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.
Related Standards
Related Access Points
Access Points
Related Resources
Formative Assessments
Lesson Plans
Problem-Solving Tasks
Student Center Activity
Tutorials
Video/Audio/Animation
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
When students plot irrational numbers on the number line, it helps reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers. This is a good time for teachers to start using the term "real number line" to emphasize the fact that the number system represented by the number line is the real numbers. When students begin to study complex numbers in high school, they will encounter numbers that are not on the real number line (and are, in fact, on a "number plane"). This task could be used for assessment, or if elaborated a bit, could be used in an instructional setting.
Type: Problem-Solving Task
Students are given a pair of numbers. They are asked to determine which is larger, and then justify their answer. The numbers involved are rational numbers and common irrational numbers, such p and square roots. This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.
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 video, you will practice comparing an irrational number to a percent. First you will try it without a calculator. Then you will check your answer using a calculator.
Type: Tutorial
In this video, you will learn how to approximate a square root to the hundredths place.
Type: Tutorial
In this video, you will practice approximating square roots of numbers that are not perfect squares. You will find the perfect square below and above to approximate the value of the square root between two whole numbers.
Type: Tutorial
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
When students plot irrational numbers on the number line, it helps reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers. This is a good time for teachers to start using the term "real number line" to emphasize the fact that the number system represented by the number line is the real numbers. When students begin to study complex numbers in high school, they will encounter numbers that are not on the real number line (and are, in fact, on a "number plane"). This task could be used for assessment, or if elaborated a bit, could be used in an instructional setting.
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
Students are given a pair of numbers. They are asked to determine which is larger, and then justify their answer. The numbers involved are rational numbers and common irrational numbers, such p and square roots. This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.
Type: Problem-Solving Task