November 2016

• ## Classroom Resource Collaboration Center

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 #NCTM_CRCC hashtag on Twitter to follow along as we share and discuss these and other NCTM classroom resources.

## Primary

One of NCTM’s Eight Teaching Practices is to build procedural fluency from conceptual understanding. Games are a great way to build this fluency, especially when the games are thoughtfully designed, chosen, and sequenced. This Teaching Children Mathematics article presents seven addition and subtraction fluency games in developmental sequence for centers and small group time in primary math classrooms. Look for instructions for and explanations of the concepts behind “High Roller,” “Roll and Total,” “Tens Go Fish,” “Double It,” “Addition Top-It,” “Subtraction Top-It,” and “Salute!”

Thanksgiving, with its emphasis on cooking, presents great opportunities to do math! “ Talking Turkey (PDF)” from the “Problem Solvers” department of Teaching Children Mathematics encourages students to work with fractions, consider whether an answer is reasonable, and justify different answers. Since “Talking Turkey” was featured in “Problem Solvers,” log in to your NCTM accout to get additional stories from teachers (PDF) including implementation tips and student work.

Access and Equity Note: In some families, ham or other foods play as prominent a role as turkey on Thanksgiving tables. Immigrant communities might serve a turkey-based dish or other festive recipe from their own culture. Encourage children to share their own Thanksgiving tradition (being sensitive to children whose families don't celebrate or who are going through hard times that are disrupting their traditions); then explain that the family in "Talking Turkey" is serving a whole turkey as their main course.

Bonus Content: If your students are ready for even more Thanksgiving recipe math, The Math Forum at NCTM's problem "Anthony's Famous Butter Rolls" is a great "side dish" for "Talking Turkey." Check out the story (PDF), our suggested problem (PDF), and Teacher Packet (PDF) with multiple strategies and student work.

Understanding and applying ratio and proportion are key concepts in the middle grades. Scale models and drawings are common applications of proportion. The Math Teaching in the Middle School article “ Exploring Proportional Reasoning through Artwork,” with accompanying student tasks, helps students make deeper connections to both artistic choice and to concepts of proportionality. Artists use proportion both in drawing figures that are larger or smaller than “in real life” and in establishing depth to make figures in a 2-D drawing appear closer or farther away. Students explore both of these applications of proportion simultaneously as they figure out how tall they would be if they were suddenly inside the world of a painting. Students also explore how artists make choices that might subvert the “right” way to draw a figure proportionally for other reasons. The article and More4U resources include an activity sheet for students and access to the paintings from the Barnes Foundation that are discussed in the article.

## Algebra 1

A key concept in Algebra 1 is rate of change. This month’s featured resource, like last month’s, includes a real-world example of a negative slope. We extend the concept further by also including an example of exponential decay, which students can compare to a linear decay model. The authors of the “ How Long Does It Take a Person to Sober Up? Some Mathematics and Science of DUI” article in Mathematics Teacher were inspired by the fact that the number of people killed in alcohol-involved traffic fatalities is equivalent to a large airplane crashing every week. They use mathematics to help students understand how alcohol is processed in the body and why someone may not be ready to drive even hours after drinking. One way to launch this lesson would be to have students make a prediction of the graph of blood-alcohol level over time and how long it takes someone to sober up. Students who have not yet explored exponential functions can simply work with the blood-alcohol level example (which is linear), while students who recognize the general form of the exponential function and can use an exponential regression feature of graphing technology can make similar predictions for the effects of caffeine in the body, and then compare the similarities and differences between the two situations. Students are encouraged to reflect on how the mathematical analysis might help them make choices around caffeine and alcohol in their own lives.

Access and Equity Note: Students may have had experiences with DUI-related injuries or fatalities or with alcohol use and abuse personally or in their families. Giving students a heads-up that the topic of this math lesson is going to be alcohol and drunk driving can help students with related traumas to make a plan for being able to focus on and participate in the lesson (or opt out to a safe space if needed). You might also connect with a guidance counselor or chapter of Mothers Against Destructive Decisions about pairing the lesson with opportunities for students to learn about alcohol abuse and dealing with peer pressure when impaired friends or family want to drive.

## Geometry

In high school geometry, students are challenged to describe all of the rotations and reflections that carry a regular polygon onto itself ( CCSS.MATH.CONTENT.HSG.CO.A.3 ). While students might have a sense that a square has 90º rotational symmetry, it might be harder to call to mind that a square also has 180º and 270º rotational symmetry. The “ Taking a Spin (PDF)” task from the Reasoning and Sense Making Task Library problematizes that understanding and encourages students to think of all of the rotational symmetries of familiar and less familiar polygons through the intriguing question: “Which polygons have 80º rotational symmetry?” This exploration led me to challenge myself to think of a polygon with 79º rotational symmetry. I know of at least one…

## Algebra II/Pre-Calculus

Last month, our featured resource had students using the physics-modeling example of the parabolic path of a horseshoe to explore structure in quadratic expressions. This month, the “ Building ConnectionsIlluminations activity helps them focus further on the relationships between linear factors, x-intercepts, and degrees of polynomials. Students may be wondering why the prime factors of a polynomial are called linear factors and what the relationships are between the lines they represent and the graph of the product function. This investigation gets students exploring that relationship and seeing polynomials from a new perspective.

## Probability and Statistics

Which U.S. state had the most power in determining the outcome of the 2016 election? Students of probability can use their skill at finding permutations and combinations to find out! The Mathematics Teacher article “ Power Indices and U.S. Presidential Elections” gives students an opportunity to dig into some applications of counting principles not covered in a traditional U.S. high-school curriculum by exploring which “swing states” actually have the most power to influence an election. Students could begin by investigating the 2012 election profiled in the original article, comparing the authors’ predictions with the election outcomes, and then discuss how they would update the authors’ assumption to account for the 2016 election where different states were considered to be “in play.” The article also provides an interesting opportunity for students to practice reading mathematics as it would be written up in a professional journal; rather than a teacher presenting the methods for determining a state’s power, students could work together to practice reading professional mathematics writing and checking their understanding of the text.

Access and Equity Note: The election of 2016 is bringing up a lot of strong emotions. Immigrant students as well as Muslim, Latino/a, African American, and female students may feel angry or afraid about rhetoric they have heard in the campaign. Many students may feel disenfranchised or upset about political issues. Give students an opportunity to talk about how they are feeling about the election before diving into its fairness, and try to keep the focus on how they feel rather than debating the merits of candidates. Also let students know of those adults in the school that they can talk to if the election is bringing up traumatic issues.

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.