Unit 7
Irrationals, iteger exponents, and scientific notation
Students will extend their knowledge of numerical reasoning and real numbers.
This unit builds upon the understanding of exponents and rational/irrational numbers. IN THIS UNIT STUDENTS WILL BE EXPECTED TO:
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LEARNING OBJECTIVES
8.NR.2.1 Apply the properties of integer exponents to generate equivalent numerical expressions.
8.NR.2.2 Use square root and cube root symbols to represent solutions to equations. Recognize that x^2 = p (where p is a positive rational number and |x| ≤ 25) has two solutions and x^3 = p (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares where x is less than or equal to 625 and cube roots of perfect cubes where x is greater than or equal to −1000 and x is less than or equal to 1000.
8.NR.2.3 Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.NR.2.4 Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).
8.NR.1.1 Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.
8.NR.1.2 Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.
8.NR.2.2 Use square root and cube root symbols to represent solutions to equations. Recognize that x^2 = p (where p is a positive rational number and |x| ≤ 25) has two solutions and x^3 = p (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares where x is less than or equal to 625 and cube roots of perfect cubes where x is greater than or equal to −1000 and x is less than or equal to 1000.
8.NR.2.3 Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.NR.2.4 Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).
8.NR.1.1 Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.
8.NR.1.2 Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.
LEARNING TARGET
- I can identify the properties of integer exponents (laws of exponents).
- I can apply properties of integer exponents when multiplying and dividing with like bases.
- I can simplify numerical expressions, by applying the laws of exponents.
- I can classify expressions according to whether or not they are equivalent w/ one property, two properties, or three properties.
- I can convert numbers written in standard form into scientific notation form (and vice versa).
- I can perform operations with numbers expressed in scientific notation without technology.
- I can compare numbers written in scientific notation and determine how many times larger (or smaller) one number written in scientific notation is to another.
- I can interpret scientific notation that has been generated by technology.
- I can apply laws of exponents to perform operations with numbers written in scientific notation.
- I can recognize and evaluate perfect square roots in the form of 1, 4, 9, …., 100.
- I can recognize and evaluate perfect cube roots of 1, 8, 27, 64, and 125.
- I can recognize the inverse operation of squared is square rooting and solve mathematical problems.
- I can solve equations of the form x^2 = 4 (x squared = 4); √x^2=√4 (the square root of x^2 = the square root of 4); x = ±2 (x = plus and minus 2).
- I can recognize the inverse operation of cubed is cube rooting.
- I can solve equations of the form x^3=27.
- I can distinguish between rational and irrational numbers.
- I can write a repeating decimal as a fraction.
- I can approximate an irrational number and locate it on a number line.
- I can estimate the value of expressions that include irrational numbers.