Today's estimation was an Everyday Math workbook. Most students overestimated. It was deceiving smaller than it looked. I did like some students that figured with 180 days in the school year, maybe 2 pages per day, so 360 pages. Others said it was 5 times bigger, so 78 times 5.

I gave students new seats and we started chapter 8. To make the lesson begin quicker, we discussed 4 graph situations to sketch. The first one was the relationship between the months of the year and average hours of sunlight per day. Students knew there were less hours in winter, more in summer, and less again in winter. I told students this is what they'll later study as a cosine wave, a trigonometric function. The second situation was months and a bank account with simple interest. I had them think pair share and then share out what interest is, and what simple interest is.

Some confused it with compound interest, but realized that simple interest takes a percentage of what you first put in and adds it each time period. I was surprised that one student knew the answer to my question, "How do banks make money if they give you money for having money in the bank?" He said that they give out loans and charge a higher interest. So, it was mini lesson on economics.

The third situation was selling an item for 50% of it's price multiple times. 2nd period suggested a popular item is a hover board. I made up that I work part time at a hover board company and got an employee discount and got one cheap. I said that I'm greedy, so I want to increase the price by 50% and sell it. Students reasoned that half of 100 is 50, so the new price is 150. One student who usually doesn't participate was totally zoned in on the discussion and was giving all the answers. The topic of money always gets students attention! After graphing it, students noticed it was a curve. I told them this was called an exponential curve.

The last situation was the relationship between the length and height of a rectangle with an area of 24 square units. This also produced a curve, but I told classes this was called a rational function that they will investigate their junior year.

The lesson was basically about the 2nd and 3rd graphs, but in greater detail. Students realized that simple interest had constant growth and the graph was linear. It was also proportional since it went through the origin. The selling of an $8 baseball card repeatedly for 50% more was an exponential curve, or non-linear. They also said it was not proportional because it did not go through the origin. I was pleased that a few students in each class saw that instead of adding the same number, it multiplied by 1.5 or 1 1/2 each time.

The 4 graphs to start class. |

Then students worked on a pre assessment. I only gave them 10 minutes which was not enough time to finish, but they will work on group posters later this week or next week that will solidify their understanding and allow them to improve their thinking for a final grade later on that pre test.

Using a generic rectangle, then a diamond, and then factoring to find the side lengths. |

Here are the two simple equations to solve it once they've factored. |

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