Equality and Inequality
The equals sign is the most misunderstood symbol in elementary mathematics. Most students interpret it as write the answer here rather than as a statement of balance. This misconception causes problems all the way through algebra. Grade 1 is the critical window to establish the correct meaning. True-and-false number sentences with expressions on both sides are the best tool for building this understanding.
The equals sign means is the same as
3+7=10 is true because 3+7 and 10 name the same quantity. But so does 3+7=8+2, because both sides equal 10. Students who only interpret = as the answer is will say 3+7=8+2 is wrong because they expect a single number after the sign. True/false sentences with expressions on both sides directly confront this misconception.
True and false number sentences
Is 5+3=4+4 true? Is 6+2=7+2 true? Each sentence is a mathematical claim that students must evaluate. They must compute both sides and compare. This structure separates understanding from answer-getting: students who can evaluate these correctly have understood the relational meaning of equality.
Inequality and the balance model
Students who used a pan balance in Kindergarten now connect that experience to symbolic notation. When both sides balance, we write =. When one side is heavier, we write the not-equal symbol. The physical model gives the symbolic notation its meaning. Keep the balance present and use it to settle disputes about true/false sentences.