Day 51: Goldfish Ratio Tables & Graphing

Regular Math Objective: Compare different slopes to determine their real-world meaning

Regular Math Standards: 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 

Regular Math Lesson Sequence: This is a summary kind of the week because I'm writing it four days into it.

Monday was a disaster with the ants and ladybug problem. It was not scaffolded well. It was also not engaging (scaffolding better could have helped here, but there was still more room for growth).

Tuesday we switched up and went to the Goldfish lesson from YummyMath. We didn't like a few things, so we tweaked the version that YummyMath had put out there.

• The font was weird and distracting. 
• There were too many words that distracted from the math and made it seem more intimidating than it was. 
• Students could easily write the wrong ratios in the wrong table, so we spelled it out for them by putting one ratio into the table. 
• The axes on the graph were not labeled. We labeled one axis to ensure that all graphs would look the same, but still hold them accountable to label the other axis. 
• The third question was too vague. We change give an estimate of 700 to 800 goldfish to 750 goldfish. 
• We neglected to give an example of a ratio table. Probably a mistake. More on that below. 

Here was our goldfish activity. 

The first day of the lesson the students spent the entire time on question one putting together the ratio tables. It was like pulling an anchored boat to shore. On Day Two, we eventually got to answering the second and third questions. Even this was an adventure. By Day Three, we finally were able to graph and discuss the steepness. Most students could not answer the seventh question because of time constraints. 

The lesson was worth it, but I would tweak this further. In the future, I would eliminate the fourth question. I would also provide all of the information for the first two ratio tables to cut the time spent on that aspect of the lesson down. I would spend significant time reteaching the vocabulary of ratios, unit rate, and proportion. I also would alter the format on the last question. The students are asked to do four different things within the framework of this one question, so I would isolate each of those three things to make it explicit what they are being asked. 

Honors Math Objective: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 

Honors Math Standards: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 

Honors Math Lesson Sequence:

1. My Favorite No. I explained nothing. Students all got either four or two units for the distance between the points (-2,-1) and (0, 1). I then did not even go over it with them. They were so angry. 
2. QSSQ
3. Exploration. Students discovered that two points distance can be discovered by just using the Pythagorean theorem with a third point. 
4. The exit ticket was My Favorite No. It was amazing to see that virtually the entire class went from not being able to do a problem to all of them being able to do a problem with just a tiny bit of prompting from me.