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Expressions and Equations Activities

Preview the standards covered within eSpark’s adaptive, self-paced pathways and assignments for Expressions and Equations math skills.

6th Grade


Expressions with Exponents

Write and evaluate numerical expressions involving whole-number exponents.


Writing Expressions

Write expressions that record operations with numbers and with letters standing for numbers.


Expressions with Exponents

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).


Equivalent Expressions

Apply the properties of operations to generate equivalent expressions.


Equivalent Expressions

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).


Writing Expressions

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.


Solve One Variable Equations

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

7th Grade


Factor and Expand

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


Generate Equivalent Expressions

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.


Multi-Step, Real-World Problems

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.


Solving Equations

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.


Word Problems: Inequalities

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.

8th Grade


Integer Exponents

Know and apply the properties of integer exponents to generate equivalent numerical expressions.


Square and Cube Roots

Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root √2 is irrational.


Scientific Notation

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.


Scientific Notation: Operations

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.


Relationships and Slope

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.


Slope Intercept Form, Triangles

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.


Solutions to Linear Equations

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).


Solutions to Linear Equations

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.


Systems of Linear Equations

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.


Systems of Linear Equations

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.