Reasoning about Equations with Tape Diagrams
The purpose of this lesson is to make connections between a tape diagram and an equation of the form \(px+q = r\) or \(p(x+q) = r.\) Students match tape diagrams to corresponding equations and sort them into categories, and then they draw tape diagrams to represent equations. They use the tape diagram and the equation to reason about a solution, but it is expected that students reason using any method that makes sense to them. It’s not yet time to teach particular methods for solving particular types of equations.
- Coordinate tape diagrams and equations of the form $px+q=r$ or $p(x+q)=r$.
- Create a tape diagram to represent an equation of the form $px+q=r$ or $p(x+q)=r$, and use it to solve the equation.
- Identify equivalent equations, and justify (using words and other representations) that they are equivalent.
Let’s see how equations can describe tape diagrams.
- I can match equations and tape diagrams that represent the same situation.
- If I have an equation, I can draw a tape diagram that shows the same relationship.
Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.
For example, \(3x+4x\) is equivalent to \(5x+2x\). No matter what value we use for \(x\), these expressions are always equal. When \(x\) is 3, both expressions equal 21. When \(x\) is 10, both expressions equal 70.
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