8NS-Know+that+there+are+numbers+that+are+not+rational,+and+approximate+them+by+rational+numbers

8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). //For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.// || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)** ===
 * ===**Common Core Standards**===

NS.1
2. Reason abstractly and quantitatively. 6. Attend to precision. 7. Look for and make use of structure. NS.2 2. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. || 8.TT.1 Use technology and other resources for assigned tasks. 8.SE.1 Analyze responsible behaviors when using information and technology resources. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== Understanding Evaluating Applying Analyzing || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**=== and irrational numbers, recognizing that any number that can be expressed as a fraction is a rational number. Students recognize that the decimal equivalent of a fraction will either terminate or repeat. Students convert repeating decimals into their fraction equivalent using patterns or algebraic reasoning. Students compare and order rational and irrational numbers. Students also recognize that square roots may be negative.
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 8.NS.1** Students understand that Real numbers are either rational or irrational. They distinguish between rational
 * 8.NS.2** Students locate rational and irrational numbers on the number line.

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**I can...**
show that there are numbers that are not rational, and approximate them by rational numbers.

I can show if a number is rational or irrational. 8.NS.2 I can create a number line with rational and irrational numbers. I can approximate irrational numbers and compare them to other irrational numbers.
 * 8.NS.1**

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
Real Numbers, Irrational numbers, Rational numbers, Integers, Whole numbers, Natural numbers, radical, radicand, square roots, perfect squares, cube roots, terminating decimals, repeating decimals, truncate

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**
Students that need additional help on NS 1 and 2 will do the hands on intervention activity. Students that understand concept will complete the Enrichment activity. Work station for square roots and cube roots: Teaching Student-Centered Mathematics: page 150

‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Intervention:**
Carnegie Learning Lesson 5.1 Common Core Math Standards with Hands-on Activities page 152 and 154

**Navigation through Problem Solving and Reasoning (NCTM)**
-page 12 Reasoning about Sums of Consecutive numbers Irrational and Rational game ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**===

__Mathematics Station Activities__
- Set 1, 2, and 3. Pages 1, 9, and 16

Lessons: 5.2 and 5.3
 * __Carnegie Learning Math Series__**

Irrational Numbers
Quantile NS.1 Quantile NS.2



===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===
 * Refer to NC DPI unpacked content page 6 and 7**
 * Refer to Arizona Academic Content standards page 4 and 5**