Students learn to simplify complex-looking exponential expressions, and they learn efficient ways to describe, communicate, and operate with very large and very small numbers.
Math
Unit 1
8th Grade
In Unit 1, eighth grade students learn how complex-looking expressions and very large or small numbers can be represented in simpler ways. Through investigation, students discover ways to write equivalent exponential expressions, and then formalize their understanding of these strategies into properties of exponents. Later in the unit, they learn efficient ways to describe, communicate, and operate with very large and very small numbers. Though there are many procedural elements in this unit, underneath these procedures are strong conceptual understandings. Throughout the unit, students look for structures and patterns that exist in exponential terms and powers of ten, and use those structures and patterns to make generalizations (MP.7 and MP.8).
In sixth grade, students wrote and evaluated expressions with exponents using the order of operations. They identified the parts of an expression, distinguishing a term from a factor from a coefficient. In eighth grade, students expand on these skills to go beyond just evaluation. They are presented with exponentials such as $$\frac{3^{16}}{3^4}$$ or $$(x^2y)^5$$ and are asked to simplify them or represent them in equivalent ways. In this way, students hone their abilities to manipulate algebraic expressions, which they will continue to do in future units in eighth grade. In fourth and fifth grades, students investigated patterns in powers of ten and how those patterns related to place value. In this unit, students will access these prior concepts and use them in representing and working with very large and small numbers.
In high school, students will need a strong understanding of exponents and exponent properties. They will apply the properties of exponents to exponential equations in order to reveal new understandings of the relationship. They will work with fractional exponents and discover the properties of rational exponents and rational numbers. In general, students’ ability to see the structure in an expression will support them in manipulating quadratic functions, operating with polynomials, and making connections between various relationships.
Pacing: 19 instructional days (15 lessons, 3 flex days, 1 assessment day)
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The following assessments accompany Unit 1.
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.
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.
base
exponential expression
exponent
power
properties of exponents
scientific notation
standard form/decimal form
To see all the vocabulary for Unit 1, view our 8th Grade Vocabulary Glossary.
To see all the materials needed for this course, view our 8th Grade Course Material Overview.
Topic A: Review of Exponents
Topic B: Properties of Exponents
Topic C: Scientific Notation
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 2
Solving One-Variable Equations