Hauptinhalt
Nebraska Math
High School: NUMBER
Students will solve problems and reason with number concepts using multiple representations, make connections within math and across disciplines, and communicate their ideas.
Select, apply, and explain the method of computation when problem solving using real numbers (e.g., models, mental computation, paper-pencil, technology).
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Determine if the context of a problem calls for an approximation or an exact value.
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Determine the rounding convention to be used based on the context of a problem.
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Estimate a value using the concept of betweenness by bounding above and below (e.g., since log(10) = 1 and log(1,000) = 3 we know log(500) is between 1 and 3).
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Determine the tolerance interval and percent of error in measurement.
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Convert equivalent rates (e.g., miles per hour to feet per second).
Determine whether extremely large or extremely small quantities can be reasonably represented by a calculator or graphing utility.
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Use scientific notation to appropriately represent large and small quantities.
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Extend the properties of exponents to rational numbers.
- Equivalent forms of exponential expressions
- Equivalent forms of exponential expressions
- Evaluate radical expressions challenge
- Evaluating fractional exponents
- Evaluating fractional exponents: fractional base
- Evaluating fractional exponents: negative unit-fraction
- Evaluating quotient of fractional exponents
- Exponential equation with rational answer
- Fractional exponents
- Intro to rational exponents
- Properties of exponents (rational exponents)
- Properties of exponents intro (rational exponents)
- Rational exponents challenge
- Rewrite exponential expressions
- Rewriting exponential expressions as A⋅Bᵗ
- Rewriting quotient of powers (rational exponents)
- Rewriting roots as rational exponents
- Unit-fraction exponents
Use properties of rational and irrational numbers.
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Demonstrate, represent, and show relationships among the subsets of real numbers and the complex number system.
- Classify complex numbers
- Classifying complex numbers
- i as the principal root of -1
- Intro to complex numbers
- Intro to complex numbers
- Intro to the imaginary numbers
- Intro to the imaginary numbers
- Parts of complex numbers
- Plot numbers on the complex plane
- Plotting numbers on the complex plane
- Powers of the imaginary unit
- Powers of the imaginary unit
- Rational vs. irrational expressions
- Simplify roots of negative numbers
- Simplifying roots of negative numbers
- Sums and products of irrational numbers
- The complex plane
- Worked example: rational vs. irrational expressions
- Worked example: rational vs. irrational expressions (unknowns)
Compute with subsets of the complex number system including imaginary, rational, irrational, integers, whole, and natural numbers.
- Absolute value of complex numbers
- Absolute value of complex numbers
- Add & subtract complex numbers
- Adding complex numbers
- Angle of complex numbers
- Classifying complex numbers
- Complex number absolute value & angle review
- Complex number operations review
- Complex number polar form review
- i as the principal root of -1
- Intro to the imaginary numbers
- Intro to the imaginary numbers
- Multiply complex numbers
- Multiplying complex numbers
- Multiplying complex numbers
- Powers of the imaginary unit
- Powers of the imaginary unit
- Powers of the imaginary unit
- Proof: √2 is irrational
- Proof: product of rational & irrational is irrational
- Proof: square roots of prime numbers are irrational
- Proof: sum & product of two rationals is rational
- Proof: sum of rational & irrational is irrational
- Proof: there's an irrational number between any two rational numbers
- Rational vs. irrational expressions
- Simplify roots of negative numbers
- Simplifying roots of negative numbers
- Subtracting complex numbers
- Sums and products of irrational numbers
- Worked example: rational vs. irrational expressions
- Worked example: rational vs. irrational expressions (unknowns)
Understand roundoff error and why roundoff error accumulates when rounding occurs prior to the last step in a computation.
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Use estimation methods to check the reasonableness of real number computations and decide if the problem calls for an approximation (including appropriate rounding) or an exact number.
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Use units to assess the validity of an answer in the context of a problem.
Communicate the meaning of an answer in the context of a problem.