Expressions and Equations 7.EE
Use properties of operations to generate equivalent expressions.
1. Apply properties of operations as strategies to add, subtract, factor,
and expand linear expressions with rational coefficients.
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.”
Solve real-life and mathematical problems using numerical and
algebraic expressions and equations.
3. Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between
forms as appropriate; and assess the reasonableness of answers using
mental computation and estimation strategies. For example: If a woman
making $25 an hour gets a 10% raise, she will make an additional 1/10 of
her salary an hour, or $2.50, for a new salary of $27.50. If you want to place
a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches
wide, you will need to place the bar about 9 inches from each edge; this
estimate can be used as a check on the exact computation.
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.
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?
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 salesperson, 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.
Use properties of operations to generate equivalent expressions.
1. Apply properties of operations as strategies to add, subtract, factor,
and expand linear expressions with rational coefficients.
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.”
Solve real-life and mathematical problems using numerical and
algebraic expressions and equations.
3. Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between
forms as appropriate; and assess the reasonableness of answers using
mental computation and estimation strategies. For example: If a woman
making $25 an hour gets a 10% raise, she will make an additional 1/10 of
her salary an hour, or $2.50, for a new salary of $27.50. If you want to place
a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches
wide, you will need to place the bar about 9 inches from each edge; this
estimate can be used as a check on the exact computation.
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.
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?
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 salesperson, 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.