May 2017

• For many U.S. classrooms, May is a tricky time of year. Teachers are balancing crazy end-of-year schedules, from testing to field trips to ceremonies, coupled with the potential distraction of warm weather and summer break. It’s a great time of year for activities that are tried and true, that get students engaged and active. That’s why we’re going to the mailbag for this month’s featured resources to shine a spotlight on some activities that members have enjoyed using and let them tell you why.

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Check out the #NCTMresources hashtag on Twitter to follow along as we share and discuss these and other NCTM classroom resources.

## Primary

Justina Cross, an early-years teacher in Northern Territories Australia, wrote to us about an Illuminations applet she loves: Displaying Number Patterns. Because this is an older Illuminations tool that accesses Java, you’ll need to use Safari or Internet Explorer to display it and add http://illuminations.nctm.org to Java’s security exceptions ( here are instructions). What Cross loves about this tool is that it lets her show very young mathematicians how to connect skip counting, number recognition, and the hundred chart. "I use it with five-year-olds. They can 'punch in' the number on the calculator and then see it appear on the 100 chart.” Cross goes on to explain that if they are counting by 2s, she can ask students to punch in the number 2, then ask another student, "Can you tell me what is 2 more?" When the answer comes back, "Four, Miss Cross," she can then ask another student, "Can you punch in the number 4?" and on it goes. This activity, according to Cross, "provides an opportunity for the child to demonstrate they know how to read and punch in numbers from 1–100."

If you are more focused on patterns and skip counting than reading and punching in numbers, you may also like the newer version of the same applet, which works on more browsers. In this version, players choose a starting number and an operation and hit the "=" button to repeatedly apply the operation to the starting value. The hundred chart visually displays the skip-counting pattern.

May is a great time of year for hands-on modeling and design projects that get middle school students making and testing hypotheses and building and rebuilding until they find the optimal design. Maybe that’s why Fawn Nguyen’s "Hotel Snap" task, in which students build "hotels" out of multifix cubes and try to maximize profit while minimizing taxes paid, always gets shared on Twitter this time of year. Students may not realize that they are practicing percentage calculations and arithmetic skills, becoming more proficient at using tables to organize their data, and making connections between surface area and volume. They might just think that they are building cool towers, winning competitions, and learning how to make a profit in the hotel industry. But you will know that there’s lots of mathematical practices happening while students are having fun.

Note: This month’s Featured Resource for Grades 3–5, Equivalent Fractions, was also recommended for grades 6–8 students who are learning about fraction addition and subtraction and connecting fractions to percentages and decimals.

## Algebra II/Pre-Calculus

Lois Burke, a high school math teacher in Virginia, had a former algebra 2 student who currently writes the Monthly Featured Resources feature for NCTM. Last week, she shared on Facebook that she was doing an activity with her students that this author still remembers from his algebra 2 class. He was fascinated to learn that the antibiotics that Burke was taking would stay in her body forever, although every day her kidneys were processing and removing a percentage of the remaining antibiotic. This lesson, which is still making students in Virginia say, “Whoa!” is available through NCTM’s Illuminations. In the Drug Filtering lesson, colored water in pitchers represents the antibiotic in the blood, and students have an opportunity to connect a real-life situation (using antibiotics) to a physical model (seeing colored water) and a mathematical model (calculating exponential decay).

## Probability and Statistics

An assets manager working at a leading global investment management firm contacted Illuminations for permission to use the State Data Map with her clients. She plans to use the feature, which allows users to type in their own data, to show clients at a glance the states in which they hold the most assets. Many students in statistics classes are doing projects at this time of year. Do you know about Illuminations’ different tools for displaying data? Data Grapher and Advanced Data Grapher allow students to construct many different kinds of data displays and use screenshots or the print feature to add their displays to any project. Students can enter their own data from a URL or use data provided by Illuminations. Canadians, we have your acreage covered: Illuminations also has a Provinces and Territories Data Map.

Shana Frank wrote to Illuminations to let us know how well the Equivalent Fractions tool worked for the student she was tutoring. She wrote that the app worked "beautifully" on many different levels. "Students can investigate and visualize important mathematical concepts and relationships." She went on to say that she especially liked cross-referencing the square or circle model with the number line, the horizontal and vertical sliders on the square to show area models, the equivalent fractions table, and the build-your-own option. She then made some specific suggestions for using the app: "As I was working with my student, I realized that it helps to be systematic about representing the fractions to highlight where the equivalent fractions come from. Let’s use 1/6 + 3/4 as an example, so the lowest common denominator is 12.

"To show that 1/6 = 2/12, start by selecting Build Your Own - New Fraction and use the Square Model. Move the horizontal slider or vertical slider in the top square to 6, so there are 6 columns or 6 rows. Color one of the columns or rows.

"Then set up a lower square the same way with either 6 columns or 6 rows. Now move the other slider to 2 to get a 6 x 2 grid with 12 rectangles. This way the scale factor of 2 is clearly represented on the second axis. Color 2 rectangles to show the equivalence."

She also let us know what her student liked about the app: watching the value of the fraction on the number line approach the target as he colored in parts of the fraction and getting to be creative in how he colored them in. Here’s one he made just for fun. Can you tell what fraction of the total squares he has shaded?

## Algebra 1

Natalie Perez shared on Twitter that she worked on Barbie Bungee with her class last week. It’s a great way to apply many of the concepts learned in algebra 1, she said, and it gets students up and about building, experimenting, modeling, and using math to give Barbie the longest ride possible that will not end in disaster. Perez and her students made a video (with the perfect soundtrack) to document their project; she was even brave enough to strap her phone to a Barbie to get footage from Barbie’s point of view!

## Geometry

Wednesday nights on Twitter at 9 p.m. Eastern Time, you’ll find NCTM journal Twitter chats. At the most recent Twitter chat for Mathematics Teacher ( #MTchat), the topic was proofs without words and the article discussed was "Proofs without Words in Geometry." Geometry teachers from across the country shared the different ways they’ve used proofs without words, from having students put words to someone else’s proofs to allowing students to create a visual version of their proofs as a “prewrite” task. Then they discussed the main idea of the article: creating a series of images on cards that students can arrange into a flowchart proof. Participants felt that having students sequence cards to create a proof without words would help students understand proof and make thoughtful choices about when and why to use specific theorems they’ve learned. You can also read the chat via Storify.

Be sure to also check out these additional resources and tools for your classroom.

## Math Forum - Problems of the Week

Get your weekly dose of math problems and puzzles from the Math Forum. You will also find more math resources and tools, as well as a Math Forum: Problems of the Week Blog, furthering discussion.

## Brain Teasers

Want quick ideas for great back-to-school icebreaker classroom activities? We've got you covered. Challenge your new students and mathematics enthusiasts alike with these staff-picked puzzles. In need of more? Browse the entire Illuminations library and discover what's in store in this amazing resource.