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## Problem Analysis: Challenging All Learners

Teachers can modify existing materials to meet new curricular goals, reaching learners at all levels.

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## Fielding an After-School Mathematics Lab

Teachers in an urban high school design a learning environment for at-risk mathematics students.

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## The Back Page: My Favorite Lesson: Aunt Sally's Code for Exponents and Logarithms

When I teach the rules for exponents, my students can understand one lesson at a time. But by the end of the chapter, many have the rules all mixed up. The question invariably arises: “Is x 2 · x 3 equal to x 5 or x 6?” We review our discussion from earlier in the unit: x 2 · x 3 = (x · x) · (x · x · x) = x 5. I also take advantage of this teachable moment. The properties for simplifying exponents are connected to the chart displayed on my classroom door. I have written the letters PEMDAS on colored paper and taped them up as a constant reminder of the order of operations (see fig. 1).

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## Making Sense of Logarithms as Counting Divisions

Describe taking a logarithm as repeated division to allow students to build on what they know about division, instead of relying solely on the exponential definition.

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## MT's letters to the editor

found the November/December 2017 issue of Mathematics Teacher more valuable than usual in its content, in particular for its focus and attention on specific interactions between teachers and their students. I also thought that the pairings of authors (such as Fitzpatrick and Dominguez or Madden and Gonzales) was especially powerful.

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## Designing for Voice and Agency

Specific teacher moves and lesson planning can facilitate student empowerment in the middle school classroom.

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## The No-to-Yes Project: Conquering Common Algebraic Mistakes That Drive Us and Our Students Crazy

Help students stop making typical, persistent errors related to misconceptions about exponents, distribution, fraction simplification, and more.

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## Calendar and Solutions – September 2013

A set of problems of many types.

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## Calendar and Solutions – March 2013

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## Calendar and Solutions – August 2014

A set of problems of many types.