Students will learn how to determine whether two expressions are equivalent. Specifically, each expression consists of positive and negative terms, and one or more of the expressions may need to be distributed, in order to compare the two expressions. For example, \(-s \cdot t \cdot s\) is equivalent to \(s \cdot (-s) \cdot t\) but not \((t - s) \cdot s\). These problems make use of the commutative and associative properties of multiplicaiton, as well as the fact that multiplication distributes over addition and subtraction. Students will not be asked to justify the equivalence by stating the property used at each step, they will simply be asked whether the two expressions are equivalent. Here's a lesson and here's practice.
Next, give your students these challenges:
Conclude by leading this investigation:
Jumping Frogs (patterns, counting, primes)