**Subject Area:**Mathematics

**Grade:**8

**Domain-Subdomain:**The Number System

**Cluster:**Level 1: Recall

**Cluster:**Know that there are numbers that are not rational, and approximate them by rational numbers. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**Assessment Limits :**

All irrational numbers may be used, excluding ??. Only rational numbers with repeating decimal expansions up to thousandths may be used.**Calculator :**No

**Context :**No context

**Test Item #:**Sample Item 1**Question:**Select all numbers that are irrational.

**Difficulty:**N/A**Type:**MS: Multiselect

**Test Item #:**Sample Item 2**Question:**Which number is irrational?

**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 3**Question:**What is written as a fraction?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 4**Question:**Determine whether each number is rational or irrational.

**Difficulty:**N/A**Type:**MI: Matching Item

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Formative Assessments

## Lesson Plans

## Problem-Solving Tasks

## Student Center Activity

## Tutorials

## Video/Audio/Animation

## MFAS Formative Assessments

Students are given several terminating and repeating decimals and asked to convert them to fractions.

Students are given a fraction to convert to a decimal and are asked to determine if the decimal repeats.

Students are asked to identify rational numbers from a list of real numbers, explain how to identify rational numbers, and to identify the number system that contains numbers that are not rational.

## Student Resources

## Problem-Solving Tasks

This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.

Type: Problem-Solving Task

By definition, the square root of a number *n* is the number you square to get *n*. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Type: Problem-Solving Task

MAFS.8.NS.1.1 requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of choice of representation. For example, 0.333¯ and 13 are two different ways of representing the same number.

Type: Problem-Solving Task

The task assumes that students are able to express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "8.NS Converting Decimal Representations of Rational Numbers to Fraction Representations."

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

In this tutorial, you will practice classifying numbers as whole numbers, integers, rational numbers, and irrational numbers.

Type: Tutorial

Students will learn the difference between rational and irrational numbers.

Type: Tutorial

Students will learn how to convert a fraction into a repeating decimal. Students should know how to use long division before starting this tutorial.

Type: Tutorial

## Video/Audio/Animation

Although the Greeks initially thought all numeric quantities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this?

Type: Video/Audio/Animation

## Parent Resources

## Problem-Solving Tasks

This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.

Type: Problem-Solving Task

By definition, the square root of a number *n* is the number you square to get *n*. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Type: Problem-Solving Task

MAFS.8.NS.1.1 requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of choice of representation. For example, 0.333¯ and 13 are two different ways of representing the same number.

Type: Problem-Solving Task

The task assumes that students are able to express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "8.NS Converting Decimal Representations of Rational Numbers to Fraction Representations."

Type: Problem-Solving Task

In this task, students explore some important mathematical implications of using a calculator. Specifically, they experiment with the approximation of common irrational numbers such as pi (π) and the square root of 2 (√2) and discover how to properly use the calculator for best accuracy. Other related activities involve converting fractions to decimal form and a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

Type: Problem-Solving Task