8.NS.A.1; Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.
Overview Information:
In this lesson work through the understanding of the standard by starting with helping students understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. Lesson Focus:
Give students a review and some exploration time to understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. Resources to Support Instruction:
Use these links and resources to find teaching strategies that will be useful in your classroom for teaching the skills needed for this particular section of the unit.- Kuta Software: Rational Numbers Worksheet (Link).
- LearnAlberta.ca: Understanding Square Roots (Link).
- Online Practice from IXL
- Regents Prep: Rational and Irrational Numbers Lesson (Link).
- Discovering Pi (Link) - Retrieved from Howard County Public School System.
- Rational and Irrational Numbers (Link) - Retrieved from Howard County Public School System.
- Integers, Rational and Irrational Numbers (Link) - Contains possible lesson seeds and practice Retrieved from Howard County Public School System.
- Rational and Irrational Numbers Rap (Link) - Rap about rational and irrational numbers. Retrieved from Howard County Public School System.
- Student "I Can" Statements (Link) - Document identifies some essential learning in the Common Core State Standards accompanied with student friendly "I Can" statements to help students grasp those essential learning components.
Lesson Elements to Support Instruction:
Here are some sample lesson plans, lesson ideas, or lesson openers that a teacher can use to introduce or teach the skills emphasized in this particular section of the unit.- Illustrative Mathematics Task: Estimating Square Roots (Link).
- Illustrative Mathematics Task: Calculating and Rounding Numbers (Link).
- Illustrative Mathematics Task: Calculating the Square Root of 2 (Link).
- Illustrative Mathematics Task: Converting Decimal Representations of Rational Numbers to Fraction Representations (Link).
- Illustrative Mathematics Task: Identifying Rational Numbers (Link).
- Mathematics Assessment Project - Repeating Decimals (Link).
- Determining whether a number terminates or repeats.
- Which fractions become terminating decimals? (Link) - Tutorial and practice
- Graph Paper Illustrations - Students will use graph paper to demonstrate the inverse relationship between squares and square roots. They will visually represent the squares for the numbers 1-12 with accompanying notes.
- Direct lesson on defining rational/irrational numbers - Use a 2 x 2 square quilt piece. Each piece is a right triangle. Eight of these pieces form the square. Find the length of the sides of the square that is formed in the center of the larger square. Square root of 2 cannot be written as the quotient of two integers a/b.
- Card Sort Activity (Link) - The students will work in their groups to organize a set of cards containing numbers (both rational and irrational) in a variety of forms. They will need to discuss amongst themselves how to determine if each of the numbers is rational or irrational.
- “That’s Irrational!” (Link) – Students will write a paragraph in response to a journal prompt to reflect their understanding of irrational and rational numbers. The teacher will informally review the journals to determine if students have an understanding of irrational numbers that is sufficient for application with the Pythagorean Theorem.
- Common Core Georgia Performance Standards Tasks (Link) - See link or see resource folder for tasks relating to this unit (Georgia Tasks 1-7,10) from the Georgia Department of Education. In this unit student will distinguish between rational and irrational numbers and show the relationship between the subsets of the real number system, recognize that every rational number has a decimal representation that either terminates or repeats, recognize that irrational numbers must have decimal representations that neither terminate nor repeat, understand that the value of a square root can be approximated between integers and that non–perfect square roots are irrational, locate rational and irrational numbers on a number line diagram, use the properties of exponents to extend the meaning beyond counting-number exponents, recognize perfect squares and cubes, understanding that non-perfect squares and non-perfect cubes are irrational, recognize that squaring a number and taking the square root of a number are inverse operations; likewise, cubing a number and taking the cube root are inverse operations, express numbers in scientific notation, compare numbers, where one is given in scientific notation and the other is given in standard notation, compare and interpret scientific notation quantities in the context of the situation, use laws of exponents to add, subtract, multiply and divide numbers written in scientific notation, solve one-variable equations with the variables being on both sides of the equals sign, including equations with rational numbers, the distributive property, and combining like terms, analyze and represent contextual situations with equations, identify whether there is one, none, or many solutions, and then solve to prove conjectures about the solutions.
SBAC Assessment Content Specifications SamplesGrade 8: SBAC Sample and Teaching Materials: The following is a list of released SBAC content specification math samples to use with your students to determine progress on the standards listed below.
The Number System (NS) 8.NS.1
- Grade 8 Claim 1 Target A (Link) Specification Table
- Grade 8 Math Claim 3 (Link) Specification Table
- Irrational Numbers (Link) Grade 8 Math Claim 3
- Classify Numbers (Link)
- Irrational Numbers (Link) Grade 8 Math Claim 3