Essential Questions:
Lesson Plan A.3: Powers of Ten
Lesson Seed A.1: Exponents
Lesson Seed A.1: Negative Exponents
Unit Overview
Content Emphasis By Clusters in Grade 8
Progressions from Common Core State Standards in Mathematics
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Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.
This unit extends knowledge of numerical and algebraic expressions and equations from previous grades, and it develops understanding of properties of integer exponents, square and cube roots, integer powers of 10, and scientific notation in authentic situations.
At the completion of the unit on Expressions and Equations, the student will understand that:
Students will be able to:
The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.
Students may
Interdisciplinary Connections:
Interdisciplinary connections fall into a number of related categories:
Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:
Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
Part I – Focus Cluster Expressions and Equations
properties of integer exponents: These properties include product of powers, quotient of powers, negative exponents, zero exponent, and power of powers.
perfect square: A perfect square is the product of a number multiplied by itself. Examples: 4 • 4 = 16, therefore 16 is a perfect square of 4; -6 • -6 = 36, therefore 36 is a perfect square of -6;
, therefore s perfect square of
perfect cube: A perfect cube is the product of a number multiplied by itself.
Examples: 2 • 2 • 2 = 8, therefore 8 is a perfect cube of 2;
-5 • -5 • -5 = -125, therefore -125 is a perfect cube of -5 • • = therefore is a perfect cube of
square root: The square root of a number is a value which, when used as a factor two times produces the given number. The square root symbol is . Example: (read as square root of 144) is 12 because 12 • 12 = = 144, it always refers to the principal, or positive square root. In addition, ± = ±12
cube root: A cube root of a number is a value which, when used as a factor three times produces the given number. The cube root symbol is . For example, (read as cube root of 216) is 6 because 6 • 6 • 6 = = 216.
relationship between square/square root and cube/cube root: For example, the square of 6 (and ‾6) = 36; the square root of 36 = 6 (and ‾6). The cube of 5 = 125; the cube root of 125 = 5. The cube of ‾3 = ‾27; the cube root of ‾27 = ‾3.
principal (positive) root and negative root: A positive number has two square roots. The principal root is positive and the other root is negative. For example the square roots of 121 are 11 (principal root) and -11 (negative root) because = 121 and = 121.
integer powers of 10: Integer powers of 10 are numbers with a base of 10 and an exponent
scientific notation: A number in scientific notation is written as the product of two factors. The first factor is a number greater than or equal to 1 and less than 10; the second factor is an integer power of 10. Example: 37,482,000 is written 3.7482 x 0.00000037482 is written 3.7482 x
decimal notation: Notation refers to symbols that denote quantities and operations.
Part II – Instructional Connections outside the Focus Cluster
rational numbers: Numbers that can be expressed as an integer, as a quotient of integers
irrational numbers: A number is irrational because its value cannot be written as either a finite or a repeating decimal such as π and √2.
real number system: The set of numbers consisting of rational and irrational numbers make up the real number system.
truncate: In this estimation strategy, a number is shortened by dropping one or more digits after the decimal point. Example: 234.56 is truncated to the tenth’s place → 234.5 by dropping the digit 6 in the hundredth’s place).
proof of the Pythagorean Theorem and it converse: In any right triangle, the sum of the squares of the legs equals the square of the hypotenuse . The figure below shows the parts of a right triangle.
distance formula: The distance d between the points A:(x1, y1) and B:(x2, y2) is given by the formula: The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the hypotenuse. The hypotenuse of the triangle will be the distance between the two points. This formula is an application of the Pythagorean Theorem for right triangles:
volume of cones:
volume of cylinders: The process for understanding and calculating the volume of cylinders is identical to that of prisms, even though cylinders are curved. Here is a general right cylinder.
Additional Resources: