For Students

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,…

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 —…

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…

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…

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…

By Michael Avidon, math editor Graphs: For Students   More in this series Lesson 1. Lesson 2. If you want to help your child, use our version for guardians. Spanish version of this lesson. Performance Expectations (CCSS) This lesson covers the following parts of 7.RP.A.2: Recognize and represent proportional relationships between quantities. a. Decide whether…

By Michael Avidon, math editor Equations: For Students More in this series Lesson 1. Lesson 3. If you want to help your child, use our version for guardians.   Performance Expectations (CCSS) This lesson covers the following parts of 7.RP.A.2: Recognize and represent proportional relationships between quantities. Identify the constant of proportionality (unit rate) in…

By Michael Avidon, math editor Tables and Verbal Descriptions: For Students More in this series Lesson 2. Lesson 3. If you want to help your child, use our version for guardians. Performance Expectations (CCSS) This lesson covers the following parts of 7.RP.A.2: Recognize and represent proportional relationships between quantities. Decide whether two quantities are in…