In this article, we investigate what constitutes a “sentence” in mathematics and how to determine whether a sentence is true or false. We then discuss open sentences, where one of the values in the sentence is not given and the student must determine it. This is one way of introducing basic ideas about variables and algebra.
Students as young as first graders learn about true and false sentences and have already been solving open sentences without knowing the terminology. (For example: 6 and what number make 10?) The explanations and activities that follow are most appropriate for students in Grades 4–5 but can be adapted for younger students.
- Key ‘I Can’ Statement: I can decide whether a mathematical sentence is true or false; if a mathematical sentence is open, I can determine what value(s) make it true.
What Is a Mathematical Sentence?
Think about what makes a sentence in English. A sentence is a complete thought, typically containing at least a subject and a verb. Mathematics can have sentences too, although they look a little different. In math, a sentence is a “complete idea” containing an equality or inequality symbol and an expression on either side. The following are all examples of mathematical sentences.
Notice that if there weren’t an equality or inequality symbol, then the combination of math symbols forms an expression, not a sentence.
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