This is a task from the Illustrative Mathematics website that is one …

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: Leanne makes the following observation: I know that \frac{1}{11} = 0.0909\ldots where the pattern 09 repeats forever. I also know that \frac{1}{9} = 0....

This 8th grade Math parent guide explains the content in straightforward terms so they …

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 …

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.

In CK-12 Middle School Math Concepts Grade 8, the learning content is …

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 …

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 …

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 lesson unit allows students to demonstrate their understanding of classifying numbers …

This lesson unit allows students to demonstrate their understanding of classifying numbers as rational or irrational and moving between different representations of rational and irrational numbers.

Standard 8.NS.1 requires students to "convert a decimal expansion which repeats eventually …

Standard 8.NS.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 1/3 are two different ways of representing the same number.

For this lesson, students know the intuitive reason why every repeating decimal …

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.

Students know that every number has a decimal expansion (i.e., is equal …

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.

In this lesson, student will know that when the square of a …

In this lesson, student will know that when the square of a side of a right triangle represented as a2, b2, c2 or is not a perfect square, they can estimate the side length as between two integers and identify the integer to which the length is closest.

This lesson unit allows students to demonstrate their understanding of finding irrational …

This lesson unit allows students to demonstrate their understanding of finding irrational and rational numbers to exemplify general statements and reasoning with properties of rational and irrational numbers.

This task requires students to determine whether a number is rational or …

This task requires students to determine whether a number is rational or irrational. The task assumes that students are able to express a given repeating decimal as a fraction.

Students will use candy to convert fractions to decimals and to discuss …

Students will use candy to convert fractions to decimals and to discuss the ways in which this application might be used on a job, and what kind of jobs requires this skill.

This awesome website allows elementary and middle school (K-8) to hone in …

This awesome website allows elementary and middle school (K-8) to hone in on their number sense and mental math skills while competing against their classmates. It levels the math to their mastery level which is awesome.

In this lesson, students will determine (without dividing) whether a given proper …

In this lesson, students will determine (without dividing) whether a given proper fraction will yield a repeating or terminating decimal form and will explain how the underlying principles determine the structure of the decimal form.

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