Common Core Standards: Math
2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
Multiplication is a bit like a Swiss army knife: it comes in handy across a huge variety of situations. Need to carve an awesome wooden figurine? Check. Open a bottle of wine at a fancy dinner party? Check. Pick a chunk of bear meat out of your teeth? Checkarino. (Also, gross. Just buy a hamburger, dude.)
So it's no surprise that multiplication works just as well with rational numbers as it did for integers and fractions. Your students probably know the ins and outs of multiplication like the backs of their hands, so this standard should be a walk in the park. We're just using familiar rules in a slightly different context.
This standard is a nice excuse for your students to review some of the basic multiplication properties, only with numbers that are a little more complex.
- They should know that multiplying two negatives gives us a positive.
- They should know that multiplying one negative and one positive gives us a negative.
- They should be able to use the distributive property with negative numbers.
As usual, the most important things to watch out for are those plus/minus signs. Multiplying two ginormous negative decimals together will still give us a positive answer, just the same as (-1)(-1) = 1. The digits will be more disgusting, but the rule is still the same.
And don't forget to throw some real-world action in there. Money problems are always a solid bet (pun intended), since decimals are usually involved. If we're in debt to the tune of $77.36 and our debt will triple this year, our problem looks like (3)(-77.36) = -232.08. So we'll owe $232.08, which really isn't bad considering we bought a huge hunk of Grade-A bear-steaks with it.