NS.1.2

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.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to plot the square root of eight on three number lines, scaled to progressively more precision.

Approximating Irrational Numbers

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CPALMS: Students are asked to find and interpret lower and upper bounds of an irrational expression using a calculator.

The Irrational Beauty of the Golden Ratio

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CPALMS: Students are asked to estimate the value of several irrational numbers using a calculator and order them on a number line.

Comparing Irrational Numbers

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CPALMS: Students are asked to graph three different irrational numbers on number lines.

Locating Irrational Numbers

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Assessment Questions
Assessment Questions
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Multiple Choice
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GRID 3
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Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers. Students are to decide which of the choices is greater and explain their reasoning.

Comparing Rational and Irrational Numbers

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Illustrative Mathematics: Students are asked to label approximate locations for the given numbers which helps to reinforce the idea that they fit into a system that includes the more familiar integer and rational numbers.

Irrational Numbers on the Number Line

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Illustrative Mathematics:The purpose of the task is to make connections between the definition and properties of squares and square roots and ordering on the number line.

Placing a Square Root on the Number Line