##
* *Reflection: Grappling with Complexity
The Story of 1 (Part 1) - Section 1: Warm up

**My goal is for as many of the mathematical big ideas to come from my students as possible.** This is really complicated for them and I haven't asked my 7th graders to do problems like this in the past. But, I have learned not to assume that I know what they are and are not capable of. In this lesson I just kept asking them:

- "some groups got the 5 candies each and some didn't. How can the math help us figure out which ones did and which didn't?"
- "why do you think these groups did and these didn't?"
- "what is it about these terms that makes you think that?"
- "what could we look for in the terms that might tell us?"
- "how might we know that a certain group got candy?"

I don't expect every kid to know exactly what to look for right away, but my goal is just that I am not the one sharing the ideas. If one member of the math family group sees it I encourage him/her to share his discovery. I may have a few of my students share with the whole class. **It feels more accessible to everyone if the idea comes from one of their peers than from me.**

I was surprised in a later Number Talk in which I asked them to add 18+36+12 mentally and she used factoring. One student said "I did 11x6 and got 66". I knew it was the right answer, but didn't know right away what she had done. I asked if anyone could see what she was thinking and some of them did. **She had factored out a six from each term 6x3+6x6+6x2 to get 6(3+6+2)**. In an even later Number Talk a student shared that he had tried to solve **32+50+28 by factoring a 4 out of both 32 and 28 to get 4(15)+50** but decided it was too hard and resorted to another strategy. Another student, who hadn't originally thought of it that way, said "no it's not, 4 fifteens on a clock is 60, which is easy to add to 50". I was very glad I had exposed my students to work that I had previously thought above them. Not only were ideas coming from them, but they were building on each others' thinking!

*Give them a chance to surprise you!*

*Grappling with Complexity: Give them a chance to surprise you!*

# 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.

## Big Idea: Students will listen and look for evidence in resource material to support or refute a claim.

*54 minutes*

#### Warm up

*15 min*

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.

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#### Movie notes

*39 min*

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.

*expand content*

##### Similar Lessons

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- UNIT 1: Order of operations & Number properties
- UNIT 2: Writing expressions
- UNIT 3: Equivalent Expressions
- UNIT 4: Operations with Integers
- UNIT 5: Writing and comparing ratios
- UNIT 6: Proportionality on a graph
- UNIT 7: Percent proportions
- UNIT 8: Exploring Rational Numbers
- UNIT 9: Exploring Surface Area
- UNIT 10: Exploring Area & Perimeter

- LESSON 1: Farmer John and Farmer Fred Day 1 of 2
- LESSON 2: Farmer John and Farmer Fred Day 2 of 2
- LESSON 3: Let's Break It Down
- LESSON 4: Halloween Candy to Zombies
- LESSON 5: Extending Farmer Frank's Field with the Distributive Property
- LESSON 6: Who's Right?
- LESSON 7: To Change or Not to Change
- LESSON 8: Let's Simplify Matters
- LESSON 9: Clarifying Our Terms
- LESSON 10: Breaking Down Barriers
- LESSON 11: Number System Assessment
- LESSON 12: Garden Design
- LESSON 13: Ducks in a Row!
- LESSON 14: The Power of Factors
- LESSON 15: Forgetful Farmer Frank
- LESSON 16: Common Factor the Great!
- LESSON 17: Naughty Zombies
- LESSON 18: Reducing Fields
- LESSON 19: Common Factor the Great Defeats the Candy Zombies!
- LESSON 20: The Story of 1 (Part 1)
- LESSON 21: The Story of 1 (Part 2)
- LESSON 22: Simple Powers
- LESSON 23: Equivalent expression assessment