Education and Early Childhood Learning

Number sense and operations: Different representations of numbers help reveal certain properties and make calculations easier. Regardless of the type of numbers or symbols used, each operation retains the same meaning, operations are interconnected, and there are multiple ways to reach a result, some of which may be more useful depending on the situation or the problem to be solved, including using estimation to assess whether a solution is reasonable.

• MAT.9.2.A.1 Determine the square root of positive rational numbers that are perfect squares.

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

• MAT.9.2.A.2 Determine an approximate square root of positive rational numbers that are non-perfect squares.

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

• MAT.9.2.A.3 Demonstrate an understanding of powers with bases that are natural numbers and exponents that are integers, by

  • using patterns to show why $a^{-n}=\frac{1}{a^n}$
  • evaluating expressions of the form
    • $a^{-n}=\frac{1}{a^n}$
    • $\frac{1}{a^{-n}}=a^n$
  • applying the laws of exponents
    • $a^m\cdot a^n=a^{m+n}$
    • $\frac{a^m}{a^n}=a^{m-n}$
    • ${\left(a^m\right)}^n=a^{m-n}$
    • ${\left({am}^m\right)}^n=a^m\cdot b^m$
    • ${\left(}^{\frac{a}{b}}=\frac{a^n}{b^n}$
    • $a^0=1$
    • $a^{-n}=\frac{1}{a^n}$
    • $\frac{1}{a^{-n}}=a^n$

  where $a$ and $b$ are natural numbers and $m$ and $n$ are intergers.

  [C, CN, ME, PS, R]

• MAT.9.2.A.4 Demonstrate an understanding of the exponential notation by expressing and interpreting decimal numbers ranging from 0.001 to 1 000 000 using powers of ten, including expanded exponential forms that reflect place value.
  [C, CN, R]

• MAT.9.2.A.5 Explain and apply the order of operations on rational numbers, including exponents (limited to whole numbers) with and without technology.
  [ME, PS, R, T]

• Patterns: Recognizing and representing patterns helps us understand the world, make generalizations, and solve problems.

  MAT.9.2.B.1 Represent and describe exponential patterns and relations using a table of values, graphs, and analyze these relationships to draw conclusions.
  [C, CN, R, T, V]

• Variables and equations: Symbols, expressions, and equations are used to represent patterns and describe relationships between quantities.

  MAT.9.2.B.2 Model and solve problems using linear equations of the form

  • $ax=b+cx$
  • $ax+b=cx+d$
  • $a(x+b)=cx+d$
  • $a(bx+c)=d(ex+f)$
  • $\frac{a}{x}=b,x\ne 0$

  where $a,b,c,d,e$ and $f$ are rational numbers.

  [C, CN, ME, PS, V]

• MAT.9.2.B.3 Explain, illustrate, and apply strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.

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

• MAT.9.2.B.4 Model, record, and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials and binomials, concretely, pictorially, and symbolically.
  [C, CN, R, V]

  Note: The intent is not to factor polynomials, but to relate multiplication of binomials to the division of a polynomial by a binomial through concrete, pictorial, and symbolic representation.

• Measurement: Measurement is a useful process for comparing the dimensions of certain attributes of two-dimensional shapes and three-dimensional objects, whether through direct or indirect methods, in order to solve problems in real-world contexts.

  There are no outcomes assigned to this sub-domain.

• Three-dimensional objects and two-dimensional figures: Two-dimensional figures and three-dimensional objects can be described, classified, and analyzed based on their attributes and the relationships between them.

  MAT.9.2.C.1 Determine the surface area of composite 3-D objects to solve problems.

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

  Note: It is intended that the composite 3-D objects be made up of objects limited to right cylinders, right rectangular prisms, and right triangular prisms.

• MAT.9.2.C.2 Demonstrate an understanding of similarity of polygons.

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

• Transformations: Two-dimensional figures can be moved using transformations and analyzed based on their position in a Cartesian plane. Their positions and movements can be described and modeled using coordinates, geometric representations, and transformations.

  MAT.9.2.C.3 Draw and interpret scale diagrams of 2-D shapes.

  [CN, R, T, V]

• MAT.9.2.C.4 Demonstrate an understanding of line and rotation symmetry.

  [C, CN, PS, V]

• Data analysis: Data can be collected, organized, represented, and interpreted to model situations, support decision-making, and solve problems.

  MAT.9.2.D.1 Develop and implement a project plan for the collection, display, and analysis of data by

  • formulating a question for investigation
  • choosing a data collection method that includes social considerations
  • selecting a population or a sample
  • collecting the data
  • displaying the collected data in an appropriate manner
  • drawing conclusions to answer the question

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

• Probability and uncertainty: Probability involves determining the likelihood that an event will occur based on past experiences or the analysis of possible outcomes in order to solve problems in uncertain situations.

  MAT.9.2.D.2 Identify the sample space and calculate the theoretical probability for an event in a random experiment involving two dependent events.
  [C, CN, ME, PS, R, T]

• MAT.9.2.D.3. Explore dependent events through experimentation, calculate, and compare the experimental and theoretical probabilities.
  [C, CN, PS, R, T, V]

• Revenue: Understanding different types of income and how effective money management supports the development of essential skills for making informed financial decisions in everyday life.

  MAT.9.2.E.1 Develop an understanding of how education, career choice, and personal goals can influence future income potential and lifestyle, recognizing the connection between individual expectations and longterm financial planning.
  [C, CN, R, T]

• Spending and borrowing: By understanding that income forms the foundation for spending decisions and that borrowing carries obligations and risks that must be managed responsibly, individuals are able to make informed financial decisions.

  MAT.9.2.E.2 Develop an understanding of available borrowing options, including a short-term loan, student loan, car loan, line of credit, and mortgage, and recognize their impact on personal finances.

  [C, PS, R, T]

• MAT.9.2.E.3 Demonstrate an understanding of borrowing decisions, the advantages and disadvantages of using credit, including credit cards, and how paying back debt can affect personal finances and influence credit scores over time.
  [C, CN, ME, PS, R, T, V]

• Saving and investing: Managing personal finances involves saving and investing wisely to prepare for the future, handle unexpected events, and achieve personal goals.

  MAT.9.2.E.4 Demonstrate an understanding of different types of investments and recognize how returns, tax implications, volatility, and risk factors, including fraud, scams, and deceptive schemes, differ among investment options.

  [C, CN, R, T]

• MAT.9.2.E.5 Demonstrate an understanding of how different types of investments can grow or lose value over time by using technology, tables, and graphs to explore simple and compound interest and compare changes across various options.
  [C, CN, PS, R, T, V]