# Math

### Lesson 2: Approximation of Irrational Numbers

By Michael Avidon, math editor For Students: Performance Expectations (CCSS) This lesson addresses the following Common Core State Standard (CCSS) for Grade 8: 8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example,…

### Summary and Vocabulary of Rational and Irrational Numbers

By Michael Avidon, math editor Vocabulary irrational number: a number that cannot be written as the quotient of two integers lower bound: or under-estimate, is a number that is less than the value of a given expression radical: a square root, cube root, or other root of a number, written with the symbol radicand: the…

### At-home math lesson: irrationality of the square root of 2

By Michael Avidon, math editor How do we know that √2 is irrational? This page provides an indirect proof (also known as a “proof by contradiction”). In general, to give an indirect proof of “Statement A,” you start with the assumption “Statement A is false.” Then you proceed logically until you obtain a contradiction —…

### Lesson 1: Decimal Expansions of Rational Numbers

By Michael Avidon, math editor For Students: Performance Expectations (CCSS) This lesson addresses the following Common Core State Standard (CCSS) for Grade 8: 8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert…

### At-home math lessons: Rational and irrational numbers

By Michael Avidon, math editor For Guardians: Performance Expectations (CCSS) These lessons address the following Common Core State Standards (CCSS) for Grade 8: 8.NS.A.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert…

### At-home lessons: the golden ratio

By Michael Avidon, math editor The ancient Greeks thought that the “most aesthetically pleasing” (nicest looking) rectangle was one whose sides conform to the following proportion: We wish to determine the numerical value of the ratio of the sides. More in this series At-home math lessons: Rational and irrational numbers Decimal expansions of rational numbers…

### Introduction to Probability

By Michael Avidon, math editor For Guardians: Performance Expectations (CCSS) This lesson addresses the following Common Core State Standard (CCSS) for Grade 7: 7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near…

### Introduction to Probability

By Michael Avidon, math editor For Students: Performance Expectations (CCSS) This lesson addresses the following Common Core State Standard (CCSS) for Grade 7: 7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near…