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PA-N-1-5

Page history last edited by Brenda Butz 6 years, 2 months ago

PA.N.1.5 Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

In a Nutshell

Real numbers are identified as either rational and irrational. By identifying square roots of whole numbers 1-400, as either perfect squares or not, students should be able to place all values on a number line, including non-perfect square root numbers between two consecutive integers.

EX:

Student Actions	Teacher Actions
Develop Mathematical Reasoning when using multiple representations of real numbers to compare and organize a set of numbers, and be able to place each on a real number line. Show the irrational number’s relationship and relative proximity to two integers. (The square root of 23 should be placed closer to 5 than to 4) Develop a Deep and Flexible Conceptual Understanding by discovering which integers, from 1-400, are perfect squares by making predictions and creating geometric models of squares, which can be organized and extended on a perfect square table. Develop Accurate and Appropriate Procedural Fluency by estimating non-perfect square numbers as values between two integers using perfect square tables, number lines, or geometric models.	Pose purposeful questions to facilitate discussions on the characteristics of irrational numbers and helping students develop strategies to estimate their value on the number line. Implement meaningful tasks that promote reasoning to help students make meaningful connections by using perfect square tables for estimation of non-perfect square roots between 2 integers on a number line.
Key Understandings	Misconceptions
A repeating decimal can be represented by an exact fraction. Every real number has an exact location on a number line. Whole numbers that are perfect squares can be written as a product of a pair of identical positive integers. If a square root is not perfect, it is an irrational number. Estimate the value of a non-perfect square root and place it's estimation on a number line.	Students might think that if a composite number has a factor that is a perfect square the composite number must also be a perfect square. Students divide by 2 instead of taking the square root of a number. Most commonly, students simplify the √2 to be 1. Students might think that a non-perfect square root is smaller than a whole number when ordered from least to greatest.