Modeling Irrational Approximations

To find rational approximations of irrational numbers students must first be able to differentiate between rational and irrational numbers (see the sorting activity highlighted in this previous Decimal Form of a Rational Number post). The geometric approach to evaluating square roots of perfect squares can be extended to approximating irrational numbers. This modeling activity provides a visual proof that square roots of non-perfect squares are indeed irrational (see the concept builder highlighted in this previous Square Roots and Cube Roots post). Consider scaffolding the geometric approach with this Stations Activity and record sheet based on square tiles.

8.NS.A.2 Resources

And then move students from the geometric model to a numeric approach with the number line (see this previous Irrational Approximations post). This will enable students to use rational approximations to compare the size of irrational numbers, locate them on a number line, and estimate the value of expressions.


This stations activity highlights Common Core State Standard 8.NS.A.2 included in MATH-8 and Accelerated MATH-7.