We started the week with a quiz on bank accounts, balancing a checkbook, and simple interest. After the kids were done with the quiz, I used a pop culture reference to introduce compound interest, which was the next thing on the curriculum calendar.
See, I am awesome. I intersperse my lessons with pop culture references.
We watched the Futurama episode “A Fishful of Dollars”. In this episode, Fry goes to check his bank balance as his old bank is still in business (unlike Visa or MasterCard). His balance in 1999 was 93 cents, and after 1000 years of accruing interest at a rate of 2.25%, he now has $4.3 billion dollars in the bank. Yes, we watched the whole episode just so we could see this one scene. Worth it.
The rest of the week wasn’t as interesting, as we learned about the compound interest formula and we learned about how to calculate the future value of an investment in which you are making recurring deposits (another formula). I learned that, in spite of my warnings and reminders, the students are still really bad at figuring out how many times per year the interest compounds, which is what the compound interest formula calls for. For example, if it compounds semiannually, they know that means every 6 months, so they plug 6 (or sometimes .6, which is weird) into the formula. It’s supposed to be 2, because the interest compounds twice in one year.
I’m not sure what to do about this misconception, except to continue to remind them to watch for it. I’m also not sure I could teach the formula any differently. We do start with an introduction to the concept (last week) where they calculate the compounding by hand using the simple interest formula. Maybe I could make a better connection between this introduction and the formula to help them see what is going on?
Because Financial Lit is the lowest-level math class we offer for seniors, this group of students has had a bad history with math. They tend to be very math-phobic and believe they can’t “do math”. They tend to want me to just give them “the formula” for everything, which is a problem when most of the questions in the class require logical thinking instead of a “formula”. (It’s also a problem because they often can’t use the formula accurately, as I mentioned above.) I love these kids, and I love teaching this subject, but I often have to remind myself that they are not “me from 10 years ago”. They are the opposite of “me from 10 years ago”.
This is why I’m not sure how to address this misconception. I’m fairly sure it’s a memory issue (what the n actually represents) not a true lack of understanding. Reminders and practice may be the only real thing that will help, in this case.
For the first 3 days of the week, we took a break from integers and number lines to introduce rate of change, which is what they learned about in their Algebra 1 classes this week. The activity we did was designed for a lower grade level, so it didn’t really get into the rate of change concept much, but it did spend a lot of time looking at the relationship between distance, speed, and time. I liked how it used those relationships within the real-life idea of a road trip in order to get students to calculate all 3 of those variables at least once during the lesson. It was very concrete. At the end of the lesson, the students were asked to choose between the option where the distance was longer but the driver could drive faster and used more gas, or the option where the distance was shorter but the driver had to drive slower and used less gas. One class even asked how much gas costs to help them make this decision.
I loved how much the kids seemed to enjoy and relate to the lesson. They needed a fair amount of hand-holding to get through the concepts, and I’m not sure how much of that is because of the concepts and/or wording in the lesson vs. the students’ lack of confidence in themselves when it comes to math (another group of kids coming from tumultuous relationships with math).
(Note: I don’t believe I can share this lesson, which came from the National Math and Science Initiative, due to copyright restrictions. If you have access to NMSI’s Laying the Foundations program, the lesson is called “Road Trip” and it’s in the middle school resources.)
On Thursday and Friday we got back to integers. I think the break was good, both in terms of helping their attitudes (much less complaining than I’m used to) and in terms of giving their brains time to process and store the information. One girl has been struggling with the whole concept of using number lines to calculate the value of integer expressions from day one. She pulled out her notes on Thursday to check that she was remembering correctly and then she counted on the number line to do the calculations. The look on her face when she realized that because of these two strategies, she had gotten every single question on the bell work correct – absolutely priceless! I loved it, and I told her so.
We are having a vertical teaming meeting with the math department at the middle school, and one of the things my department head wants to bring up is the way they teach integers – using tricks instead of understanding.
If the signs are the same then you add the numbers and put the sign in front if the signs are different you subtract the absolute values and put the sign of the bigger number but this only works for adding/subtracting if you are multiplying/dividing then you do the operation and if the signs are the same the answer is positive and if the signs are different the answer is negative.
Maybe I should print out business cards or stickers that just have links to Tina’s Nix The Tricks book on them and leave them EVERYWHERE during this meeting.
The kids NEVER remember these rules correctly so what’s the point in spending 3 years on them? They constantly want to apply the adding/subtracting rule to multiplying (“But miss, I multiplied and the bigger number is negative so the answer is negative!”) and vice versa (“But miss, -3-3 is 6 because both signs are the same so the answer is positive!”). Just use a number line! In fact, why don’t we teach addition and subtraction this way in 1st grade – just use a number line! Imagine all the misconceptions we could deal with just by teaching kids that all numbers (including fractions/decimals) have a value and a location on a number line, and any number line can extend infinitely in both directions, and can be “zoomed in” or “zoomed out” as far as you need! Number sense! Comprehension of fractions and decimals! Algebraic reasoning! Equivalence!
I should write a commercial – “Number lines will solve all your math teaching problems!”
The kids took quizzes on Friday, and I haven’t graded them yet. I did see a lot of kids counting on their number lines during the quizzes, however, so I have high hopes.
Number Lines that I use: