High School Resource

Classroom Idea: Math and Time

• Have students make multiplication and addition charts for a 12-hour clock, using only the numbers 1-12.
• Have students determine if the system is closed under addition and multiplication. If not, they should give a counterexample.
• Have students determine if multiplication and addition are commutative under the system, and if not, give a counterexample.
• Have students determine if there is an identity element for addition and multiplication, and if so, what are they?
• Have students determine if addition and multiplication are associative under the system, and if not, give a counterexample.
• Does each element have an additive and multiplicative inverse?
• Determine if multiplication is distributive over addition (if not give a counterexample) and if addition is distributive over multiplication (if not, give a counterexample).

Related NY State Academic Standards: MST3.C.NN2.MA.C, MST3.C.OP3.MA.D

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