Considering that this resource is apparently not core-aligned and hard to understand for all but the most conversant mathematicians in the class, you should probably limit use to advanced individual reference or reserve it for AP classes focusing on advanced terminology.Continue reading Show less
Mathwords provides easily-to-locate, formal definitions for about 2000 mathematic terms including a few from physics, finance, and modeling. Most definitions contain multiple references to other terms plus either diagrams or examples, but fewer have textual explanations. About 20 terms are accompanied by a dynamic diagram from McGraw-Hill's Geometer's Sketchpad, and 36 terms populate the real-world application list. Terms can be accessed using four search methods: A to Z, full list, subject areas, or Google powered native-and-paid-web-sites search.Continue reading Show less
If you just need a little nudge to remember a concept or term you already knew and understood, Mathwords will be a helpful reference. If you don't already have a really strong foundation, it could be quite frustrating. It seems like kids who can easily understand these definitions wouldn't need to look them up here in the first place. For example, multiple careful readings of the interrelated terms accuracy, precise, and significant digits built some understanding but raised unanswered questions as well. A comparison of two definitions of function, the first from the Common Core Standards, demonstrates the problems inherent in Mathwords's formal and reference-laden approach.
Common Core: "A function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output."
Mathwords: "function: A relation for which each element of the domain corresponds to exactly one element of the range."
You have to look up four other words to understand Mathwords' definition, which is a lot of work. Even with this formal approach intact, expanded definitions with better examples and diagrams would improve learning significantly.Continue reading Show less
Key Standards Supported
Ratios And Proportional Relationships
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1
The Number System
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real- world contexts.