Standards in Unit:
• NC.8.NS.1: Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a non-repeating, non-terminating decimal.
• NC.8.EE.1: Develop and apply the properties of integer exponents to generate equivalent numerical expressions.
• NC.8.EE.2: Use square root and cube root symbols to:
• NC.8.EE.3: Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is as the other.
• NC.8.EE.4: Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both decimal and scientific notation are used.
• NC.8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving:
• NS.8.G.6: Explain the Pythagorean Theorem and its converse.
• NS.8.G.7: Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.
• NS.8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Summary of Unpacking for Each Standard:
NC.8.NS.1 - Students understand that Real numbers are either rational or irrational. They recognize that any number that can be expressed as a fraction is a rational number. Students recognize that the decimal equivalent of a fraction will either terminate or repeat. Fractions that terminate will have denominators containing only prime factors of 2 and/or 5. Students convert repeating decimals into their fraction equivalent using patterns or algebraic reasoning.
NC.8.EE.1 -Students discover and apply common properties of exponents, including the multiplication and division properties, power to a power, exponents of 0 and 1, and negative exponents. All exponents are integers at this level, and students should be able to expand and simplify expressions.
NC.8.EE.2 - Students are introduced to the radical symbol in this standard to solve equations and evaluate perfect squares and cubes. A key element of this standard is understanding the effects of exponents on negative and positive bases and how many solutions there are to equations with exponents of 2 and 3.
NC.8.EE.3 - Students will understand why scientific notation is an important tool for scientists, economists, and other real-world professions, and they will be able to write large and small numbers using scientific notation and interpret and expand numbers written in scientific notation.
NC.8.EE.4 - Students will apply laws of exponents in multiplying and dividing numbers expressed in scientific notation, giving a rationale for applying the laws of exponents. Additionally, addition and subtraction of numbers in scientific notation is no longer in the 8th grade standards.
8.NS.2 - Students locate rational and irrational numbers on the number line. Students compare and order rational and irrational numbers. Students also recognize that square roots may be negative and written as -√68.
8.G.6—Students use visual models to understand the Pythagorean Theorem, explore how to set up a proof of the Pythagorean Theorem, complete a geometric proof of the Pythagorean Theorem, complete an algebraic proof of the Pythagorean Theorem, demonstrate their understanding of the general form of the Pythagorean Theorem, and complete a proof of the converse of the Pythagorean Theorem.
8.G.7— Students read a problem and answer a series of questions using the Pythagorean Theorem, review the Pythagorean Theorem and learn the length of a side of a right triangle is often an irrational number, read a problem and decide how to model it using a right triangle and represent the problem using the Pythagorean Theorem, study models that show how to apply the Pythagorean Theorem to three-dimensional figures, and use the Pythagorean Theorem to solve word problems.
8.G.8—Students use the coordinate system to explore and extend the Pythagorean Theorem by discovering that they can use the Pythagorean Theorem to find distance between any two points in the coordinate plane and set up a model for finding the distance between two points by building a right triangle.
Prerequisite Skills:
Future Skills:
Key Vocabulary:
Cornerstone Task
Applying the Pythagorean Theorem (Links to an external site.)Links to an external site.
Pythagorean Theorem: Square Areas (Links to an external site.)Links to an external site.
MTSS/Remediation Resources
Math Topic/DPI Bucket: Properties of Exponents/Rational Numbers
Engage NY F2F Intervention: Grade 8, Module 1 (Links to an external site.)Links to an external site., Topic A
Edgenuity Online Intervention: Grade 8, Working with Exponents Unit, Lessons 1-5
Math Topic/DPI Bucket: Scientific Notation/Rational Numbers
Engage NY F2F Intervention: Grade 8, Module 1 (Links to an external site.)Links to an external site., Topic B
Edgenuity Online Intervention: Grade 8, Working with Exponents Unit, Lessons 6-8
Math Topic/DPI Bucket: Irrational Numbers/Rational Numbers
Engage NY F2F Intervention: Grade 8, Module 7 (Links to an external site.)Links to an external site., Topic A and B
Edgenuity Online Intervention: Grade 8, Pythagorean Theorem and Irrational Numbers Unit, Lesson 2
Math Topic/DPI Bucket: Pythagorean Theorem/Geometry
Engage NY F2F Intervention: Grade 8, Module 7 (Links to an external site.)Links to an external site., Topic C
Edgenuity Online Intervention: Grade 8, Pythagorean Theorem and Irrational Numbers Unit, All Except Lesson 2