February 2017

• NCTM is excited to offer a featured resource in your grade band this month to help you make the most of your NCTM membership. As we launch our new Classroom Resource Collaboration Center, we'll keep members informed through Summing Up and social media. Check out the #NCTMresources hashtag on Twitter to follow along as we share and discuss these and other NCTM classroom resources.

## Primary

Subitizing, the ability to immediately recognize how many objects are in a small collection, is a skill that underlies a lot of students' early mathematics. Breaking apart numbers, practicing one-digit addition facts, and more can all be supported by subitizing. NCTM's eBook Mathematics for the Curious focuses on math for prekindergarten and kindergarten students. Check out the free preview of the Counting and Cardinality section. The Subitizing with Dot Plates activity (click the owl to download the activity) is a great activity for helping young students subitize and can be extended for older students by including dot patterns up to 10 or even dot patterns arranged in multiple ten-frames. Quick recognition tasks are excellent prompts for mental math practice; hearing different answers to "How did you see the dots? How could you count them?" sets our young students up for seeing mathematical structure in algebra, too.

Did you know that Illuminations has some games that students can play on iPads®, Chromebooks™, tablets, and even their phones? The Factor Game allows students to practice their multiplication and division fact families while strategizing about prime, perfect, abundant, and deficient numbers. In The Factor Game, students take turns selecting numbers from the board. Once students pick a number, their opponent selects all the available factors of that number. Their total points are the sum of all the numbers they have selected. For example, 6 is not such a good selection because 6 has 3, 2, and 1 as its factors and 3 + 2 + 1 = 6. Students and their opponents get the same score! That's why 6 is called a perfect number. The number 12 is an even worse choice. If students pick 12 on their first turn, their opponent gets 1, 2, 3, 4, and 6; 1 + 2 + 3 + 4 + 6 = 16. That's why 12 is called a deficient number. Abundant numbers are the key to winning The Factor Game. Can your students find the best moves? If they enjoy playing against the computer, they might also like to play Factor Dazzle against other students on NCTM's Calculation Nation.

Have your students been to see the movie Hidden Figures? If they are wondering what it might have been like to be a human computer, the "Space Shuttle" Illuminations lesson about distance, rate, and time in the vastness of space may appeal to them. Students get a chance to practice working with very large numbers and to look for patterns in calculations that help them simplify their work while remaining accurate. Challenge your students to be like Katherine Johnson, the physicist and mathematician who worked with NASA and who is honored in Hidden Figures. She and her fellow mathematicians used their deep knowledge of math and their ability to "see beyond the numbers" to carry out complicated calculations accurately, even when there were a lot of problems to do and very little time.

## Algebra 1

Are any of your students planning to buy Valentine's Day chocolates for a friend, parent, or sweetheart? Then they will be interested in the sweet Name Letters puzzle from NCTM's Illuminations. As students try to figure out the cost of each individual chocolate letter based on the price of certain names, they are exploring concepts related to solving algebraic equations and systems of equations. However, they usually just think they're solving a delicious puzzle! The interactive tool is an additional fun component if students have computer access. They can use the tool to check their solutions by seeing if they got the right value for their own name (or the name of their Valentine, or any other name they choose). In classrooms with only one computer, the class can work together to generate values to check, or students can check a name as an "exit ticket" to demonstrate that they've solved the problem.

## Geometry

In February, many geometry curricula are introducing students to the Power Theorems (Chord-Chord, Secant-Secant, and Tangent-Secant). The "Power of Points" lesson from NCTM's Illuminations introduces these theorems as a single, unified theorem, the Power of Points theorem. Students use technology to conjecture about the value of certain products in different cases (if point P is in, on, or outside of the circle). They then use their conjectures to find unknown values in several different cases and to answer the launch question: Where is the optimal location for a soccer player to take a shot on the goal? Studying the single Power of Points theorem means that students don't feel that they have three theorems to memorize, and supporting students to discover and discuss the different cases helps them notice, pay attention to, and remember the differences in the calculations depending on the location of point P (one of the challenging parts of the Power Theorems).

## Algebra II/Pre-Calculus

What do your students understand about functions? How might they do with a scenario in which distance is a function of something other than time? Can your students put co-variation into words? Can they sketch a graph of a scenario? The article "Investigating Functions with a Ferris Wheel" from the December/January issue of Mathematics Teacher describes what happens when a teacher, a researcher, and a mathematician asked high school students to graph and describe the relationships between the height of a car on a Ferris wheel and the distance the car had traveled. The article includes an interactive animated Ferris wheel for students to search on their own or investigate as a class. The tool can be used to explore nonlinear functions, co-variation and function notation, and trigonometric functions.

## Probability and Statistics

This month's featured resource comes from Mathematics Teacher's "Technology Tips" department. In October, the featured technology was Tuva Labs, a website that allows students to look at freely available data sets using the power of TinkerPlots™, without having to download or purchase any software. "Promoting Statistical Literacy through Tuva" explains how the author used the Tuva website to investigate gender bias in college admissions with her students. The article then walks readers through how to set up a Tuva Labs account, use the built-in data, and get students online exploring different representations and using real data to make convincing arguments about the world around them.

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.