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Algebraic expression Simplifying expressions Expanding expression Evaluate the expression ExponentsHere you will learn about math equations, including what they are and how to solve them.
Students will first learn about math equations as part of expressions and equations in 6th grade. They continue to expand upon this knowledge in 7th and 8th grade.
Every week, we teach lessons on math equations to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.
Math equations are statements made up of algebraic expressions and an equal sign. Math equations include defined math formulas that can be solved with substitution.
For example, here is a rectangle with base katex is not defined and height katex is not defined
The area of any rectangle can be found with the formula katex is not defined
Step-by-step guide: Math formulas
For example,
Does katex is not defined make the equation katex is not defined true?
Substitute katex is not defined for katex is not defined and follow the order of operations:
katex is not defined
katex is not defined
katex is not defined
Substituting katex is not defined for katex is not defined does not make the equation true, so katex is not defined is not a solution of the equation katex is not defined
Step-by-step guide: Substitution
One step equations are algebraic equations with a single variable that can be solved with one step.
In order to solve, you will need to isolate the variable (get it alone) on one side of the equation. This can be done with a model or by using the inverse operation.
For example, katex is not defined
Using a model: | Using inverse operations: |
---|---|
![]() Sort the katex is not defined tiles so an equal amount are with each katex is not defined tile. ![]() There are five katex is not defined tiles for each katex is not defined tile. katex is not defined | katex is not defined Get the variable alone by using the inverse operation. The inverse operation of multiplication is division. Divide katex is not defined on both sides of the equation. katex is not defined Since katex is not defined the left side can be written as katex is not defined or katex is not defined The right side of the equation can be written as katex is not defined katex is not defined You can check your answer by substituting the value for katex is not defined into the original equation. katex is not defined |
Step-by-step guide: One step equations
To solve equations with fractions, apply the inverse operation to both sides of the equation – a strategy also referred to as the “balance method.”
The inverse operation of division is multiplication.
For example, katex is not defined
katex is not defined *Multiply each side by katex is not defined
katex is not defined
katex is not defined *Subtract katex is not defined from both sides.
katex is not defined
Check your work by substituting the answer into the equation.
Step-by-step guide: Solve equations with fractions
Test your grades 6 to 12 students’ skills on how to solve math equations with this 15-question worksheet complete with answers for easy assessment. Save time and quickly identify learning gaps!
DOWNLOAD FREETest your grades 6 to 12 students’ skills on how to solve math equations with this 15-question worksheet complete with answers for easy assessment. Save time and quickly identify learning gaps!
DOWNLOAD FREEHow does this relate to 6th grade math, 7th grade math, and 8th grade math?
There are a lot of ways to use math equations. For more specific step-by-step guides, check out the pages linked in the “What are math equations?” section above or read through the examples below.
Find the volume of the cube using the formula, katex is not defined or katex is not defined
Use the formula katex is not defined to find the volume of the cube.
The sides of the cube are all 8. Substitute the measurements into the given formula.
katex is not defined
2Work carefully to answer the question, one step at a time.
katex is not defined
3Write the final answer clearly.
The final answer is katex is not defined unitskatex is not defined
Does katex is not defined make the inequality katex is not defined true?
Substitute each variable with its given value.
katex is not defined
Solve using the order of operations.
There is nothing to calculate, but you read the inequality katex is not defined is less than or equal to katex is not defined Also consider the inequality on a number line.
Since katex is not defined is not less than or equal to katex is not defined substituting katex is not defined for katex is not defined makes the inequality false. This means katex is not defined is NOT a solution for katex is not defined
*Note that there are an infinite amount of solutions for this inequality – any number less than or equal to katex is not defined makes the inequality true.
Find the value of katex is not defined when katex is not defined and katex is not defined
Substitute each variable with its given value.
katex is not defined
Solve using the order of operations.
katex is not defined
katex is not defined **Remember katex is not defined is the same as katex is not defined
katex is not defined
Solve the equation for katex is not defined
katex is not defined
Identify the inverse operation to use.
katex is not defined
Because of the commutative property, this equation could also be written as:
katex is not defined inverse operation is subtraction because subtraction undoes addition.
Do the inverse operation to both sides of the equation.
katex is not defined
katex is not defined
Solve for the unknown variable.
On the left side of the equation katex is not defined leaving just katex is not defined which is the same as katex is not defined
On the right side of the equation:
katex is not defined
Check the answer.
Solve the equation, katex is not defined for katex is not defined
Identify the inverse operation to use.
katex is not defined inverse operation of division is multiplication.
Do the inverse operation on both sides of the equation.
katex is not defined
Solve for the unknown variable.
On the left side of the equation: katex is not defined
On the right side of the equation: katex is not defined
katex is not defined
Check the answer.
Solve for katex is not defined
Identify the operations that are being applied to the unknown variable.
The unknown is katex is not defined
Looking at the left hand side of the equation, katex is not defined is subtracted from katex is not defined and then divided by katex is not defined (the denominator of the fraction).
katex is not defined
Apply the inverse operations, one at a time, to both sides of the equation.
First, multiplying both sides of the equation by katex is not defined
Then, add katex is not defined to each side.
katex is not defined *Multiply each side by katex is not defined
katex is not defined
katex is not defined *Add katex is not defined to both sides.
katex is not defined
Write the final answer, checking that it is correct.
The final answer is katex is not defined
You can check the answer by substituting the answer back into the original equation.
katex is not defined
Use this quiz to check your grade 6 to 8 students’ understanding of math equations. 10+ questions with answers covering grades 6, 7 and 8 math equations topics to diagnose learning gaps!
DOWNLOAD FREEUse this quiz to check your grade 6 to 8 students’ understanding of math equations. 10+ questions with answers covering grades 6, 7 and 8 math equations topics to diagnose learning gaps!
DOWNLOAD FREE1. Find the area of the triangle using the appropriate formula.
Use the formula katex is not defined to find the area of the triangle.
Substitute the measurements into the formula and solve.
katex is not defined
The area of the triangle is katex is not defined
2. Find the value of katex is not defined when katex is not defined
Substitute each variable with its given value.
katex is not defined
Solve using the order of operations.
katex is not defined
3. Which number is a solution for katex is not defined
Substitute each variable with its given value and then read each inequality:
katex is not defined is greater than katex is not defined
katex is not defined is greater than katex is not defined
katex is not defined is greater than katex is not defined
katex is not defined is greater than katex is not defined
Substituting katex is not defined for katex is not defined makes the inequality true, so katex is not defined is a solution for katex is not defined
4. Solve the equation for katex is not defined
katex is not defined The inverse operation is division, so divide both sides of the equation by katex is not defined
katex is not defined
On the left side of the equation: katex is not defined and katex is not defined
On the right side of the equation: katex is not defined
katex is not defined
Check:
5. Solve the equation for katex is not defined
katex is not defined The inverse operation is addition, so add katex is not defined to both sides of the equation.
katex is not defined
On the left side of the equation: katex is not defined so katex is not defined is left.
On the right side of the equation: katex is not defined
katex is not defined
Check:
6. Solve: katex is not defined
First, multiply both sides of the equation by katex is not defined
Next, add katex is not defined to both sides.
Finally, divide both sides by katex is not defined
The final answer is katex is not defined
You can check the answer by substituting the answer back into the original equation.
katex is not defined
Math formulas make work in mathematics more efficient.
While students always spend ample time working to build ideas around a mathematical concept, formalizing it with the use of a formula (like the area of a triangle as katex is not defined allows them to move forward in their understanding and answer more complex questions.
Growing shape patterns start with a shape and grow in a constant way from term to term. Students learn how to write general rules for these patterns. For example, “Start with 2 circles and add 3 circles each time.” This can then be translated into a math equation for the pattern: katex is not defined, where n = the pattern term number and t = the total number of circles.
See also: Shape patterns
Students will learn about the Pythagorean theorem in the 8th grade.
Students start with simple equations and math formulas in elementary school and then progress to solving linear equations and systems of equations in middle school.
In high school, students continue to expand their knowledge by learning more advanced equations such as quadratic equations (including the quadratic formula), exponential equations, and trigonometric equations.
As they move into college level courses such as precalculus and calculus, they will solve rational equations, logarithm equations, parametric equations and differential equations
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
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Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
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