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Mathematics > Course Model Mathematics I (Integrated Pathway) > Creating Equations
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Mathematics | Course : Model Mathematics I (Integrated Pathway)

Domain - Creating Equations

Cluster - Create equations that describe numbers or relationships.

[MI.A-CED.A.1] - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions with integer exponents.*

Resources:


  • Exponent
    The number that indicates how many times the base is used as a factor, e.g., in 43 = 4 x 4 x 4 = 64, the exponent is 3, indicating that 4 is repeated as a factor three times.
  • Exponential function
    A function of the form y = a •bx where a > 0 and either 0 < b < 1 or b > 1. The variables do not have to be x and y. For example, A = 3.2 • (1.02)t is an exponential function.
  • Integer
    All positive and negative whole numbers, including zero.
  • Linear function
    A function with an equation of the form y = mx + b, where m and b are constants
  • Variable
    A quantity that can change or that may take on different values. Refers to the letter or symbol representing such a quantity in an expression, equation, inequality, or matrix.

Predecessor Standards:

  • 7.EE.B.4
    Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
  • 7.EE.B.4.a
    Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
  • 7.EE.B.4.b
    Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a sales-person, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions..
  • 8.EE.A.2
    Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
  • 8.F.B.4
    Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MI.N-Q.A.1
    Use units as a way to understand problems; and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*
  • MI.A-SSE.A.1
    Interpret expressions that represent a quantity in terms of its context.*
  • MI.A-SSE.A.1.a
    Interpret parts of an expression, such as terms, factors, and coefficients.
  • MI.A-SSE.A.1.b
    Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P.
  • MI.A-CED.A.2
    Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
  • MI.A-CED.A.3
    Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.* For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
  • MI.A-REI.B.3
    Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • MI.F-IF.B.6
    Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
  • MI.F-LE.A.1
    Distinguish between situations that can be modeled with linear functions and with exponential functions.*
  • MI.F-LE.A.2
    Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).*
  • MII.A-REI.B.4.b
    Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.