December 2016

• 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

Kindergarten teacher Varnelle Moore created a series of primary-level lesson plans for the Math Forum that focus on using multiple modalities to explore a key concept: manipulatives, technology, and paper and pencil. The lessons also include literature connections. Varnelle's Introduction to Fractions web unit focuses on the connection between fractions and geometric reasoning emphasized in the K-2 geometry Common Core standards. In these brief, hands-on lessons, students share cookies fairly, make gator pie, explore sections of citrus fruit, and play with virtual manipulatives, all while learning how to talk about and write about fractional quantities.

Solar energy is a hot topic these days... and in the "Collecting the Rays" lesson from NCTM's Illuminations, it's literally a hot topic. In this lesson plan, students are challenged to make a box out of cardstock that they think will best warm up 36 cubic inches of air. Not only do students reason about volume and dimensions as they come up with different boxes that will hold exactly 36 cubic inches of air, but they have to make sense of what properties their different designs will have. This lesson can move students from thinking procedurally about finding three numbers that multiply to 36, to actually visualizing the boxes, as they reason about how to design a shallow box with lots of surface area to catch the sun, or a deep box that might hold heat better. In addition, students collect and display data and reason about experiment design, all while learning about how energy can be collected from the sun.

Join us in celebrating the 20th anniversary of the Math Forum's Year Game! Students are challenged to write expressions using only the digits 2, 0, 1, and 7 and all sorts of interesting operations that are equal to every whole number from 1 to 100. With 100 challenges ranging from pretty easy (10 = 2 + 0 + 1 + 7) to probably impossible (most years there have been some values no one can find expressions for), every student can get started and every student can find something to really puzzle over. In addition, the Year Game masterfully reinforces order of operations concepts, as students have to tell the computer what operations to do in what order, all in a single expression. Year Game submissions open on January 1st, but students and teachers can preview the 2017 rules and start working on the printable worksheet with or without the manipulative kits.

## Algebra 1

As an Algebra 1 teacher, I taught students that in order to solve a system of equations with two variables, you needed to have two equations (or two constraints). But I didn't know of any good counter-examples that were accessible to my students where they could experience a situation with three variables and figure out just how far we can get with only two constraints in that context. Enter the Math Forum Problem of the Week, Math Club Mystery (PDF). In this scenario (PDF), students, parents, and teachers all go on a field trip to see the movie. We know how many people went on the trip, the total cost of tickets, and the cost of tickets for adults and students. We are asked to figure out how many parents, how many teachers, and how many students went on the trip. This problem turns out to be an accessible example of a Diophantine equation, as well as a great opportunity to talk about unknowns and constraints, and to compare methods such as making a table vs. graphing vs. writing equations to solve problems. Be sure to check out the Teacher Packet (PDF) to see multiple possible solution paths. A scoring rubric (PDF) is also available.

## Geometry

Grappling with quadrilateral hierarchies is (surprisingly!) challenging for middle- and high-school Geometry students. One reason for that might be because they come to us with some baggage about squares, rectangles, rhombuses, and parallelograms. They've had years to decide for themselves what made something a rectangle, and hearing from us that squares are special rectangles might be challenging a belief they're held for a decade! The Diagonals to Quadrilaterals lesson from NCTM's Illuminations provides a tool and structure for students to come at quadrilateral relationships from the inside out... by considering the properties that quadrilaterals inherit when we specify certain properties of their diagonals. The interactive tool supports students to notice, wonder, and make and test conjectures, and the extension and reflection questions open up even more interesting avenues to explore.

## Algebra II/Pre-Calculus

While we mostly feature content from journal articles, Illuminations, the Math Forum, and other special NCTM projects, NCTM conferences can also be great opportunities for members to find new resources. Michael Pershan and I ( Max Ray-Riek) presented a session called Contexts for Complex Numbers at NCTM's annual meeting in Boston in 2015. Through the online conference planner, you can still access our session description and handouts, which include student worksheets and a link to a Google folder of the complete complex numbers unit that Michael and I designed. If you're curious to learn more about the session itself, it was live blogged by NCTM members Bob Lochel and Ashli Black.

## Probability and Statistics

The teacher notes for Old Faithful (PDF), this month's featured resource from the Reasoning and Sense-Making Task Library provide a sense of the wide range of solutions students could come up with for the challenge of visualizing Old Faithful's eruption wait times – and that's what makes this task so interesting. One of the most important roles of data professionals is figuring out how to visualize data to support effective decision making, and this task gives students a chance to practice the art and science of data visualization using an interesting dataset. In addition, the rich library of examples in the teacher resources gives you options to pull other visualizations your students might not have thought of into the conversation, and perhaps inspire your students to get even more creative!

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.