Mathematics Grade 7 Expressions
& Equations
Develop an understanding of operations
with rational numbers and working with expressions and linear equations
Students develop a unified
understanding of number, recognizing fractions, decimals (that have a finite
or a repeating decimal representation), and percents as different
representations of rational numbers. Students extend addition, subtraction,
multiplication, and division to all rational numbers, maintaining the
properties of operations and the relationships between addition and
subtraction, and multiplication and division. By applying these properties,
and by viewing negative numbers in terms of everyday contexts (e.g., amounts
owed or temperatures below zero), students explain and interpret the rules
for adding, subtracting, multiplying, and dividing with negative numbers.
They use the arithmetic of rational numbers as they formulate expressions and
equations in one variable and use these equations to solve problems.
Resources
Use properties of operations to generate
equivalent expressions.
7.EE.1.
Apply properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients.
7.EE.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.
7.EE.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.
7.EE.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.
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?
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
Mathematics Grade 7 Expressions
& Equations
|
|||
Develop an understanding of operations
with rational numbers and working with expressions and linear equations
|
|||
Students develop a unified
understanding of number, recognizing fractions, decimals (that have a finite
or a repeating decimal representation), and percents as different
representations of rational numbers. Students extend addition, subtraction,
multiplication, and division to all rational numbers, maintaining the
properties of operations and the relationships between addition and
subtraction, and multiplication and division. By applying these properties,
and by viewing negative numbers in terms of everyday contexts (e.g., amounts
owed or temperatures below zero), students explain and interpret the rules
for adding, subtracting, multiplying, and dividing with negative numbers.
They use the arithmetic of rational numbers as they formulate expressions and
equations in one variable and use these equations to solve problems.
|
|||
Resources
|
|||
Use properties of operations to generate
equivalent expressions.
|
|
||
7.EE.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.
|
7.EE.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.
|
|
7.EE.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.
|
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?
|
||
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
|
|||
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