Today's estimation was estimating the length of an industrial garden hose. A previously estimated garden hose next to it was pictured. While it was taller, some students reasoned that it was the same length, just a thicker hose. I was pleased to hear them catch this.

One group made their data points extra big. |

After making a scatter plot of Team 1's data individually yesterday, each table was assigned a poster of teams 2 through 5's data. Students voted with their thumbs for what type of association it was. Thumbs up for positive, thumbs down for negative, and thumbs sideways for no association. It was a great way to get instant feedback of the class. It also made students that were not paying attention stick out even more.

Notice how one group drew a line of best fit for one with no association. If it's not positive or negative associations, it's no association. |

If there was an association, they filled out the sentence frame As ______ gets larger, then ______ gets ______. If no association, "There appears to be no association between ______ and _____."

This took awhile, and we also talked about whether each was linear or non-linear. Also, we talked about whether or not there were clusters or any outliers. It took longer than expected, so they barely got to start the next lesson. It will be an abbreviated version tomorrow with an assessment.

In accelerated students started on Chapter 8. Here they reviewed concepts from Chapter 3 when they started factoring quadratics using algebra tiles. Then they practiced factoring using a generic rectangle. They saw that they were basically factoring out the greatest common factor of each column and row, so they could write the area as a product of two binomials. Then they were asked to notice the relationship between the two diagonals of a generic rectangle. Some students did not see the pattern. I scaffolded it at small groups by asking could you add them? One diagonal you could, the other one you couldn't because they were not like terms. I asked what else you could do with the two terms. "Ohhh, maybe multiply?" I don't know if they saw the connection between this and cross products, but we will discuss this.

Here they were given 2x^2+7x+6. You can see the side lengths are (x+2)(2x+3) |

Here students demonstrated that x^2+4x+1 is not factorable because it doesn't form a rectangle. |

Here students made 6x^2+7x+2. Their side lengths were (2x+1) and (3x+2) |

While students were not required to draw their algebra tiles out, this was a great to scale diagram that I was quite impressed by that Zoe made. |

Gabriel demonstrated how he found the side lengths of the middle generic rectangle. |

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