October 2017

  • In October, we often feel the “click” of a class settling into a groove. Students know the routines, and weeks go by without interruptions for holidays or testing, thus giving you time to focus on teaching and learning. NCTM’s Classroom Resources Committee selected this month’s resources, which focus on the major work of each grade band or course. We hope that you find these resources helpful as your class shifts into high gear.

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    Primary

    "Linking the Van Hiele Theory to Instruction" connects a series of geometric reasoning activities to research on how children learn about shape and geometry. The activities guide students from simply noticing visual attributes of shapes to sorting all shapes with the same attribute, connecting attributes to definitions of shapes, and using Venn diagrams to think about how shapes can have more than one attribute. The lessons culminate with a Scrabble-like game in which children compete to place all their shapes on a Venn diagram.

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    Grades 3-5

    Asking students to write stories to go with number sentences can provide a window into their thinking. Which models of multiplication and division do they rely on? Can they illustrate their story in a way that makes sense? Do they believe that marbles like to eat lollipops? The article "Capturing Children’s Multiplication and Division Stories" includes several examples of actual students’ work to illustrate typical and creative responses.

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    Grades 6-8

    Proportional reasoning, perhaps the most important concept in middle school mathematics, helps build the foundational concepts that students will use to understand linear functions and algebraic reasoning. It also plays a part in helping students understand issues of fairness and whether an outcome is disproportionate or expected. "Social Justice and Proportional Reasoning" describes three contexts in which students can use proportional reasoning to explore complex, real-life issues of social justice.

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    Algebra 1

    The Illuminations Algebra Tiles tool, which has been optimized to run on both computers and tablets (Chromebooks, iPads, etc.), supports using algebra tiles to make sense of a variety of tasks in algebra. Students can use algebra tiles to model substitution, solve equations, expand expressions involving the distributive property, and factor linear and quadratic polynomials. Students can use these virtual manipulatives, a great complement to physical manipulatives, when doing homework. If algebra tiles are not available at your school, consider using this interactive to introduce them to students virtually.

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    Algebra II/Pre-Calculus

    As students deepen their understandings of inverse functions and radical functions, their understanding of square roots and equivalent expressions of the same root needs to deepen as well. The "Stacking Squares" lesson provides a context in which students can use problem solving and sense making to discover equivalent roots and make sense of why, for example, 5√3 is equivalent to √75.

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    Geometry

    Students studied the volume of prisms in middle school, so the "Popcorn, Anyone?" lesson is a great review to build on what students already know while introducing important high school topics such as analyzing different components of a formula to understand how different terms and factors affect the total. The problem can be extended to make popcorn containers with other bases as well, giving students the opportunity to practice area and volume formulas for shapes such as pentagons, hexagons, and octagons, and comparing polygons with increasing numbers of sides to circles.

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    Probability and Statistics

    If you wanted to predict someone’s height and could only make one measurement, which would be best to measure: shoe size, arm span, hand size, or femur length? This intriguing question sets the stage for a lesson on r, the correlation coefficient. The lesson focuses formally on best-fit lines and the meaning of r, or can be adapted to focus informally on how to tell whether one variable is a good predictor for another.

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    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.

    Problems of the Week Samples

    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.

    Sliding Triangle

    Golden Ratio

    Heart Shaped Words

    Browse Illuminations