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[6.RP.A.3] -
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Mathematics | Grade : 7
Domain - Ratios and Proportional Relationships
Cluster - Analyze proportional relationships and use them to solve real-world and mathematical problems.
[7.RP.A.3] - Use proportional relationships to solve multi-step ratio, rate, and percent problems.
For example: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.
[7.RP.A.2] -
Recognize and represent proportional relationships between quantities.
[7.SP.C.7] -
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
[7.SP.C.8] -
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
[AI.A-SSE.B.3.c] -
Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
[AI.F-IF.C.8.b] -
Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as identifying appreciation and depreciation rate for the value of a house or car some time after its initial purchase: Vn=P(1+r)n. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2)t /10, and classify them as representing exponential growth or decay.
[AI.F-LE.A.1] -
Distinguish between situations that can be modeled with linear functions and with exponential functions.*
[AI.F-LE.A.1.a] -
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.*
[AI.F-LE.A.1.b] -
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*
[AI.F-LE.A.1.c] -
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*
[MI.F-LE.A.1] -
Distinguish between situations that can be modeled with linear functions and with exponential functions.*
[MI.F-LE.A.1.a] -
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.*
[MI.F-LE.A.1.b] -
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*
[MI.F-LE.A.1.c] -
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*
[MII.A-SSE.B.3.c] -
Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.15 1/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
[MII.F-IF.C.8.b] -
Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as Identifying appreciation/depreciation rate for the value of a house or car some time after its initial purchase: Vn=P(1+r)n. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, and y = (1.2) t /10, and classify them as representing exponential growth or decay.
[8.PS.1.1] -
Develop a model to describe that (a) atoms combine in a multitude of ways to produce pure substances which make up all of the living and nonliving things that we encounter, (b) atoms form molecules and compounds that range in size from two to thousands of atoms, and (c) mixtures are composed of different proportions of pure substances. Clarification Statement: Examples of molecular-level models could include drawings, three-dimensional ball and stick structures, and computer representations showing different molecules with different types of atoms.
State Assessment Boundary: Valence electrons and bonding energy, the ionic nature of subunits of complex structures, complete depictions of all individual atoms in a complex molecule or extended structure, or calculations of proportions in mixtures are not expected in state assessment.