New Brunswick

12.S Statistics

• Develop statistical reasoning

  • 12.S1 Demonstrate an understanding of normal distribution, including standard deviation, z-scores.

    • Find probabilities using the normal distribution I (12-Z.12)
    • Find probabilities using the normal distribution II (12-Z.13)
    • Find z-values (12-Z.14)
    • Find values of normal variables (12-Z.15)

  • 12.S2 Interpret statistical data, using confidence intervals, confidence levels, margin of error.

    • Find confidence intervals for population means (12-AA.12)
    • Find confidence intervals for population proportions (12-AA.13)
    • Interpret confidence intervals for population means (12-AA.14)

12. LR Logical Reasoning

• Develop logical reasoning

  • 12.LR1 Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.

  • 12.LR2 Solve problems that involve the application of set theory.

  • 12.LR3 Solve problems that involve conditional statements.

    • Truth tables (11-W.3)
    • Truth values (11-W.4)
    • Identify hypotheses and conclusions (12-X.1)
    • Counterexamples (12-X.2)
    • Conditionals (12-X.3)
    • Negations (12-X.4)
    • Converses, inverses and contrapositives (12-X.5)
    • Biconditionals (12-X.6)

12.P Probability

• Develop critical thinking skills related to uncertainty

  • 12.P1 Interpret and assess the validity of odds and probability statements.

    • Introduction to probability (12-Y.1)

  • 12.P2 Solve problems that involve the probability of mutually exclusive and non–mutually exclusive events.

    • Calculate probabilities of events (12-Y.2)
    • Find probabilities using two-way frequency tables (12-Y.5)

  • 12.P3 Solve problems that involve the probability of two events.

    • Identify independent events (12-Y.6)
    • Find conditional probabilities (12-Y.7)
    • Independence and conditional probability (12-Y.8)
    • Find conditional probabilities using two-way frequency tables (12-Y.9)

  • 12.P4 Solve problems that involve the fundamental counting principle.

    • Counting principle (11-Y.4)

  • 12.P5 Solve problems that involve permutations.

    • Combinations and permutations (12-Y.3)
    • Find probabilities using combinations and permutations (12-Y.4)

  • 12.P6 Solve problems that involve combinations.

    • Combinations and permutations (12-Y.3)
    • Find probabilities using combinations and permutations (12-Y.4)

  • 12.P7 Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).

    • Pascal's triangle (12-D.14)
    • Pascal's triangle and the Binomial Theorem (12-D.15)
    • Binomial Theorem I (12-D.16)
    • Binomial Theorem II (12-D.17)

12.RF Relations & Functions

• Develop algebraic and graphical reasoning through the study of relations

  • 12.RF1 Represent data, using polynomial functions (of degree ≤ 3), to solve problems.

  • 12.RF2 Represent data, using exponential and logarithmic functions, to solve problems.

    • Domain and range of exponential and logarithmic functions (12-G.1)
    • Match exponential functions and graphs (12-G.3)
    • Exponential functions over unit intervals (12-G.9)
    • Describe linear and exponential growth and decay (12-G.10)
    • Exponential growth and decay: word problems (12-G.11)

  • 12.RF3 Represent data, using sinusoidal functions, to solve problems.

    • Find properties of sine functions (12-O.1)
    • Graph sine functions (12-O.4)