Fluency within 5: Shout-out to all the Kinders out there!

Building fluency within a particular range is SO much more than just "knowing your facts." Fluency with numbers is about understanding everything there is to know about numbers. It's just as important to be able to identify a number by what it is as to be able to identify a number by what it is not. When people ask me about my job and tell me that math is "black and white" or that math is a subject that doesn't NEED all these crazy strategies I can't help but smirk to myself.  On the contrary math IS all these "crazy strategies." Math is about understanding numbers and relationships among numbers. That's the part that keeps nerds like me fascinated :)

It is a Kindergarten standard to be fluent within 5, a 1st grade standard to be fluent within 10, and a 2nd grade standard to be fluent within 20. Essentially this means that within these ranges children should have opportunities to explore all of the different relationships among the numbers. I whole heartedly want every child to "just know" 2+2 is 4 (I promise!), but I also want them to know 2 + 1 + 1 is 4, and 5 - 1 is 4, and 4 + 0 is 4 too!

I titled this blog post fluency within 5 because we have a few ideas to help give your kiddos chances to explore all these combinations!
 **This first idea can be easily scaffolded to explore any combinations of numbers 1-12. Odd range, you say?! You'll understand why in a second! :)

Bet the range of 1-12 makes a little more sense now! Egg cartons!! These are great to fill with any sort of counters you have laying around. For this version I rolled a 0-5 dice, filled in the 4 that I rolled with one color and filled the rest of the egg-frame with another color to see the combination that made 5. Just something a little different to shake things up in your classroom. We obviously think it's an eggcelent idea! (Brittany is going to roll her eyes at that pun when she sees I wrote that...)

Can't get enough practice within 5?! Make sure you download our Valentine's Day Mystery Picture for FREE at our store! The puzzle focuses on addition and subtraction practice within 5.

Until next time,

Lindsey  

Introducing Brittany, the (usually) silent partner

So Lindsey finally convinced me to blog - if you’ve ever met me, you will truly understand how big of a deal this is. Writing was never my favorite; math was truly my only interest in school all the way through college, so when I finally landed a job as a math interventionist, it was like winning the lottery (maybe not the most recent powerball, but you get where I’m going with this). I started my new role a year and a half ago and can officially say I will never willingly leave this position. Being able to work individually with the most struggling math learners and see real growth is truly invaluable, and having the best partner to work with is a bonus!

As Lindsey mentioned in the first post, we don’t really consider ourselves serious bloggers or expect a million followers any time soon - it should take at least a couple months to hit the million follower mark, right? We really just want to get our ideas out there to try and open people’s minds about math. The first thing I wanted to discuss is the idea of “new math.” Note: the following rant was inspired by a man very important to me - I won’t give away his real name, but I usually call him “dad.”

So this “new math” stuff…spoiler alert, it’s not new! For as long as humans have had a brain and been learning math, the way the brain develops and understands the concepts of numbers has not changed. School curriculums, however, have changed more than I care to think about. I have been a teacher for five years and have already been exposed to two math curriculums and three literacy curriculums. We’re always trying to find the newest, best way to teach kids; everyone definitely has good intentions, but we’ve made things far too complicated. Currently in Wisconsin we teach the Common Core standards (cue the booing, hissing, and grimaces). Alright… you’re still here? Good, glad we got that out of the way. The point of Common Core - and hopefully all newer curriculums - is to get back to basics. Get back to letting kids play with manipulatives and discover the foundational mathematical concepts of how numbers work. We need to stop teaching tricks and shortcuts before they understand why they work. That’s it! Everyone was so worried about getting our math scores to advance that we forgot to make sure they were understanding the math we were teaching. Instead we jumped to teaching meaningless, memorized procedures. The Common Core does not tell teachers how to teach math, it simply states what each student should know by the end of a given school year. Teachers are now allowed to use their college degree, along with creativity and professional judgement, to design instruction that best meets the needs of their students - crazy, right? So you’re probably wondering what my dad has to do with this… well, here’s the story: I was vacationing with my whole family in Las Vegas last summer (we went to see a Rush concert, don’t judge) and my dad made a comment about the “new math” and how we shouldn’t change the way it was taught when he learned math. So I decided to explain my stance through the application of a math problem, of course! I told him to do the following problem mentally: 16 x 6. He quickly came up with the answer 96. When prompted how he solved the problem, he said that he knew 10 x 6 was 60 and 6 x 6 was 36, and 60 + 36 = 96. Boom! Without even knowing it, he fully validated the common core. A lot of students I work with now do not have these flexible, mental strategies. They only know the written algorithm, which would have taken twice as long, required a pencil and paper, and even the slightest error could have made the answer far from reasonable (which they probably wouldn’t have recognized as unreasonable, but I’ll save that for another day). We want our students getting back to understanding how numbers work together so math makes sense to them. The Common Core emphasizes slowing down the learning process, giving kids time to make sense of their problems, and encourages students to use multiple strategies. We also encourage our students to explain their strategies; if you can explain why something works or doesn’t work, then you’ve shown a true understanding of that concept.

Phew, we made it! Thanks for sticking through to the end. Like I said earlier, I’m not much of a writer - but when I get started with something I’m so passionate about, I tend to get a little worked up :)

100 Charts... Improved!

I know the 100th day of school is approaching and that is very exciting, but it’s also a great time to bring up an issue I have:

I have beef with 100 charts. I know, pick your battles right? Well I am choosing this one. 

At one point during one of my extensive training regarding mathmatics there was a brief conversation about how 100 charts would be better written if they started at 0. I wrapped my brain around the idea rather quickly because it really did make sense to me. Typically I am not a proponent of change, but this one was something I could really get behind. After working with struggling math learners the last year and a half I can definitely attest that our “typical” 100 chart is confusing for students who already find the subject confusing to begin with. I am constantly striving to help my students discover the relationships between numbers and be able to make sense out of the patterns, but a lot of this goes out the window when you look at 100 chart and the number 20 and 25 are on two completely separate lines.

It’s such a simple fix, but it just hasn’t been made. All we have to do is regard zero as a number - and it is! But who am I to have an opinion on how every 100 chart has been made in the history of all 100 charts, right?! For the sake of my intervention students it was time to take control of the issue and do what every teacher does: I printed off something someone else created! :) Brittany, my colleague, to be exact. We(she) had been creating the 100 charts for our packets to go to 109 and beyond just to be able to line numbers up like I mentioned above. Within a day I saw a difference with one of my students - it was remarkable! Here’s a photo of the finished product:

My coloring skills are lackluster, but printing in colored ink is something to be avoided at all costs :)

To celebrate this 100 chart that I do NOT have issues with here is a list of ideas of how to use a 100 chart as a teaching tool:

*Connect number identification to number sequence: Have a student find a number and start counting! It’s a simple, yet great review for our Kinders and Firsties.
*Use the 100 charts to notice all of the really great relationships numbers offer:
How numbers change into new decades after a “9” number.
How after every decade number the next number is a “1.”
Counting backwards the number before every decade number has a “9” in it.
The columns all have the same digit in the ones place.
Everything follows a pattern - even how it sounds! Except those tricky teens :)
*Find a colored chip and cover up a number, or two, or three, or an entire row! Point out the counter that you want the child to identify.
*Use a 100 chart to help adding by 10s - Remember to start at numbers other than zero, too!
*Grab a blank one hundred chart and throw it in a sheet protector, write in one column or row and have students identify blank spaces by using the numbers provided to figure it out. 

Thanks for reading my vent session :) If you're in love with this type of 100 chart like we are snag this freebie on our TPT site!

-Lindsey

Obligatory First Blog Post - From Lindsey

Wow. To be honest, this is a moment for me; I never every thought I would be writing a blog post, so here goes nothing! :)

Blogging just never seemed like something I would find myself doing. I am a decent writer and most definitely never at a loss for something to say, but I honestly just never felt like what I had to say was important enough that it needed its own social media platform, and arguably I still feel that way. I am still convinced no one, besides maybe my mom and other friends I guilt, will follow our blog. (*Our blog raises a good point, maybe Brittany's mom will follow too!!)  However, the selling point for me was that even if no one ever reads this besides those already near and dear, a blog can and will be a great reflection tool for me. I am super passionate about my career and the position I ended up in and I feel like I do have a lot to share with the world to make it a better place, mathematically at least!

So that's why I (we) are here. We love math. So much it hurts sometimes! In the Fall of 2014 my career changed dramatically when I began a new role to my district: a math interventionist. I have learned and am still learning SO much about how students learn math. Want to know the absolute craziest thing so far about my job? When I tell people (adults) what I do for a living, easily over half of the time their response is that they "could have used me growing up" or that they "could really use me right now." Really? Is that seriously a socially acceptable thing to say as an adult?! There is literally an entire population of capable people walking around who are absolutely okay with admitting they are "not math people." I don't know about you but I have never heard an adult speak the same way about literacy. No one is running around proudly professing they cannot read or write. So what's the deal with math? When I was growing up math was treated just like it was described above, it was something you either understood, or didn't understand - and that was that. Facts and algorithms were memorized, and those of us who got it did not question it because it worked. Those of us who didn't get it just stared at the clock waiting for the end of the period.

My passion about this subject is fueled by these realities. I want every student to have conceptual understandings in mathematics because that is what they deserve. There are studies done, most notably by Jo Boaler, that every single student is capable of learning math to high levels. There are amazing things to find on her website: www.youcubed.org -  I really encourage you to check it out sometime!

Our blog is our blog because there are two of us. I am Lindsey, a bilingual math interventionist, and I work with my partner Brittany, who is also a math interventionist. So basically our jobs are two-fold: We work with students in an intervention setting for math, and we also support our staffs in implementing math from a more conceptual place through a math workshop. We are not math workshop experts, but at the current time we are the most knowledgable people in our buildings regarding math thanks to how much our district has invested in us so we are who our teachers go to when they are looking for guidance and/or ideas. We began to create materials for ourselves and our teachers that fit this conceptual understandings ideal we hold near and dear.  One day we were encouraged to try and sell the things we have created on Teachers Pay Teachers. Again, feeling a bit inadequate, we tossed the idea around at first for quite awhile before diving in. We browsed the site for what kinds of products were out there and selling well and decided to give it a shot. We already had a lot of products made, now we just had to make them marketable and visually appealing to a buyer.  We are both pretty tech savvy and that has definitely played to our advantage.  Mid-November we opened up our store and we are gaining momentum every week! It's been a lot of fun and a great experience for us - our significant others also enjoy a reason to spend time together doing all sorts of "productive male things" on the weekends while we hold our TPT workshops in the kitchen over a bottle(s) of wine. I look forward to this piece of the puzzle and how it unfolds :) Thanks for reading!

-Lindsey