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## A Study of Statistics Through Tootsie Pops

Students construct confidence intervals, write hypothesis tests, and use sampling data to evaluate claims–all by using candy wrappers.

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## The Back Page: My Favorite Lesson: Modeling Exponential Decay

Our favorite lesson, an interactive experiment that models exponential decay, launches with a loud dice roll. This exploration engages students in lively data collection that motivates interest in key components of the Common Core State Standards for Mathematics: functions, modeling, and statistics and probability (CCSSI 2010).

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## The Back Page: My Favorite Lesson: All Knotted Up

Our favorite lesson is a hands-on activity that helps students visually “tie” (pun intended) the concepts of rate of change and y-intercept together in a meaningful context using strings and ropes. Students tie knots in ropes of various thicknesses and then measure the length of the rope as the number of knots increases. We provide clothesline, twine, bungee cord, and other ropes found at local crafts, sporting goods, and home stores. We avoid very thin string, such as thread or knitting yarn, because the knots are small and the string length does not change enough to explore a rate of change. A variety of thicknesses is important because this allows for variability in the rates of change.

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## Students as Mathematics Consultants

Five problems—relating to gas mileage, the national debt, store sales, shipping costs, and fish population—require students to use functions to connect mathematics to the real world.

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## Model-Eliciting Activities for Teaching Mathematics

### research matters for teachers

Teaching about, teaching for, and teaching through problem solving are explored.

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## Solve It!: Suit Up!

### little problems with big solutions

An open-ended problem elicits creative student thinking.

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## Delving Deeper: Differentiated Insurance Contracts

By examining pricing for insurance for a moped, students can explore the theory of systems of inequalities and the topic of distributions in statistics. Fair systems for determining the premium (taking into account cautious and reckless drivers) are considered.

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## Representations and Rafts

Building a rod raft allows students to make mathematical connections among a model, a table, a formula, and a graph.