The focus of this lesson is situations that lead to equations of the form \(px+q=r.\) Tape diagrams are used to help students understand why these situations can be represented with equations of this form, and to help them reason about solving equations of this form. Students also attend to the meaning of the equation’s solution in the context (MP2). Note that we are not generalizing solution methods yet; just using diagrams as a tool to reason about solving equations.
- Coordinate tape diagrams, equations of the form $px+q=r$, and verbal descriptions of the situations.
- Explain (orally and in writing) how to use a tape diagram to determine the value of an unknown quantity in an equation of the form $px+q=r$.
- Interpret (in writing) the solution to an equation in the context of the situation it represents.
Let’s see how tape diagrams can help us answer questions about unknown amounts in stories.
- I can draw a tape diagram to represent a situation where there is a known amount and several copies of an unknown amount and explain what the parts of the diagram represent.
- I can find a solution to an equation by reasoning about a tape diagram or about what value would make the equation true.
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.