Cracking the Code, Monico Briseno
 We’re always excited to learn where our lessons are being used across the country, and we are always delighted to hear when our international users have found success with our resources! Today, Monico Birseno, a middle school math teacher in Guadalajara, Mexico, shares with us how he uses the lesson Variable Machine in his classroom.
Birseno decided to use and adapt the lesson, Variable Machine, to his classroom to help his students gain a better understanding of algebraic variables. He started by translating the activity sheet, and by creating a Spanish number strip to coincide with the Spanish alphabet.
Birseno’s students were eager to discover the numeric value of their names, and began looking up other words to carry on the lesson further.
“I allowed students to use other classroom textbooks in my class to help them determine different words and their numeric values. It was a good challenge for them,” said Birseno.
Birseno’s was able to build upon the concepts of Variable Machine and in doing so was inspired to use a cipher in his class to further extend the key concepts of math variables.
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Illuminations Down Under, Chelsea Cutting
We are continually amazed as Illuminations reaches an international audience of teachers and students. Chelsea Cutting from Mount Gambier, South Austr alia, tells us about the real-world connections her students are able to make after using Illumination resources.
As a year 3 teacher at Tenison Woods College, she incorporates Illuminations lessons throughout her curriculum, but her students enjoy the online activities the most. She was particularly surprised when a disinterested but particularly bright student approached her during the activity "Concentration."
"He said to me, 'I really like the way I can match the fraction with the picture and percentage. It makes me understand which ones go together—just like in 'real maths,'" said Cutting.
For Cutting, this demonstrated the student’s ability to connect the concepts to real-world contexts, and that an otherwise disinterested student could see a purpose and an enjoyment of mathematics.
Cutting also enjoys using the lesson, "What Comes Nex_?" She uses it as an introduction to a pattern and algebraic reasoning unit.
"I like this lesson because it really gives students' the opportunity to investigate patterns in a range of different contexts while developing students' skills in making conjectures, generalizations, and justifications," said Cutting.
Next year, Cutting will be stepping into a new role as Numeracy Key Teacher. In this position, she hopes to work with teachers to develop and incorporate more of the illuminations resources into the mathematics programs at their junior school.
Kid Tested, Mom Approved, Dana Slevin
Teachers are not the only ones who encourage students to play Calculation Nation--parents do too! Dana Slevin, and her middle school daughters play Calculation Nation at home.
As a parent, Slevin takes an active role in her childrens’ education. She is a member of the PTA, assists with homework and volunteers with the Girl Scouts. But this busy mom has time for one more thing--giving Calculation Nation her seal of approval.
“It’s a great way for kids to have fun with math. They really enjoy playing with kids across the country and enjoy making their own Calculation Nation citizen,” said Slevin. Slam Ball and Ker-Splash are family favorites. She attributes the clean layout and fun colors as a reason why her daughters continue to come back to Calculation Nation for fun learning and games.
The Slevins and all math strategy gamers will love the improvements recently made to Calculation Nation. Students can now safe chat with opponents, register from any country and continue to challenge themselves and others to fun, exciting mathematical games!
Mapping Out the School Year, Jessica Woolard
Jessica Woolard, recent graduate of the Ontario Institute for Studies in Education of the University of Torontoher, spent part of her summer interning for NCTM before she returned to Canada to complete her degree in education. While here, she helped to create and edit lessons for Illuminations. Today we spotlight Where is Everybody?, a fun lesson written by Jessica that compares U.S. and Canadian data using two Illuminations activities
Many great things have come from our neighbors to the north, Blackberry PDA's, IMAX technology, and if you ask any teenage girl, Justin Bieber. "Where Is Everybody?" not only quizzes students on their Canadian trivia knowledge, but also serves as a way for students to work flexibly with decimals, fractions and percents to make comparisons and solve problems. The lesson also utilizes the online Illuminations activities, State Data Map and Canada Data Map.
"My hope in creating this lesson was to enable students to think more critically about data," said Woolard. "Students should also walk away with a better overall awareness of geography and demographics."
Woolard strived to create a lesson that was inline with how she interpreted the Illuminations site, which is as a site that offers a wealth of lesson and applets for exploration, but teachers can take what they like from the lesson and adapt it to their classroom.
"In creating the lesson and questions for students, I wanted to create an opportunity for teachers to allow students to work in groups. Group work can lead to the development of new questions for the class based on the group's results," Woolard said.
During her time at NCTM Woolard also worked to create a couple, other new lessons and also spent her time in the NCTM publications department. Be sure to watch for the rest of her lessons on the Illuminations site soon!
Inspirational Teachers, Illuminations Staff
 Patrick Vennebush, Online Projects Manager, pvennebush@nctm.org
Dr. Hoye taught psychology to high school seniors. In a lesson on how the brain works, he gave us the following puzzle: “There are 64 teams in a single elimination tournament. How many games are needed to determine a champion?” We were allowed to work in pairs. Nathan Horstman, our eventual class valedictorian, and I spent about three minutes working out the solution—there must be 32 games the first round, then 16 games the next round, then 8 games, 4 games, 2 games, and finally the championship. That’s a total of 32 + 16 + 8 + 4 + 2 + 1 = 63 games. We presented our solution to the class. Then Joey Wygant and Troy Snyder—both known more for their athletic, not academic, accomplishments—presented their solution: “There are 64 teams, and 63 teams gotta lose. That’s 63 games.”
Dr. Hoye often asked us to do things in his class, including solving problems and sharing our solutions. His class taught me two important lessons about life. First, I didn’t know everything, and kids who I thought knew nothing actually knew quite a bit. Second, doing things helped me learn more than just reading or listening. Both of those were important lessons that I took with me to the classroom as a teacher, and they’re still important for me now as a parent and project manager.
Throughout my time in high school I had math teachers that encouraged and nurtured my natural love of math. They helped me see the beauty in math—the math beyond computation and only one right answer. I was a math geek, and proud of it. With enthusiasm, I entered college as a math major. Unfortunately, some of the math professors I encountered there focused more on instruction and less on inspiration. Without great teachers, I struggled because my love of math turned to apathy.
Then, in my third semester of college, I had Professor Eduardo Sontag. He re-infused me with what I’d lost. He had passion, so I had passion. He shared his math knowledge along with that passion. Sometimes, he even shared tangential bits of interest, like this new search engine called Google that used some of the same math we were learning to revolutionize internet searching. This was in 1999. Professor Sontag gave me back what I so desperately needed in my math career. It is most certainly in part due to him that I went on to a career in education, not just math.
 Christa Koskosky, Marketing & Communications Coordinator, ckoskosky@nctm.org
Seeing a teacher outside the classroom is often an odd encounter for most students, but for me it was quite commonplace. I saw one math teacher on a particularly regular basis. I saw her grading papers, creating new problems of the day and devoting part of her summer to professional development courses. That woman, I am proud to say, is my mom, the world’s best math teacher!
Although I did not grow up to be the next Mandelbrot, I’ll always appreciate the long nights my mom spent explaining pre-algebra, algebra, and geometry to a weary teenager. And although I absolutely loathed doing math worksheets during my summer break, I came to realize that my mom was only trying to make sure I took full advantage of my education.
My mom made me believe in my math abilities and myself. She was the best role model I could have had growing up—even if I didn’t realize it at the time. And, although I am not a famous mathematician, I think working for some of the most inspiring math teachers is a close second.
Originally Appeared in Bright Ideas 5/13/10
Warming Up with Illuminations, Wan Chow
 Much like an athlete must warm up their muscles before heading into a game, students often warm-up with engaging classroom activities or problems of the day before diving into the daily math lesson. Wan Chow of Bishop Strachtan School in Toronto finds the perfect warm-up in Illuminations.
“I use Krypto as a 5-minute warm-up, partner activity when my students are working on an order of operations assignment,” said Chow.
When students work together Chow observes how students discover multiple approaches to reaching the target number, as in Krypto. Chow finds that while she enjoys watching her students work together to discover the answer, she also likes to bring the class back together for a discussion.
“What I enjoy the most is the sharing of students’ strategies on how they reached their answers. Students are able to learn the different methods of approaching the activity from their classmates,” said Chow.
Chow is fairly new to the Illuminations website, as she recently learned about the site from an NCTM e-workshop, but she looks forward to continuing to use lessons and activities in her classroom.
“I have found that activities can be modified. For example, in Decimal Maze I can modify the puzzle to include fractions, integers or square roots.”
Chow hopes that lessons will continue to provide her opportunities to encourage cooperative partner activities in her classroom.
If you would like to participate in an NCTM e-workshop, like Wan Chow, click here. NCTM E-Workshops allow you to connect with math educators around the globe and come away with teaching strategies, classroom activities, and new resources!
Originally Appeared in Bright Ideas 4/7/10
Get Cooking with Illuminations, Matthew Jaques
 Matthew Jaques, ninth and tenth grade teacher for Cathedral High School in Springfield, Massachusetts, discovered Illuminations by way of Bright Ideas and has been using, modifying and creating his own lessons ever since. “I consider Illuminations to be like a good recipe book,” said Jaques. “Any good cook knows the best recipes are the ones that have been tried and tested to perfection.”
Just as any good cook isn’t afraid to add new ingredients to a recipe, Jaques isn’t afraid to modify lessons to fit his classroom. “I’m able to modify the lessons to fit my students, which allows them to connect to the materials in a different, more effective, manner.”
He has seen his students take to the Illuminations lessons, because the lesson apply topics discussed in class in a way that is creative and thought-provoking. Students in his class particularly enjoy being able to use tactile objects to develop their mathematical thinking.
“From a teaching perspective, seeing that ‘a-ha,’ Illumination moment that comes from these lessons is certainly fulfilling.”
One lesson such lesson is Inequalities in Triangles in which students use spaghetti noodles to demonstrate how the sum of two sides of a triangle is always larger than the third. Through this activity, Jaques’ students were able to discover the inequalities for themselves, making them more knowledgeable.
Jaques doesn’t rely solely on Illuminations, though. He also holds an annual golf tournament in his classroom as a way to prepare his students for geometry. In the Mr. Jaques Protractor Mini Golf Classic, students review angle measure estimation as they guess the angle and distance it would take to make a shot.
In the future, Jaques will continue to develop his own lessons and looks forward to integrating Illumination lessons that allow students to use technology.
Discover Matthew Jaques Protractor Lesson here (PDF). Also, check out the article “Reflections on Miniature Golf” that appeared in The Mathematics Teacher, October 1994.
Originally Appeared in Bright Ideas 3/10/10
Barbie Badge of Honor, Beth Anthony
“Students love throwing Barbie off the side of a wall outside our school,” said Beth Anthony, 7th grade teacher at Lexington Middle School. “Students dangle their doll through the hallways, and they are sure everyone else in school is jealous of them.” Anthony incorporates Illuminations lessons into her curriculum, but she also expands, tweaks and creates new materials to ensure these lessons are meeting the needs of her students.
“I have collected several kinds of dolls now [for Barbie Bungee], and I will have students compare data and graphs of lighter and heavier dolls,” said Anthony.
This lesson affords Anthony the opportunity to bring her students into the computer lab to track their data. It also allows her the chance to introduce her students to Excel as a means to organize their information.
“My favorite part is seeing those smiles when student guesses for best fit lines are almost perfect with the computer models!” Anthony has also incorporated the lesson Paper Pool into her classroom, and has expanded on the lesson by creating a pentagon-shaped organizing poster. Anthony references the poster throughout the lesson as a way to draw connections between pictorial representations and algebraic formulas.
“Students really enjoy using the Paper Pool tool. It served as a good intro for beginning to generalize patterns, as well as, helping students take intellectual risks in a safe way,” said Anthony.
Anthony has a student who struggles with writing, but with the aid of the Paper Pool tool, he was able to explain what would happen with pool tables of various dimensions and have his ideas proven quickly.
Now that she has found success with two lessons and more, Anthony continues to look for Illuminations resources that “will be exciting enough to capture the attention of my active, busy students.”
Big Math and Fries , Michael Weingarden
 Losing weight is a popular New Year’s resolution. Some people turn to exercise to help them achieve this goal, but one teacher wonders if it’s possible to keep this resolution while following a diet of fast food.
Michael Weingarden, algebra teacher at Newbury Park High School and 2009 Illuminations Summer Institute participant, challenges his students to discover if it’s possible to follow the Zone Diet while only eating items from the McDonald's menu.
“Calorie counting can be confusing because one gram of fat does not have the same number of calories as a gram of protein or carbohydrates,” said Weingarden. “When you look at the quantity of nutrients in food, the percentage of fat is not always obvious.”
Weingarden created the lesson, Big Math and Fries, while participating in the 2009 Illuminations Summer Institute. The lesson was based on the successes he found in the book, The Zone Diet. He was given the book as a gift and was drawn to the diet because of the math proportions it presented.
“It’s definitely a popular lesson with my students, because of the real world applications,” said Weingarden. It’s not surprising that a former engineer and designer of the Rat Zapper, a humane rat trap, likes to bring applications into his classroom.
Weingarden often draws on contemporary examples in his classroom by creating several lessons with everyday applications—including another lesson he developed at the summer institute, “Too Hot to Handle,” which allows students to explore asymptotes and exponential decay while investigating how fast a hot liquid cools.
Not Just for Math Teachers, Terry Johanson
 Illuminations reaches a wide audience of math teachers, spanning from prekindergarten to high school and from teachers in the United States to those abroad, but now it's being used in science classrooms, too.
Terry Johanson, learning support facilitator for Prairie Spirit School Division, and Kirsten Dyck, physics teacher at Saskatchewan High School, worked together to team plan and teach an Illuminations lesson.
The Illuminations lesson, Varying Motion, created by Johnanson when she participated in the 2008 Illuminations Summer Institute, allowed Dyck’s students to explore simple and complex ideas with a hands-on approach.
“I found that my students ‘got it’,” said Dyck. “They came away from the lesson with a deep understanding of the relationships among displacement, velocity and acceleration throughout this hands-on inquiry.”
Students were happy to have an out-of-the-desk activity that they could apply mathematical ideas to, and they liked the fact that the knowledge built on itself, progressing logically from simple to complex ideas.
Varying Motion also provided not just one day of instruction, but it progressed to more than seven hours of class experiences and was the springboard for approximately 90% of Dyck’s unit content.
“I will definitely continue to see what other Illuminations lessons fit my physics curriculum,” Dyck said. “The detailed lessons give me enough information so I can tailor it to fit my classroom needs.”
As for Johanson, she will continue to encourage teachers to use Illuminations. She feels the lessons fit with the emphasis that specific school divisions, schools, and teachers have chosen.
Originally Appeared in Bright Ideas 11/12/09
Love at First Site, Victoria Miles
 It has often been said that love happens when you least expect it, and now the same can be said for finding math resources. Victoria Miles, 7th grade math teacher at Abigail Adams Middle School, came upon Illuminations after a Google search directed her to the site.
“I was looking for an interactive tool to enhance instruction for volume of prisms. I did a Google search and found the Illumination Cubes applet,” said Miles.
Miles strives to incorporate technology into her classroom whenever possible, and now regularly uses Illuminations tools to help actively engage her students. She also has created activity sheets to accompany student exploration for each Illuminations tool.
“My students are actively engaged when they work on applets. After students explore mathematics using technology, I have noticed more students participating in classroom discussion,” said Miles.
Miles brought her insights to the 2009 Illuminations Summer Institute in which she and several other exceptional teachers worked to develop new lessons for the site. Miles worked diligently to bring her tessellations tool from a dream to reality.
“I really wanted a tessellation tool that could do it all: copy, clone, and use shapes from polygons to dodecagons,” said Miles. “This new tessellations tool has everything I wanted for construction and exploration of the concept.”
Students can now explore tessellations using the friendly, easy-to-use Tessellations Creator suggested by Miles and built by Illuminations. Moving forward, Miles hopes to incorporate new Illuminations lessons to help her students in areas where they may be struggling. She will also continue to spread the love, as she works with colleagues, as they share ideas for bringing technology into their classrooms using Illuminations.
Originally Appeared in Bright Ideas 10/7/09
Binding Success, Cindy Stofferahn
 Imagine having your whole year planned out before stepping foot in your classroom. Cindy Stofferahn, third grade teacher at Sturgis Elementary School in South Dakota, already knows what she is teaching today, tomorrow and for the rest of the year.
Stofferahn, with the assistance of another teacher, created a binder filled with Illuminations lessons from which she will teach throughout the school year. “I am confident the lessons I am teaching from are beneficial to student learning, because the lessons are inquiry-based and follow the standards I need to teach,” said Stofferahn.
Stofferahn has applied the lessons to promote student learning across grade levels, as first and third graders worked to complete the lesson As People Get Older, They Get Taller. Stofferahn and a fellow teacher brought their classes together in order to gather data and chart their results.
The teachers observed that student pairs helped one another throughout the lesson, and coming together allowed older students to actively engage younger students and deepen their learning. “Students were working in groups and supporting each other in their learning,” said Stofferahn. “They were openly discussing the lesson. ”
Moving forward, Stofferahn plans to continue to use Illuminations lessons that align with the South Dakota third‑grade standards. She encourages her colleagues to use Illuminations as well, because it can often times support the textbook material and—simply put—because it’s free.
Originally Appeared in Bright Ideas 9/9/09
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Julia Zurkovsky, Content Coordinator, 
