Today I started class by asking students what activity they did with the cut up shapes on Friday. Students remembered we saw which of the figures were similar to the original shape. They remembered that shapes D and G were not similar. So, I asked them to think pair share about what must be true for two shapes to be considered similar after only about 3-5 students raised their hand in each class. They came up with:
Then students found the scale factor between 2 shapes.
Here we had a discussion about a new shape, shape R with a base of 25. They had to figure out the scale factor.
|I like how one student knew a regular tape measure had about 25 feet, so since this one was small it was about half of it.|
|They saw that the sides of Q were all multiplied by 2.|
|Students talked about how 10 times 2 was 20, and 10 times 1/2 was 5, and 20 and 5 was 25.|
In 2nd period students had confusion about how to multiply a whole number by a fraction, and I'm sure there were students confused in other classes. Some tried cross multiplying. I discussed how cross multiplying is a strategy for solving proportions. What some of them meant by that was cross canceling or cross simplifying, which is a valid step to have an easier multiplication problem. Unfortunately, some students even confused multiplying fractions with dividing fractions by thinking you had to invert one of the fractions. Nope.
|2 strategies for multiplying fractions|
|I forgot to take a picture before erasing but didn't erase this students reasoning completely. She reasoned a tape measure is about 3 inches around. It would go around about 50 revolutions. 50 times 3 is 150 inches. Then she divided by 12, got 12.5 feet and rounded down to 12 feet.|
|When the x is zero y is 100. So, 100 is the y-intercept or A value in the exponential. To get y when x is -1, you divide 100 by 1/2 or raise 1/2 to the -1 to get 2, then multiply by 2, technically the same operation.|
|After a Mathography where a student said she likes writing with her 3D pen, I was curious what she had made with it. I don't know if she made this especially for me, but she gave me this rainbow with clouds. Pretty cool!|