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It is the goal of this inquiry to introduce students to many instances within the disciplines (besides math, alone), in which the concept of "infinite" appears. After students have completed all eight inquiries, they cycle back and start on this one again,choosing a new question and group from which to base the rest of the eight inquiries that follow.


  • Mathematics > General
  • Mathematics > Algebra
  • Mathematics > Applied Mathematics
  • Mathematics > Arithmetic
  • Mathematics > Graphing
  • Mathematics > Measurement
  • Mathematics > Number Sense & Operations
  • Mathematics > Patterns
  • Mathematics > Problem Solving
  • Science > General
  • Science > General Science
  • Science > Physical Sciences

Education Levels:

  • Grade 3
  • Grade 4
  • Grade 5
  • Grade 6
  • Grade 7
  • Grade 8


patterns variables functions formative assessment constructivist teaching and learning mulitple intelligence approach learning stations infinity math science



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Update Standards?

MA.8-12.AI.1.1: Mathematics

Students use properties of numbers to demonstrate whether assertions are true or false.

MA.8-12.AI.2.0: Mathematics

Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

MA.8-12.AI.3.0: Mathematics

Students solve equations and inequalities involving absolute values.

MA.8-12.AI.4.0: Mathematics

Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) = 12.

MA.8-12.AI.5.0: Mathematics

Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

MA.8-12.AI.6.0: Mathematics

Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

MA.8-12.AI.7.0: Mathematics

Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

MA.8-12.AI.8.0: Mathematics

Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

MA.8-12.AI.9.0: Mathematics

Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

MA.8-12.AI.10.0: Mathematics

Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

MA.8-12.AI.11.0: Mathematics

Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

MA.8-12.AI.12.0: Mathematics

Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

MA.8-12.AI.13.0: Mathematics

Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.

MA.8-12.AI.14.0: Mathematics

Students solve a quadratic equation by factoring or completing the square.

MA.8-12.AI.15.0: Mathematics

Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

MA.8-12.AI.16.0: Mathematics

Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

MA.8-12.AI.17.0: Mathematics

Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

MA.8-12.AI.18.0: Mathematics

Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

MA.8-12.AI.19.0: Mathematics

Students know the quadratic formula and are familiar with its proof by completing the square.

MA.8-12.AI.20.0: Mathematics

Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

MA.8-12.AI.21.0: Mathematics

Students graph quadratic functions and know that their roots are the x-intercepts.

MA.8-12.AI.22.0: Mathematics

Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

MA.8-12.AI.23.0: Mathematics

Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

MA.8-12.AI.24.1: Mathematics

Students explain the difference between inductive and deductive reasoning and identify and provide examples of each.

MA.8-12.AI.24.2: Mathematics

Students identify the hypothesis and conclusion in logical deduction.

MA.8-12.AI.24.3: Mathematics

Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.

MA.8-12.AI.25.1: Mathematics

Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

MA.8-12.AI.25.2: Mathematics

Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

MA.8-12.AI.25.3: Mathematics

Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.
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