Use square root and cube root symbols to represent solutions to
equations of the form x² = p and x³ = p, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots
of small perfect cubes. Know that √2 is irrational.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
This lesson is designed to help teachers assess how well students can work with square numbers. Upon completion of the lesson, students should be able to describe and explain their findings and why results are possible or impossible. This lesson is a bridge towards proofs. The materials required for this lesson are worksheets, plain paper, large sheets of paper for making posters, and felt-tip pens. The entire lesson requires 110 minutes, broken down into a 20-minute pre-lesson, an 80-minute lesson (or two 40-minute lessons), and a 10-minute follow-up lesson.
Students listen to a video that describes Kepler's determination that planetary orbits are elliptical and then will use data for the solar distance and periods of several of the planets in the solar system, then investigate several hypotheses to determine which is supported by the data.