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# 6-A-3-2

last edited by 2 years, 6 months ago

6.A.3.2 Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = q and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.

In a Nutshell

An equation is a mathematical statement in which an equal sign is used to show that the mathematical expression on the left of the equal sign has the same value as the mathematical expression on the right. Equations in the form x + p = q and px = q, where x, p, and q are nonnegative rational numbers, can be solved by performing the appropriate inverse operations on both sides of the equal sign in order to isolate the variable, x.  Once the variable has been isolated, the value equal to the variable represents the solution to the equation.  The solution can then be graphed by placing a point at the value of the solution on a number line. The solution should also be assessed for reasonableness by interpreting the solution in the original context of the problem.

## Teacher Actions

• Develop the ability to model equations using tools such as pan balances and algebra tiles as a strategy for solving and making sense of real-world and mathematical problems involving equations.

• Develop accurate and appropriate procedural fluency in solving equations by engaging in real-world and mathematical tasks that encourage use of a strong sense of numbers, properties of operations, and maintaining equality on both sides of the equal sign.

• Develop the ability to communicate mathematically through writing and discussion with a partner, in small groups, or with the teacher  about using number sense, properties of operations, and maintaining equality on both sides of the equal sign to solve equations.

• Develop strategies for problem solving by interpreting the solutions for equations that represent real-world or mathematical problems by verifying and assessing the reasonableness of solutions in context of the original problem.
• Engage students in making connections among mathematical representations such as the pan balance for equations and using inverse operations to maintain equality on both sides of the equal sign while solving equations.

• Build procedural fluency by facilitating student exploration with of properties of operations and equality in solving equations.

• Pose purposeful questions while students are solving equations to assess the student’s understanding of using number sense, properties of operations, and maintaining equality on both sides of the equal sign.  (Ex. Why are inverse operations important when solving equations?)

## Misconceptions

• The equal sign in an equation sets up a condition in which the expression on the left of the equal sign has the same value as the expression on the right.
• Inverse operations (addition/subtraction and multiplication/division) are used to maintain equality on both sides of the equal sign while solving equations.

• The symmetric property of equality can be used to rewrite an equation like 5 = x + 2 as x + 2 = 5. The same property can be used to rewrite 10 = 2x as 2x = 10.

• Solutions to equations can be any rational number.
• Solutions to equations in the form x + p = q and px = q, where x, p, and q are nonnegative rational numbers can be graphed by placing a point on a number line at the value of the solution.
• Think of the equal sign as a symbol that means "to calculate" rather than "is the same as."

• Struggle to solve equations such as 5 = x + 2 or 10 = 2x, where the variable is on the right side.

• Believe that equations always result in whole number solutions.

OKMath Framework Introduction