This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Place $\sqrt{28}$ on a number line, accurate to one decimal point....

This 8th grade Math parent guide explains the content in straightforward terms so they can support their children’s learning at home and will encourage caretaker engagement with lessons.

Our Teacher Guides are meant to support the use of our online course and unit content. Please use these to accompany the use of our content and for ideas to support struggling learners, those needing extension and for additional resources.

Students classify the different types of numbers we use, and learn how numbers and operations relate to one another. They start with counting numbers and then add integers, rationals, algebraic, and, finally, real numbers to the line.

In CK-12 Middle School Math Concepts Grade 8, the learning content is divided into concepts. Each concept is complete and whole providing focused learning on an indicated objective. Theme-based concepts provide students with experiences that integrate the content of each concept. Students are given opportunities to practice the skills of each concept through real-world situations, examples, guided practice and explore more practice. There are also video links provided to give students an audio/visual way of connecting with the content.

This task is intended for instructional (rather than assessment) purposes, providing an opportunity to discuss technology as it relates to irrational numbers and calculations in general. The task gives a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

For this lesson, students calculate the decimal expansion of pi using basic properties of area. Students estimate the value of expressions such as pi2.

This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.

In this lesson, students place irrational numbers in their approximate locations on a number line.

For this lesson, students know the intuitive reason why every repeating decimal is equal to a fraction. Students convert a decimal expansion that eventually repeats into a fraction. Students know that the decimal expansions of rational numbers repeat eventually. Students understand that irrational numbers are numbers that are not rational. Irrational numbers cannot be represented as a fraction and have infinite decimals that never repeat.

In this lesson, students calculate the decimal expansion of ? using basic properties of area.

In this lesson, students use rational approximation to get the approximate decimal expansion of numbers like ?3 and ?28.

Students know that every number has a decimal expansion (i.e., is equal to a finite or infinite decimal). Students know that when a fraction has a denominator that is the product of 2’s and/or 5’s, it has a finite decimal expansion because the fraction can then be written in an equivalent form with a denominator that is a power of 10.

Grade 8 Module 7: Introduction to Irrational Numbers Using Geometry. Contains 23 Lessons.

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.

For this lesson, students know that the long division algorithm is the basic skill to get division-with-remainder and the decimal expansion of a number in general. Students know why digits repeat in terms of the algorithm. Students know that every rational number has a decimal expansion that repeats eventually.

With this assignment, students locate and identify irrational numbers at the approximate location on a number line. Students will also compare and/or order any real numbers (rational and irrational may be mixed).

This course was created by the Rethink Education Content Development Team in partnership with the North Carolina Virtual Public Schools. This course is aligned to the NC Standards for 8th Grade Math.