April 2017

• This month, we are excited to feature two new treasure troves of resources for NCTM members. Our Activities with Rigor and Coherence (ARCs) have expanded to ten offerings, from counting in kindergarten through revisiting Barbie Bungee in statistics courses. The Math Forum at NCTM is proud to present sixty-two sets of Math Forum Problems of the Week Resources that are free to NCTM members. Each Problem of the Week includes a scenario and a problem based on the scenario, and a teacher packet includes student work, standards alignment, sample solutions, and a problem-solving and communication rubric. Check out the #NCTMresources hashtag on Twitter to follow along as we share and discuss these and other NCTM classroom resources.

## Primary

The "Combinations That Make 10" ARC supports students in recognizing combinations that sum to ten and identifying missing addends in sums to ten. Students use manipulatives, games, and stories across four lessons to explore ways to make ten. Extensions and reflections support teachers to connect making tens to strategies for efficient addition and subtraction. This ARC helps illustrate one of the Teaching Practices from Principles to Actions: Ensuring Mathematical Success for All: "Build procedural fluency from conceptual understanding."

April ushers in Earth Day, which presents an excellent context for elementary mathematicians to explore rectangular garden plots. The Teaching Children Mathematics article "Area Conceptions Sprout on Earth Day" describes a lesson in which children measure and compare the areas of different gardens, each made with the same amount of fencing. Students use craft sticks and paper squares to make sense of the context and develop unique solution methods, which are described in the article. The lesson ends with students planning an indoor garden using craft sticks to mark out the space needed for each seed.

NCTM's Principles to Actions Toolkit contains great resources for coaches and leaders. Did you know that it also has rich tasks and lesson plans for supporting teachers to implement the eight Teaching Practices as well as reflect on their practice? NCTM member and coach AnnMarie Varlotta from Howard County, Maryland, reports that her teachers applaud the quality of "The Case of Mr. Donnelly and the Candy Jar Task" and the detailed lesson plan that illustrates how teachers can effectively orchestrate mathematical discussions.

## Algebra 1

Have your students played factor bingo in Algebra 1 yet? Exploring winning moves in the "Factor Bingo" Math Forum Problem of the Week (PoW) gives students a chance to use multiple strategies to decide whether a particular monomial or binomial is a factor of a given trinomial. The context of matching factors to polynomials can help students who struggle learn to factor directly. It also gives students the opportunity to use number sense to find likely candidates for factors.

## Algebra II/Pre-Calculus

Springtime finds many students wandering in an imaginary world... the world of the complex plane, that is. Robin O'Dell's article, "Not So Complex: Iteration in the Complex Plane," invites students to use Excel to make beautiful artwork based on applying iterative rules of complex multiplication and addition. The striking images provide an interesting context to motivate students to learn the algebra of complex multiplication. O'Dell's article also provides explanations using both polar and rectangular forms of complex numbers.

## Geometry

Given four points on a coordinate plane, how specific can you be about what quadrilateral is formed? "Four Point Puzzle," a Math Forum Problem of the Week (PoW), gives students a chance to apply their knowledge of coordinate geometry and quadrilateral properties. Check out the Teacher Packet PDF to see the wide range of approaches that students can take. Then challenge your students to make sense of and compare approaches that were different from their own.

## Probability and Statistics

You are likely already familiar with the Barbie Bungee activity from NCTM's Illuminations. The "Barbie Bungees Again" ARC encourages students of statistics to find the line of best fit for their data and then analyze their residuals to consider whether a linear model is the best fit for the data. Students also learn about the difference between interpolating and extrapolating and why that distinction might matter to Barbie's safety.

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.