of Fractions
Visualize and practice multiplying fractions using an area representation. With the “Show Me” option selected, the virtual manipulative is used to graphically demonstrate, explore, and practice multiplying fractions. A rectangular grid, representing a whole, shows the areas of two fractions to be multiplied, one fraction in red on the left and another in blue at the bottom. The area of the overlapping region, shown in purple, represents the product of their multiplication. The “Test Me” option provides problems to be solved using the same graphical representation.

Multiplying Fractions
This tutorial site offers instruction as well as practice in multiplication of fractions. The fractions are modeled with either circles or lines (rectangular areas). The visual display matched with the numerical makes an effective demonstration.

Divide and Conquer
This lesson is based on the idea that middle school students can better understand the procedure for dividing fractions if they analyze division through a sequence of problems. Students start with division of whole numbers, followed by division of a whole number by a unit fraction, division of a whole number by a non-unit fraction, and finally division of a fraction by a fraction. Activity sheets and guiding questions are included.

Dividing Fractions
In this activity, students divide fractions using area models. They can adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. Full access to ExploreLearning is available through an annual subscription, but you can apply for a month’s free access in order to test out the applets.

Fraction Bars
This applet offers a classroom-adaptable idea of how to explain division of fractions. Adjustable colored bars are used to illustrate arithmetic operations with fractions on the number line. The initial seeding shows a division problem, dividing 7/5 by ½.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/08/2011.

Fractions: Adding and Subtracting

As teachers, we all want our students to understand those concepts underpinning addition and subtraction of fractions— the concept of equivalent fractions, in particular. These resources offer teaching ideas on both the concepts and the skills, including demonstrations of addition and subtraction as well as problems for practice. I looked hard for material that would visually or interactively engage middle school students. If you have ideas to share on how you teach these operations, please use the comments area to put them online.

Visual Fractions
An exceptional tutorial on fractions, including step-by-step, illustrated explanations of addition and subtraction. Both circle and line models help students visualize the operations with like and unlike denominators. Interactive problems allow students to use these visual models as they figure the numerical answers.

Adding Fractions
Students must do the usual exercise of finding equivalent fractions with common denominators, but here the fractions are represented visually as portions of a square. Once the computer checks that the fractions are correct, students can drag the representations into a third box and enter the sum of the fractions. This is a real learning experience!

The Fractionator
Created by math teacher Jeff LeMieux, the site offers online and offline tools to help students understand fractions. The online tools use unit squares to model two fractions to be added (or subtracted) and then create equivalent fraction models; with this visual aid, students complete the operation. They can request a new problem for each exercise or enter the two new fractions themselves. Also provided are links to printable materials.

Soccer Shootout
Practice time! Students can practice the addition and subtraction of fractions at levels of difficulty ranging from Easy to Super Brain. Students play against the computer and are provided with a full solution when a wrong answer is entered.

Classic Middle-Grades Problems for the Classroom
The king finds a bowl of mangoes and eats 1/6 of them; the queen eats 1/5 of the remaining mangoes; the prince eats 1/4, etc., until only 3 are left. How many were in the bowl to begin with? A complete lesson plan is given, including activity sheets. A thought-provoking problem to cap this work on fractions!


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/10/2011.

Let’s Talk Teaching: Games in Math Class

In my years of teaching grades 6 through 8, I generally used games only for reviewing before a test. What I didn’t realize was how effective games can be for teaching the content. Each of the games below has a learning objective; each could be embedded in a lesson plan for middle school math. And, as you know, games focus students’ attention as few other teaching strategies can. Use our comment box below to share with other teachers the games you use in class!

Polygon Capture
This excellent lesson uses a game to stimulate conversation about the properties of polygons. A player draws two cards, one about the sides of a polygon, such as “All sides are equal,” and one about the angles, such as “Two angles are acute.” The player then captures all the polygons on the table that fit both of the properties. Provided here are handouts of the game cards, the polygons, and the rules of the game.

Maze Game
This online activity allows the player to practice their point plotting skills by having them move a robot through a mine field to a target location.  Great for learning to visualize coordinates on the Cartesian plane!

The Factor Game
In this two-player game, one person circles a number from 1 to 30 on a game board. The second person circles (in a different color) all the proper factors of that number. When no numbers remain with uncircled factors, the person with the largest total wins. A lesson plan outlines how to help students analyze the best first move in the game, which leads to class discussion of primes and squares as well as abundant and deficient numbers.

Data Picking
In this interactive game, students first create a table using data they collect from the onscreen characters. They then select a scatter plot, a histogram, a line graph, or a pie chart that best represents the data. The amount of data increases and the type of data representation changes according to which of three levels of difficulty is selected.

Fraction Track
Working in two-player competition or individually students practice finding equivalent fractions and ways of combining fractions as they move their pieces across the board. Both sites use applets, but the basic game play can be set up using only paper game boards and chips.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/10/2011.

Speaking in Math Terms

—————————–“Words! Words! Words!” sang Eliza Doolittle in the musical My Fair Lady. “I’m so sick of words!” But students have to master the vocabulary of mathematics. This is especially difficult for those learning a new language even as they struggle with new mathematics vocabulary. The first two resources deal with mathematical terms themselves, while the other three offer classroom activities in Spanish and English.

A Maths Dictionary for Kids
This animated, interactive mathematics dictionary for kids explains over 500 common mathematical terms in simple language. Each term is illustrated and, often, accompanied by an interactive applet that makes visual and immediate the definition of the term.

Terms and Formulas from Beginning Algebra to Calculus
This interactive mathematics dictionary offers many terms and formulas appropriate for older middle school students. The illustrations, diagrams, and applets help define the terms every bit as much as the text does.

Biblioteca Nacional de Manipuladores Virtuales
This is the Spanish equivalent of the National Library of Virtual Manipulatives. Together they offer interactive, web-based virtual manipulatives, mostly in the form of Java applets, for mathematics instruction. On any page, users can easily switch between English and Spanish by using a drop-down menu.

Multicultural Math Fair
Here are ten activities used successfully in a math fair at Frisbie Middle School in Rialto, California. Each activity is available in English and Spanish. Links connect the teacher to information on setting up a fair and locating software.

Who Wants Pizza?/Quien Quiere Pizza?
A fun way to learn about fractions in English and in Spanish. Four activities, each followed by practice exercises, lead students to explore the basic definition of fractions and addition with fractions.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 4/03/2012.