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.
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)
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
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exponential expression
base
exponent
power
scientific notation
properties of exponents
standard form/decimal form
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8.EE.A.1
Review exponent notation and identify equivalent exponential expressions.
8.EE.A.1
Evaluate numerical and algebraic expressions with exponents using the order of operations.
8.EE.A.1
Investigate patterns of exponents with positive/negative bases and even/odd bases.
8.EE.A.1
Investigate exponent patterns to write equivalent expressions.
8.EE.A.1
Apply the product of powers rule and the quotient of powers rule to write equivalent, simplified exponential expressions.
8.EE.A.1
Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.
8.EE.A.1
Reason with zero exponents to write equivalent, simplified exponential expressions.
8.EE.A.1
Reason with negative exponents to write equivalent, simplified exponential expressions.
8.EE.A.1
Simplify and write equivalent exponential expressions using all exponent rules.
8.EE.A.3
8.EE.A.4
Write large and small numbers as powers of 10.
8.EE.A.3
Define and write numbers in scientific notation.
8.EE.A.3
8.EE.A.4
Compare numbers written in scientific notation.
8.EE.A.4
Multiply and divide with numbers in scientific notation. Interpret scientific notation on calculators.
8.EE.A.4
Add and subtract with numbers in scientific notation.
8.EE.A.1
8.EE.A.3
8.EE.A.4
Solve multi-step applications using scientific notation and properties of exponents.
Key: Major Cluster Supporting Cluster Additional Cluster
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