Notation

Decimals in Word Form: Basics

We’ve been looking at the place value concept, and writing number in expanded form(s); but how about the word form of decimals? This can be confusing at several points. We’ll start with reading a number and writing its word form, and then do the reverse. Reading decimals: the basics We’ll start with this, from 1997: …

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What is Expanded Form?

A concept regularly taught along with place value is “expanded form”, a way to write a number that displays each place separately. As we’ll see, there is considerable variation in terminology here, so parents may have to check what form a teacher wants, rather than look it up and expect a single answer! Whole numbers …

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Place Value: Decimals

Last time we looked at the concept of place value as children first learn it, with whole numbers. Here, we’ll expand that to look at decimals. What do we mean by decimal? First, we need to deal with what the word means, because it is used ambiguously. Here is a question from 2004: Defining Decimal …

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Place Value: Whole Numbers

We’ll be looking at various aspects of place value, starting here with the basic concepts. As soon as you learn to write numbers beyond 10, you have to start understanding this concept; so we have to begin at a concrete level and move gradually to something more abstract. Place value for children Our first question …

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Order of Operations: Trigonometric Functions

(An archive question of the week) Last time we looked at some details that are rarely mentioned in stating the conventions for interpreting algebraic expressions. I couldn’t fit a discussion of the most complicated case: trigonometric functions, which when written without parentheses, as they traditionally have been, can raise several issues. (Much of the same …

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Six Distinguishable People in Four Distinguishable Rooms

(An archive question of the week) Last time we looked at some elementary problems in combinatorics, where we counted the number of ways to choose or arrange elements of a set. Let’s look at a somewhat more complicated problem, which will demonstrate issues that come up in interpreting such a problem and in choosing a …

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Conditional Probability and Multiple Choice

(A new question of the week) A recent question about probability has ties to Venn diagrams, tables, and Bayes’ Theorem.¬†Questions about answering multiple-choice questions are common; this one offers a twist that provided opportunity to discuss several important concepts. Here is the initial question, from August: On a multiple choice question, only one answer is …

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What is Multiplication? How (Not) to Teach It

Last time we looked at the roles of multiplier and multiplicand from several perspectives. This time, I want to focus on one extended discussion about how children should be taught to think of multiplication.