The Story of 1 (Part 1)
Lesson 20 of 23
Objective: SWBAT partially factor variable expressions that can not be completely factored. SWBAT document evidence from an instructional video to support a claim.
This is a warmup shy zombies to extend their learning of factoring variable expressions. It refers to a story I tell when I first introduce the distributive property (Halloween Candy to Zombies) about handing out a certain number of candies to each trick or treater (zombie) on Halloween. For example I may distribute 5 candies each to groups of 2x and 3 zombies, which results in 5(2x+3). We have extended the story to factoring in more recent lessons (Naughty zombies & Common Factor the Great Defeats the Candy Zombies).
Today I give them two expressions [5n+15p+20x+2 & 4e+10k+25x+3] which represent some groups of zombies in which each zombie got candy from me (5 pieces each) and some groups of zombies who were too shy to come to my door to get candy. They are asked which zombies could not have gotten candy from me and are asked to explain.
I expect them to notice that if they have come to my door they should contain a factor of 5, so those that don't have a factor of 5 did not come to my door. I ask students to come up and put parentheses around the groups that received candy. It should look like:
(5n+15p+20x)+2 and 4e+(10k+25x)+3
Then I ask them what they think the expression should look like if we factored just this part to show the number of candies and the groups. They are less likely to forget to put the 5 in front of the parentheses in the first one, but they might in the second. If they do I would remind them that the expression still needs to be equivalent and still show the candy. So it should look like:
5(n+3p+4x)+2 and 4e+5(2k+5x)+3
We also go over the homework factoring subtraction from last night. The most common errors I expect are that they didn't factor the expressions on the second part after simplifying them and some of them still may be having trouble finding the greatest factor in common.
I am showing a PBS movie called "The Story of 1". This is a fun movie about the history of numbers, expecially 1 and zero. My students recently worked on a problem called "consecutive sums" (Number System Assessment, Garden Design, & Power of Factors ) which generated a lot of curiosity about the number 1. They found that they were unable to make 1 or powers of 2 by adding consecutive positive whole numbers after which we generated a list of questions that they wondered about. I think fostering their curiosity in math is so important, because they have been taught for so many years not to ask "what if" questions and just to follow directions. This is their reward for their curiosity.
They don't get off completely scott free however. I use Movie notes the story of one in this case, not for content, but to engage them in a search for evidence in support of a given claim. I have given them a table in which I have made 3 claims. They need to look and listen for evidence for and against each claim and write it into the table. This is a really good format for having students support with evidence and evaluate, compare, & critique claims, which are necessary components of argumentation. This can be used for reading notes as well.
At the end of the table I also ask 3 more questions to connect to their curiosity. I ask them to write down something they learned, something that surprised them, and something they wonder after watching the movie.
Their Take home practice test distributive tonight is a take home practice test that is due in two days.