Teacher Tune-ups

Teacher Tune-ups are concise explanations prepared for teachers by math experts.

Teachers raise GREAT questions about mathematics! Select from those listed below to read a response from a math educator or mathematician. To recommend an additional Teacher Tune-up, complete the form at the bottom of this page.

Ratio and Proportional Relationships What's the difference between a ratio and a fraction, and why should I care? What are the shortcomings of cross-multiplication? What is unit rate as opposed to rate? Why is "per" so important? How is "scaling" related to proportional relationships?

Number Systems Why is –1 x –1 = 1? Number Line Models for Sums and Differences with Integers Difference, Distance, and the Truth about Absolute Value What are the three basic ways we think of division? Making Sense of Division of Fractions Delaying "Invert and Multiply" Multiplication makes things bigger and division makes things smaller, right? Well, not so fast...

Expressions and Equations The Algebraic Alphabet: Unknowns, Variables, and Parameters How do you generate equations from patterns? Algebraic Terms Sixth and Seventh Graders Encounter What are ways to represent different start points and different speeds? How can focusing on expressions prevent students from rushing to answer-getting? Getting Insight from Graphs

Geometry What is a net? What can you learn from a net? Triangles and Constraints Drawing Triangles: Conventions and Mechanics

Statistics and Probability How should students describe the center and spread of a data set? We use dot plots, histograms, and box plots...which one to use? Probability Basics for Middle-School Teachers Variability and Randomness within Classroom Activities Recording Data: Setting Up the System Using T-Tables to Study Patterns

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