The title of this post is from a conference session at the California Math Council conference at Asilomar in December, 2009. You may download the handout through the following link:

Games and Puzzles that Reach the Kids and Teach the Standards

Here’s the handout with instructions for some activities:

Games and Puzzles that Reach the Kids and Teach the Standards – download file

Puzzles and Games are a great way to build enthusiasm, excitement, and skills in a math classroom. When these are used properly, there is always an underlying mathematical theme that is being explored or reinforced. Students learn the value of logical thinking, proper planning, and long-term focus.

Mathematical games can develop a lot of creativity and number sense in students. Many times a game or puzzle at first looks overwhelming, but becomes manageable after focusing on the key concept. Motivation is almost always inherent in a game or puzzle; this creates conceptual emotion which is a key to successful learning.

Opportunities for transitioning from number sense to algebra thinking abound with puzzles. Number properties show their strength in supporting algebra throughout puzzle activities. It’s always a pleasure to watch the enthusiasm and skills grow in students!

Some of these activities are from Teacher to Teacher Press books:

Simply Great Math Games

Simply Great Math Activities:  Algebra Readiness

Simply Great Math Activities:  Number Sense

Put these activities, puzzles, games, and ideas into regular practice, you will find increased skills and motivation in your students and more joy in your teaching.

Best wishes,

Bill Lombard (a.k.a. Mr. L)

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5. Make Math a Fun Summer Activity – Guest Post by Alexis Montgomery

This is a video introduction to the activity Nuggets and Scales from Brad & Bill’s book Simply Great Math Activities: Algebra Readiness. Teachers can use this video in the classroom as an easy way to introduce unknown quantities, set up and solve linear equations, and incorporate language in the process. This can be used to easily show students a nice transition from a visual representation to the abstract algebra.

The preceding post has a video showing teachers the pedagogical structure of the activity.

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1. Algebra Activities that Reach the Kids and Teach the Standards

Here’s a video introduction to the activity Nuggets and Scales from Brad & Bill’s book Simply Great Math Activities: Algebra Readiness. It shows the teacher the pedagogical structure of the activity. This can be used to easily show students a nice transition from a visual representation to the abstract algebra, as well as incorporating language.

This video will be followed by a video for students that can be used for instruction in the classroom.

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Ask people the following problem, and almost all of them will get it wrong: “If a car goes up a hill at 20 m.p.h. and comes down the same hill at 30 m.p.h., what is the average rate of speed for the whole trip?”

The “obvious” answer is 25 m.p.h., but that would be wrong. Take a quick look at a slideshow of some of the projects my students have done to see some nice explanations of confounding problems like these.

Simply stated, since the car spends more time traveling at the slower speed, this has the effect of reducing the average rate of speed below the average of 20 and 30. The surprising answer to this poser is 24 m.p.h.

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1. Games and Puzzles that Reach the Kids and Teach the Standards

Friday Afternoon Lifesavers are exactly what they sound like: at the end of the week when you and your students are running out of gas, these activities come to the rescue. They are mathematical, engaging, fun, and give the teacher a much-needed break.

Here’s a project that’s good for both algebra and geometry subjects. It has simple directions and teaches students to make accurate measurements and pay attention to symmetry and overall page layout. You can learn how to present the project to your students by viewing this screencast, or simply use  an LCD projector to show your students directly in class. Pause the screencast as needed during construction steps.

Enjoy your projects and your students will thank you when they see how nice their projects look!

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Here’s a sure-fire winner for Pi Day: have your students create Haiku poems about pi, called Pi-ku’s. Students can create one, two, or three Haiku stanzas, as well as a graphic depicting their poem. This is a great way to bring language arts, graphic arts, and mathematics together in one place! My 10th graders are doing this for Pi Day this year, and my 9th graders are creating other artistic works for mathematicians’ favorite day. You can see some of their work from prior years at Mr. L’s Student Project Work.

- From Mr. L – You can view the embedded slideshow above or download my PowerPoint presentation to introduce Pi-ku to your students. This includes several examples so kids can get the idea.

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Friday Afternoon Lifesavers are exactly what they sound like: at the end of the week when you and your students are running out of gas, these activities come to the rescue. They are mathematical, engaging, fun, and give the teacher a much-needed break.

Kids become better problem solvers by solving spatial visualization puzzles. Part 7 of Friday Afternoon Lifesavers featured Twins; it asked students to dissect a figure into two smaller, congruent figures. This activity asks for a subdivision into three congruent parts. Students are given non-standard shapes and asked to divide them into two congruent parts. Kids love this type of challenge; this activity engages all students and gives the teacher the opportunity to circulate the room and give encouragement and advice as needed without student management issues.

This activity provides the teacher the option to teach/reinforce the concepts of congruence and geometric transformations. Also available here are area, distance, angular measure, and perimeter teaching opportunities.

After students solve as many shape puzzles as they can, the teacher has the chance to take them to the next level. Hand out some blank grid paper and encourage them to create their own Triples; the only requirement is that line segments must begin and end on the intersection of two grid lines. By asking them to design these types of puzzles, students can appreciate the skill it takes to create a good puzzle by turning two congruent shapes into a larger shape and “disguising the line of separation.”

The downloadable pdf file includes the Student Puzzle Page, a Solution Page, and a blank grid page.

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Projects are a great way for students to demonstrate their understanding of mathematics in a colorful, artistic way. When using GeoGebra, the open-source Geometry-Algebra-Graphing software, their projects rise to a new height. Many of these projects are as good as those you run across on the internet, and many can be used as instructional aids in the classroom.

Last week my 9th grade classes spent two days in the computer lab creating these projects. Each student signed up for a different parabola, then created its graph using GeoGebra. They were asked to use a font large enough to read when their projects were displayed using an LCD classroom projector, and also to use color to enhance understanding. When they completed the graph in GeoGebra, they exported it to MS Word for final editing. Using Text Boxes in Word they were able to list some of the properties of their parabola. This was a nice project since it required students to learn skills needed to communicate their ideas to others. When done, students printed their projects, my Teacher Aides uploaded them to my Picasa website, and now anyone can view their finished works of art/math. Below is a slideshow of their work.

Projects can be created on computer, or can be made using paper/pencil. The end result is a demonstration of mathematics in an alternative way. I encourage you to give projects a try; your students will surely thank you!

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4. Algebra Activities that Reach the Kids and Teach the Standards

Friday Afternoon Lifesavers are exactly what they sound like: at the end of the week when you and your students are running out of gas, these activities come to the rescue. They are mathematical, engaging, fun, and give the teacher a much-needed break.

One way to help kids become better problem solvers is to pose spatial visualization puzzles like this one. Students are given non-standard shapes and asked to divide them into two congruent parts. Kids love the challenge of finding how to create two identical shapes; this activity engages all students and gives the teacher the opportunity to circulate the room and give encouragement and advice as needed without student management issues.

This activity provides the teacher the option to teach/reinforce the concepts of congruence, line symmetry, and rotational symmetry. Also available here are area, distance, and perimeter teaching opportunities.

After students solve as many shape puzzles as they can, the teacher has the chance to take them to the next level. Hand out some blank grid paper and encourage them to create their own Twins. By asking them to design these types of puzzles, students can appreciate the skill it takes to create a good puzzle by turning two congruent shapes into a larger shape and “disguising the line of separation.”

The downloadable pdf file includes the Student Puzzle Page, a Solution Page, and a blank grid page. Another dissection puzzle can be found at Friday Afternoon Lifesavers, Part 8, Triples.

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1. Games and Puzzles that Reach the Kids and Teach the Standards

Friday Afternoon Lifesavers are exactly what they sound like: at the end of the week when you and your students are running out of gas, these activities come to the rescue. They are mathematical, engaging, fun, and give the teacher a much-needed break.

INTRODUCTION: Hex is a board game played on a grid made of hexagons. It can be played on a board of different sizes; the graphic above shows a typical 11×11 game board in the shape of a rhombus.

HISTORY: The game was invented by the Danish mathematician Piet Hein, who introduced the game in 1942 at the Niels Bohr Institute. It was also independently invented by the mathematician John Nash in 1947 at Princeton University. In 1952 Parker Brothers marketed a version and called their game Hex, as it is known today.

GAME PLAY: Players take turns claiming a hexagon of their color. The goal is to form a connected path of your color linking the opposing sides of the board marked by your colors, before your opponent connects his sides in a similar fashion. The first player to complete his connection wins the game. The four corner hexagons each belong to both players. John Nash proved that the game can never end in a tie. The only way to prevent your opponent from forming a connecting path is to form a path yourself, thereby winning. (N.B. – information edited from wikipedia.org)

From Mr. L – Here’s a downloadable pdf. file with five different size game boards. I’d suggest that beginners start with the 7×7 game board, then work their way up to the 11×11 board as they gain skill and familiarity with the rules and strategy. It’s also a good idea for the teacher to model this on the overhead projector or LCD projector before students play. This is a game of strategy, and there is a lot of learning going on, even though we “can’t see it.” The 1973 movie Paper Chase, starring John Houseman playing a Harvard law professor, has a great line, which I’ll paraphrase. John Houseman is talking to his students, saying: “You will learn the law, but I will train your mind.” This is how I feel in the classroom working with students and also in training seminars working with teachers. Mathematics can be found in books, but how to think about mathematics needs to be taught by a teacher passionate about mathematics.

Some interesting Hex links to investigate (links current as of Feb 2009):
Math Academy Platonic Realms
Mathworld
Thomas Maarup
Hexwiki
Hexwiki printable boards
Cut-the-knot

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