Real Life Examples Are Not Always Real!

 

I've come to the conclusion that so many "Real life" examples we find in books or on the internet are seen by students as fake.  Look up real life uses of fractions and you always get recipes showing up.  The idea behind that is when you want to change a basic recipe to feed more or cut it so it feeds fewer people, you will either multiply or divide by a specific number.  The problem with this scenario is that people seldom actually do that.  

For instance, my father is the dump it in until it tastes right and looks like it should feed everyone while my mother takes the measurements in the recipe and just makes two of them rather than multiplying everything by 2 or dividing the materials in half physically.  She never bothered with the math.  Most of the people I know, fall into one or the other although I actually do know an engineer type who does sit down and mathematically adjusts all the measurements before he prepares the food.

A more practical example using fractions for my students is the idea of needing to purchase wood for a project such as building a bookcase or a bed, or a house where the measurements include fractions.  It is easier to use a drawing with measurements and have students calculate how much total wood they'd need to purchase at the store.  This is something they can relate to because people around here build houses, and other things.  Another area that uses fractions is sewing where one has to buy enough fabric to create dresses or clothing. Often the measurements are in given in fractions so when one has to read the back of a pattern, they are encountering fractions.

The standard example of a pizza is something most people do not really talk about in terms of fractions.  They see pizzas as having pieces.  Yes you might eat a half of it if you are rather hungry but few people go out and talk about eating 3/8th of a pizza which is what some problems have you calculating. 

As for inequalities, the textbook we use doesn't give any real life examples my students can relate to.  I ended up asking them about their ATV's and the amount of gas they held.  I asked if they always filled the tank with the exact same amount each time they needed gas?  I also asked them what would happen if they tried to put more gas into the tank than it could hold?  Eventually we ended up with the idea that filling a gas tank is an inequality.  If the tank takes 8 gallons and x represents the amount of gas being put into the tank is the inequality x < 8.  If you try to put more than 8 gallons, it will overflow and spill all over the ground. That was an example they could relate too.

I took time to mention budgeting in regard to inequalities such as planning a certain amount for rent so that you don't end up spending more than that. Or how much you budget for eating out might be no more than $180 per month. A person has determined they should not spend over a certain amount such as the rent < $1500 per month, or entertainment < $200.  

As far as using integers, there are so many real examples such as temperature changes such as a rise of 23 followed by a drop of 25 degrees or money deposited or withdrawn out of an account.  Or one getting paid money for doing a job and the person who pays the salary is having to subtract it.

No matter what type of real life example you use with students, make sure you include context as you teach the math so it makes more sense to the students.  Let me know what you think, I'd love to hear.  I'm attending another webinar on distance teaching and I hope I get something I can use and share with everyone.  Have a great day.