Category Archives: Engineering School Mathematics

Engineering School Mathematics is a blog about writing mathematics curricula. Find out all sorts of “behind the scenes” questions that were debated or discuss in creating the Eureka/Engage NY curriculum!

You can use pictures to explain column addition!

In this video, Autumn shows how to add two large numbers using column addition (The Addition Algorithm). In the process, she explains how column addition works using pictures. Continue reading

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Why should a parallelogram also be a trapezoid? The answer may surprise you.

Find out the real reasons why parallelograms should also be considered trapezoids. Continue reading

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Growing up with Eureka Live: Mathematical reasons for introducing a different solution method

In this video, 7 year old Autumn answers math questions in front of a live audience! Watch her win everyone’s heart. Continue reading

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The Secrets of my Teaching Success: James Tanton

I recently asked James Tanton, “What are some of the secrets for your success as a teacher?” Here’s what he said. Continue reading

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A Quick Comparison of a State Assessment and Eureka Math

We compare types of problems expected on new state assessments with examples from the Eureka Math curriculum. Continue reading

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Remarks on the History of Ratios

What was the definition of ratio used 2400 years ago? Jim Madden expounds on the different definitions of ratio used throughout the centuries. Continue reading

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Ratios, ordered pairs versus points, proportional relationships, and proportions

What are ratios, proportional relationships, and proportions according to the CCSS-M progressions documents, and what is the difference between a point and an ordered pair? Continue reading

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Fluency without Equivocation

What is the difference between fluency and blind memorization, and how does the EngageNY math curriculum achieve automaticity? Read on to find out! Continue reading

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Is it okay to write, “1 inch = 13 feet?” to set up a scale factor?

Why is this statement incorrect in setting up a ratio relationship? Hint: the = symbol. Continue reading

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First grade: Is, “3 girls + 2 boys = 3 kids + 2 kids,” a number sentence?

This statement appears to be perfectly okay, but causes problems due to the precise language of mathematics. Continue reading

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Simple example of Textbook School Mathematics.

An example of Textbook School Mathematics. Continue reading

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What is a variable? Part II: Expressions.

We describe expressions in this continuation of Part I. Continue reading

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What is a proportional relationship?

The Common Core State Standards (CCSS) use the term “proportional relationship” throughout the standards. Fortunately, the standards clearly describe what is meant by that term. Continue reading

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What is a variable? Part I: Symbols.

There are three important types of symbols used in mathematics: constant symbols, placeholder symbols, and operator symbols. Which of the three types is a variable? Continue reading

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What is a quantity?

Well….it makes sense that “3 liters” is a quantity, but what is it really? Learn more by reading this post! Continue reading

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Eradicating Textbook School Mathematics (TSM)

It is apropos to begin this blog with a short discussion of Textbook School Mathematics (or TSM). Continue reading

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