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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.
- 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
Formative Assessments
Lesson Plans
In this lesson students will gain an understanding of how repeating decimals are converted into a ratio in the form of 
by completing an exploration worksheet. They will conclude that any number which can be written in this form is called a rational number.
Type: Lesson Plan
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
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 the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.
Type: Problem-Solving Task
The task assumes that students can express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "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
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 the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.
Type: Problem-Solving Task
The task assumes that students can express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "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 (p) and the square root of 2 (v2) 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
