Students learn about irrational numbers, approximating square roots of non-perfect square numbers, and investigate the well-known Pythagorean Theorem to solve for missing measures in right triangles.
In Unit 7, eighth-grade students extend their understanding of the Number System to include irrational numbers. This new understanding supports students as they study square and cube root equations and relationships between side lengths in right triangles, both concepts that fall within the major work of the grade. Students start the unit by investigating solutions to equations like $$x^2=2$$ and realize that the solution is not an exact point on the number line. They approximate square roots of non-perfect square numbers and represent rational numbers written in decimal form as fractions. The focus of the unit shifts to right triangles, and students investigate the well-known Pythagorean Theorem. They apply their understanding of square roots to solve for missing measures in right triangles and other applications. They look closely at geometric figures to identify and create right triangles, opening up the opportunity to apply the Pythagorean Theorem to find new information (MP.7). The focus shifts once more as students learn about cube roots and apply this new concept to various volume applications involving cylinders, spheres, and cones. Throughout the unit, students must attend to precision in their work, their solutions, and their communication, being careful about specifying appropriate units of measure, using the equals sign appropriately, and representing numbers accurately (MP.6).
Prior to this unit, students learned many skills and concepts that prepared them for this unit. Since elementary grades, students have been learning about and refining their understanding of area and volume. They have learned how to use composition and decomposition as tools to determine measurements, they’ve learned formulas and how to use them in problem-solving situations, and they’ve encountered various real-world situations. Standard 8.G.9 is a culminating standard in the Geometry progression in middle school, which will lay the foundation for much of the work they will do in high school geometry.
In high school, students will more formally derive the distance formula and other principles, they will expand their work with right triangles to include trigonometric ratios, and they will solve more complex problems involving volume of cylinders, pyramids, cones, and spheres.
Pacing: 20 instructional days (16 lessons (17 days), 2 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 8th Grade Scope and Sequence Recommended Adjustments.
This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.
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hypotenuse
legs
square root
cube root
perfect square
irrational number
rational number
converse statement
pythagorean theorem
pythagorean triplet
cylinder
cone
sphere
To see all the vocabulary for this course, view our 8th Grade Vocabulary Glossary.
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To see more information about the materials in this unit, view the Unit Materials Overview.
Key: Major Cluster Supporting Cluster Additional Cluster
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