FP10.2
Demonstrate understanding of irrational numbers in both radical (including mixed radical) and exponent forms through:
  • representing
  • identifying
  • simplifying
  • ordering
  • relating to rational numbers
  • applying exponent laws.

[C, CN, ME, PS, R, V]

Indicators for this outcome
(a)

Sort, with justification, a set of numbers into rational and irrational numbers.

(b)

Create and explain a pattern that describes the decimal form of an irrational number (e.g., write the digits from 0 to 9 in order, then put two of each digit – 0011223344... – followed by three of each digit and so on).

(c)

Approximate the value of a given irrational number and explain the strategy used.

(d)

Order a set of Real numbers, including rational and irrational numbers, on a number line and explain the strategies used.

(e)

Express a radical as a mixed radical in simplest form (limited to numerical radicands).

(f)

Express a mixed radical as an entire radical (limited to numerical radicands).

(g)

Explain, using examples, how changing the value of the index of a radical impacts the value of the radical.

(h)

Represent, such as through the use of a graphic organizer, the relationships among the subsets of the Real numbers: natural, whole, integer, rational, and irrational.

(i)

Analyze patterns to generalize why $a^{-n}=1/a^n$, $a ≠ 0$

(j)

Analyze patterns to generalize why $a^{1/n}=^n√a,n ≠ 0,n∈I$ and $2 > 0$ when $n$ is an even integer.

(k)

Extend and apply the exponent laws to powers with rational exponents (limited to expressions with rational and variable bases and integral and rational exponents):

  • $(a^m)(a^n)=a^{m+n}$
  • $a^m÷a^n=a^{m-n},a ≠ 0$
  • $(a^m)^n=a^{mn}$
  • $(ab)^m=a^mb^m$
  • $(a/b)^n=a^n/b^n,b ≠ 0$
(l)

Analyze simplifications of expressions involving radicals and/or powers for errors.

(m)

Express powers with rational exponents as radicals and vice versa.

(n)

Create a representation that conveys the relationship between powers, rational numbers, and irrational numbers.

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R053238
Pearson Foundations and Pre-calculus Mathematics 10. Student Edition(WNCP ed.)
The student text encourages the "big ideas" approach to develop concepts on what is important to think, do and understand. The teaching for understanding instructional approach develops deeper understanding of the concepts. Each chapter in the student text includes checkpoints, a study guide, a review, a practice test and a project.
•  Pearson Foundations and Pre-calculus Mathematics 10. Teacher Resource with CD
Media and Formats : Book
Price : $100.01
Record posted/updated: August 13, 2019