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.
Math
Unit 7
8th Grade
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)
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The following assessments accompany Unit 7.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 11.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
converse statement
cone
cube root
cylinder
hypotenuse
irrational number
legs
perfect square
pythagorean triplet
pythagorean theorem
rational number
sphere
square root
To see all the vocabulary for Unit 7, view our 8th Grade Vocabulary Glossary.
To see all the materials needed for this course, view our 8th Grade Course Material Overview.
Topic A: Irrational Numbers and Square Roots
Topic B: Understanding and Applying the Pythagorean Theorem
Topic C: Volume and Cube Roots
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 6
Systems of Linear Equations
Unit 8
Bivariate Data