Standard #: MAFS.8.NS.1.2 (Archived Standard)

• Translate between decimal and fraction notation, particularly when the decimals are repeating.
• Create and solve simple linear equations to find the fractional equivalent of a repeating decimal.
• Understand the effect of multiplying a decimal by a power of 10.

Students are asked to find and interpret lower and upper bounds of an irrational expression using a calculator.

Students are asked to plot the square root of eight on three number lines, scaled to progressively more precision.

Students are asked to graph three different irrational numbers on number lines.

Students are asked to estimate the value of several irrational numbers using a calculator and order them on a number line.

Students will use number lines to approximate the square root value of non-perfect square numbers to the tenth place. This lesson supports plotting, comparing, and ordering irrational numbers as well as graphing them on a number line, specifically those in the form of nonperfect square roots.

Students will use their knowledge of perfect squares and square roots to determine a rational number to approximate an irrational number and find their locations on a number line. They will complete an activity that guides them to zoom further into a number line to find more accurate approximations for irrational numbers. They will conclude that between two rational numbers is another rational number and therefore the further the place value in the approximation, the more accurate the location on the number line.

Students will learn to approximate non-perfect square roots as rational numbers. Understanding that irrational numbers can be approximated by rational numbers can assist students and their understanding of the real number system.

This lesson allows students to explore and estimate the values of imperfect squares, using perfect square anchors and number lines as resources. The conversations throughout the lesson will also emphasize that imperfect squares are irrational numbers that must be estimated to compare.

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.

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.

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.

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.

In this video, you will learn how to approximate a square root to the hundredths place.

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.

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.

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.

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.

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.

In this video, you will learn how to approximate a square root to the hundredths place.

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.

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.

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.