8.NS.A.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.
Overview Information:
In this lesson work through the understanding of the standard by starting with helping students 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).
Lesson Focus:
Give students a review and some exploration time to 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).
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.
- Math Games Online
- Online Practice from IXL
- The Name Game (Link) - Retrieved from Howard County Public School System.
- Patio Predicament (Link) - Retrieved from Howard County Public School System.
- Environmental Garden (Link) - Retrieved from Howard County Public School System.
- Computing Pi (Link) - Students approximate pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Retrieved from Howard County Public School System.
- Skill in Algebra (Link) - Students learn to solve simultaneous linear equations using the method of addition and substitution.
- BiteSize Math (Link) - This site offers examples and several elements of help for students solving simultaneous linear equations.
- 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: Comparing Rational and Irrational Numbers (Link).
- Illustrative Mathematics Task: Irrational Numbers on the Number Line (Link).
- Illustrative Mathematics Task: Placing a Square Root on the Number Line (Link).
- Mathematics Assessment Project - Repeating Decimals (Link)
- The Fascinating Irrational Numbers (Link) - A teaching guideline/lesson plan to give more insight to irrational numbers
- Rational and Irrational Numbers (Link) - Review guideline
- Enzenberger, Hans Magnus. The Number Devil: A Mathematical Adventure.
- Irrational Numbers (Link) - Tutorial
- Irrational Square Roots Video (Link) - Excellent video on the expansion of √2, shows that √2 is between 1 and 2, then between 1.4 and 1.5, and explains how to continue on to get better approximations.
- Critical Area of Focus: Formulating and reasoning about expressions and equations
- Formative Assessment Lesson: Repeating Decimals (Link) - See pages 10 through 11 or see resource folder for a lesson relating to this standard from the Georgia Department of Education.
- 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 Samples
Grade 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.2
- Grade 8 Claim 1 Target A (Link) Specification Table
- Grade 8 Math Claim 2 (Link) Specification Table
- Mars and Jupiter Asteroids (Link) Grade 8 Math Claim 2
- Environmental Garden (Link) - Retrieved from Howard County Public School System.
- Mars and Jupiter Asteroids (Link) Grade 8 Math Claim 2