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Mathematics | Course : Model Mathematics II (Integrated Pathway)
Domain - Seeing Structure in Expressions
Cluster - Write quadratic and exponential expressions in equivalent forms to solve problems.
[MII.A-SSE.B.3] - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- Expression
A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a).
[7.EE.A.1] -
Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.
For example, 4x + 2 = 2(2x +1) and -3(x – 5/3) = -3x + 5.
[7.EE.A.2] -
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” A shirt at a clothing store is on sale for 20% off the regular price, “p”. The discount can be expressed as 0.2p. The new price for the shirt can be expressed as p – 0.2p or 0.8p.
[8.F.A.3] -
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
[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.