After a rough start to the school year, things are finally settling down. And by settling down, I mean moving full steam ahead. Now that all the classroom rules and procedures have been set and burned into their brains, we can finally start diving into the mathematics! Yahoo!
This week we started with our first unit in Pre-Algebra, functions! Identify them. Create them. Change them. Characterize them. All kinds of good stuff! The standard below is the specific Common Core State Standard we learned last week (you can find all the CCSS Math Standards here):
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Every day we do a problem to start class. You can call it whatever (bell ringer, bell work, etc.) but in our class we call it the Right Now Rowe (get it? Like, hey you guys, do this.. right now!). Across the hall, Miss Danner calls it the Daily Danner, and even farther down the hall Mr. Eiguren calls it the Everyday Eiguren. But I think my favorite name for bell work in the building is the Stoddard Starter. Might as well make it fun right? Sometimes the problem is review, sometimes it is a foreshadowing/pre-teach type problem, but on Fridays we focus on the language! Every Friday students are given a word that we have learned that week. Their task is write two complete sentences using that word correctly, both grammatically and mathematically. That's it! It seems so basic, but the rewards of doing this have been HUGE in my class.
While taking the WIDA professional development class through the Boise School District, we were taught extensively about the WIDA components of language. The basics can be summarized in the graphic below:
The minute I saw this I had a major AH-HA moment. I took 8 years of Spanish through high school and college and sadly, I cannot speak Spanish at all. I can translate words back and forth okay, but as far as understanding how all the words work together to actually communicate, I am a lost cause. My Spanish career started and stopped at the Vocabulary Usage level. I never learned how to use the vocab together to create more than just a bunch of random words. This is exactly how students must feel in my math class when they are learning the "language of mathematics". I don't want students to just tell me what a function is, I want them to be able to do more than that. This is where our Friday vocab word comes in. We practice taking the word, translating it, defining it, and then USING it to communicate.
Students write their sentences independently and then we share a whole bunch up on the board. As they read their sentence aloud, I type it for the class to see. This way students can hear the sentence, and see it in writing. Great for ELL's! Sometimes I will clarify the grammar or ask if I can add or take away something for it to make more sense. Sometimes I ask if there is a way to keep their idea but change some of the language to be more specific or precise. By the end of the quick 5-10 minute activity, students have seen the word used a dozen different ways and their brains start making even more connections.
This week our word was : output
Check out some of the sentences that students came up with (my edits/suggestions are in parenthesis):
- There can be many inputs all with the same output, and it (the relationship) will still be a function.
- If every input has one and only one output, then it (again, what is it?) is a function.
- If you have an input with more than one output, that is not a functioning relationship.
- Inputs are the x-values and outputs are the y-values.
- The outputs are like the y-values.
- The y-value in an ordered pair is the output.
- A function is when each input has only one output.
- A function has both inputs and outputs. (Although this is true, it's not especially impressive. But I included it to show that not all the sentences were mind blowingly awesome).
- You can show inputs and their matching outputs in a table, a mapping, a graph, or in a set of ordered pairs.
There were a few more, but you get the idea. I love this because I know that every Friday we are going to take a minute and specifically focus on the language. If the week gets away from me and we don't specifically target language integration, I feel better knowing that Friday we will talk language no matter what. Stay tuned for more Friday Right Now Rowe's to come!