Today was the last day of estimating song lengths. I was sad. It went out with a marathon song, Jethro Tull's Thick as a Brick. Notice the contrasting reasoning here. The first student multiplied 5:47 by 3 and got 16:41. Another student thought it was 1/4 of the song, but converted to seconds first and then multiplied by 4. This got him 1388 SECONDS, which was then divided by 60 to get 23 remainder 8.
I pointed out to all classes how important it was to interpret the different units of minutes and seconds and asked why the first method didn't work. I also liked how some classes students shared their distributive property thinking and did 3 times 5 minutes, to get 15. Then 3 * 47 then converted the last product to minutes and seconds, then added those together.
|Interpreting the division process.|
|Here's the student with distributive property thinking.|
The classwork was continuing investigating terminating versus repeating decimals. I loved how I got as many explanations as I could get for why 57/100 was not equivalent to 0.57 repeating. Not pictured is students saying that one was .57575 and if rounded was .576. The other fraction, 57/100, terminates. It's 0.57. I added that a terminating decimal can have as many zeroes to the right of it and not change the value. One student shared this thinking, then subtracted them. You got a remainder she said, which meant that the two values were not the same.
|Terminating decimals. Comparing. Then fraction to repeating decimal. Students reasoned that the number of 9's in the denominator told you how many numbers were repeating. For example, 19/999 is .019019.... because there rare 3 nines in the denominator.|
|I liked this students thinking on the test.|
|This student wanted to point out the difference between the thousandths place of each decimal form.|
|These students called me over. The bottom right calculator gave the number 1/999 as 1.001 x 10^-1. I thought that that was somewhat odd, and discussed it with them.|
|When the text said there were 2 solutions, some students realized that when you square root both sides you can't forget the plus or minus sign. This equation has positive and i and negative i as a solution. 2 imaginary solutions.|