This week's algebra worksheets.

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Standards alignment

What this algebra math content covers

Worksheets are mapped to the following published standards. Pick a standard to focus your worksheet on the matching skill.

• CCSS

  6.EE.A.2Grade 6

  Write, read, and evaluate expressions in which letters stand for numbers.

• CCSS

  6.EE.B.7Grade 6

  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q.

• CCSS

  7.EE.A.1Grade 7

  Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

• CCSS

  7.EE.B.4Grade 7

  Construct simple equations and inequalities to solve word problems.

• CCSS

  8.EE.C.7Grade 8

  Solve linear equations in one variable, including those with rational coefficients and variables on both sides.

• CCSS

  8.EE.C.8Grade 8

  Analyze and solve pairs of simultaneous linear equations.

• CCSS

  HSA.SSE.A.1High School

  Interpret expressions that represent a quantity in terms of its context.

• CCSS

  HSA.CED.A.1High School

  Create equations and inequalities in one variable and use them to solve problems.

• CCSS

  HSA.REI.B.3High School

  Solve linear equations and inequalities in one variable, including with letters as coefficients.

Common mistakes

Misconceptions students bring to algebra

Specific errors to watch for when reviewing student work — pulled from classroom research and teacher reports.

1. 1

   Distributing only over the first term in parentheses.

   What to teach instead: The factor outside the parentheses multiplies every term inside.

   3(x + 4) = 3x + 12, not 3x + 4.

2. 2

   Confusing a negative sign with subtraction inside an expression.

   What to teach instead: A negative coefficient sticks with the variable when you move terms.

   In 5 − 2x, the −2 is the coefficient of x, not just a subtraction.

3. 3

   Thinking x² and 2x are the same.

   What to teach instead: x² = x · x; 2x = x + x. They're only equal when x = 0 or x = 2.

4. 4

   Cancelling terms from a sum like factors of a product.

   What to teach instead: You can only cancel factors that multiply the whole numerator and denominator, not addends.

   (x + 3)/3 ≠ x. You can't cancel the 3s because the numerator is a sum.

5. 5

   Forgetting to flip the inequality when multiplying or dividing by a negative.

   What to teach instead: Multiplying or dividing both sides of an inequality by a negative reverses the direction.

   −2x < 6 → x > −3 (not x < −3).

Key vocabulary

Algebra terms students should know

A short glossary of core vocabulary you can drop into any worksheet, quiz, or study guide.

Variable

A letter or symbol that stands for a number that can change or is unknown.

Coefficient

The number multiplied by a variable. In 4x, the coefficient is 4.

Constant

A fixed number with no variable attached.

Expression

A combination of numbers, variables, and operations without an equals sign.

Equation

A statement that two expressions are equal, with an equals sign.

Inequality

A comparison using <, >, ≤, or ≥ instead of an equals sign.

Solution

A value of the variable that makes an equation true.

Like terms

Terms that have the same variables raised to the same powers, so they can be combined.

Distributive property

a(b + c) = ab + ac. Lets you 'distribute' multiplication over addition.

Slope

The steepness of a line, computed as rise over run.