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# 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,…

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### 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…

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### 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 —…

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### 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…

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### 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…

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### 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…

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### 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…

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### 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…

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### Lesson 3: Proportional Relationships

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…

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### Lesson 2: Proportional relationships

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…

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