Arithmetic

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: …

Decimals in Word Form: Basics Read More »

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 …

What is Expanded Form? Read More »

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 …

Place Value: Decimals Read More »

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 …

Place Value: Whole Numbers Read More »

“Order of Operations” Puzzles

We have often received questions about things called “Order of Operations problems”, or some similar name. Generally, what that means is simply that they are puzzles to give lots of practice evaluating expressions using the order of operations. I have collected a few quite different puzzles in this broad category. A free-form expression We’ll start …

“Order of Operations” Puzzles Read More »

The 24 Game and Kin

We are looking at various mathematical puzzles and games, with a focus on discussing rules and strategies, and then letting you play. Last time we discussed Four Fours, in which we are given a fixed set of “inputs” to a calculation (usually 4, 4, 4, 4), and want to find expressions that yield as many …

The 24 Game and Kin Read More »

Four Fours and Friends

This has been a good time for doing puzzles to stay busy (as a family, or a class, or as distanced friends, for instance). The next few posts will present various mathematical puzzles and games you might enjoy. Although often when a problem I quote was originally left unsolved, I have filled in the gap …

Four Fours and Friends Read More »