In this lesson, students consolidate their equation writing and solving skills. In the first activity they solve a variety of equations with different structures, and in the second they work to match equations to situations and solve them. Students may choose any strategy to solve equations, including drawing diagrams to reason about unknown quantities, looking at the structure of the equation, or doing the same thing to each side of the equation. They choose efficient tools and strategies for specific problems. This will help students develop flexibility and fluency in writing and solving equations.
- Interpret and coordinate sentences, equations, and diagrams that represent the same addition or multiplication situation.
- Solve equations of the form $x+p=q$ or $px=q$ and explain (in writing) the solution method.
Let's solve equations by doing the same to each side.
- I can explain why different equations can describe the same situation.
- I can solve equations that have whole numbers, fractions, and decimals.
A coefficient is a number that is multiplied by a variable.
For example, in the expression \(3x+5\), the coefficient of \(x\) is 3. In the expression \(y+5\), the coefficient of \(y\) is 1, because \(y=1 \boldcdot y\).
solution to an equation
A solution to an equation is a number that can be used in place of the variable to make the equation true.
For example, 7 is the solution to the equation \(m+1=8\), because it is true that \(7+1=8\). The solution to \(m+1=8\) is not 9, because \(9+1 \ne 8\).
A variable is a letter that represents a number. You can choose different numbers for the value of the variable.
For example, in the expression \(10-x\), the variable is \(x\). If the value of \(x\) is 3, then \(10-x=7\), because \(10-3=7\). If the value of \(x\) is 6, then \(10-x=4\), because \(10-6=4\).