## Friday, January 22, 2016

### Day 86: undoing dilations & compound interest

Today's estimation was how much money is the chair made of. A lot of students underestimated this. Also, some students assumed the coins were quarters, when they were half dollars.

In class students looked at a shape that was dilated by a scale factor of 4, and wrote down how to undo that dilation and plotted the points. Then they plotted points of a shape that had been dilated by multiplying all the coordinates by 1/3. Most realized they had to then divide by 1/3 to get the original shape, and many forgot how to divide fractions. Some students made the jump that if you multiplied by 1/3 to get it, that means you divided by 3. So, the opposite of that is multiplying by 3. Some students did not see the connection between dividing by 1/3 and multiplying by 3 being mathematically equivalent.

During our closure discussion, I talked about 2 whole pizzas that I baked. I was really hungry so I didn't want to make small slices so I cut the pizzas into slices that were 1/3 of the whole. So, 2 divided by 1/3 is literally how many 1/3's are in 2 wholes? They clearly saw that it was 6. I think this illustration helped students make the connection stronger.

 Students recalled that dividing by a fraction is like multiplying by the reciprocal.

In accelerated I passed back assessments. Some students struggled with coin problems. Some struggled with writing the equations. Others could not settle on a strategy to use to solve it. I've highlighted some of the strategies I observed below:

 This student multiplied his 2nd equation on the left by 4, and then used that to eliminate the q variable, then solve for d.
 This student isolated the variable d and then used substitution. With all those decimals, it was a lot of work. Could have been easier to eliminate the decimals first.
 This student did a LOT of work to solve the problem. First they used fractions and multiplied by 10, which didn't get rid of the fraction 1/4. Then solved for y. Then used substitution. Eventually, it got him the answer. Was it the easiest way? I think not but it worked.
In class students worked on comparing simple and compound interest. Many didn't get to the graphing part, where it's the first time they graph a piecewise function. I think I am going to show them what that looks like and then move on to the next section today.