Standards Map

Mathematics > Grade 7 > Expressions and Equations
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Mathematics | Grade : 7

Domain - Expressions and Equations

Cluster - Use properties of operations to generate equivalent expressions.

[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.

Resources:


  • Coefficient
    Any of the factors of a product considered in relation to a specific factor.
  • Expression
    A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a).
  • Properties of operations
  • Rational number
    A number expressible in the form a∕b or – a∕b for some fraction a∕b. The rational numbers include the integers.

Predecessor Standards:

  • 6.EE.A.3
    Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
  • 6.EE.A.4
    Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Successor Standards:

  • 8.EE.C.7.b
    Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
  • AI.A-SSE.A.2
    Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2 ) – 3).
  • AI.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.
  • AI.A-SSE.B.3.a
    Factor a quadratic expression to reveal the zeros of the function it defines.
  • AI.A-SSE.B.3.b
    Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • 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.A-APR.A.1
    Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.
  • AI.A-APR.A.1.a
    Perform operations on polynomial expressions (addition, subtraction, multiplication), and compare the system of polynomials to the system of integers when performing operations.
  • AI.A-APR.A.1.b
    Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive property.
  • AI.F-IF.C.8
    Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • AI.F-IF.C.8.a
    Use the process of factoring and completing the square in a quadratic function to show zeros, maximum/minimum values, and symmetry of the graph, and interpret these in terms of a context.
  • 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.
  • AII.N-CN.A.2
    Use the relation i2 = –1 and the Commutative, Associative, and Distributive properties to add, subtract, and multiply complex numbers.
  • MII.N-CN.A.2
    Use the relation i2 = –1 and the Commutative, Associative, and Distributive properties to add, subtract, and multiply complex numbers.
  • MII.A-SSE.A.2
    Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2) – 3).
  • 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.
  • MII.A-SSE.B.3.a
    Factor a quadratic expression to reveal the zeros of the function it defines.
  • MII.A-SSE.B.3.b
    Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • 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.A-APR.A.1
    Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.
  • MII.A-APR.A.1.a
    Perform operations on polynomial expressions (addition, subtraction, multiplication), and compare the system of polynomials to the system of integers when performing operations.
  • MII.A-APR.A.1.b
    Factor and/or expand polynomial expressions; identify and combine like terms; and apply the Distributive property.
  • MII.F-IF.C.8
    Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • MII.F-IF.C.8.a
    Use the process of factoring and completing the square in a quadratic function to show zeros, minimum/maximum values, and symmetry of the graph and interpret these in terms of a context.
  • 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.

Same Level Standards:

  • 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.