Help me DECOMPOSE this TEKS!

Did anyone want to throw in the towel when they realized our second and third graders were expected to "decompose numbers in more than one way"?

No? Just me!?

I don't buy it; you weren't too fond of this concept either. After all, those of us who taught older students certainly inferred that students were already struggling with place value in their younger years because when they show up in 4th and 5th grade, they're exhibiting misconceptions with place value. I remember sitting with some teachers in our first PLC before the school year began a few years back and deconstructing the following TEKS:

Use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens and ones. (2.2A)

Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate. (3.2A)

I'd like to submit, however, I believe this NEW standard will significantly assist our students with building a stronger foundation in mental math and their ability to fluently manipulate numbers as they develop in math. 

This video blog is dedicated to my 2nd and 3rd grade teachers!

[image from http://whoswhoandnew.blogspot.com/]

Partial Quotients Part III- Traditional Algorithm

Much like division being a complex concept for students to grasp, so teaching the concept can be quite daunting for teachers. For that reason, this video blog series centered around division has been "divided" (no pun intended) into three parts.

In efforts to avoid cliche and ill-advised "tricks" such as "DSMB: Does McDonalds Sell Cheeseburgers" to help students remember a myriad of steps, the video blogs I've created have been designed to assist with building the traditional algorithm from the ground-up.

If you haven't already seen Part I and II, it's imperative that you do, prior to watching this final video. After all, this blog is built on the premise that you as the teacher, have laid the foundation from parts 1 & 2, respectively.

With that being said, scroll back in my blog site to find those videos...otherwise, click play & enjoy!

Fractions on a Number Line

Happy Holidays! (In my native language, "Merry Christmas")

So what fraction of Christmas day do you spend with your family? What fraction of Christmas dinner are you able to eat? What fraction of the year is spent celebrating holidays? Okay, okay, okay...enough fraction questions already, right?

Well students aren't too fond of fractions either, but I think all of that is due to misunderstanding of the concept. Fractions don't have to be a tedious concept when we scaffold how students develop in this area. What fraction of a role do we, as educators, play in that developmental process? 1 out of 1!!

Although the idea of fractions begins as early as Kinder (and in some programs, Pre-K), in Texas, 3rd Grade is when students begin to see fractions in their numerical form and plotting fractional points on a number line. This can seem overwhelming for a Third grade teacher, but the fact that students are coming from 2nd grade with experience in fractions, and will move into 4th and 5th continually plotting fractions on various number lines (with decimals and graphs), this might help you breathe easier. Third grade teacher, you are only laying the foundation for fractions on number lines. But so we ensure we lay a great one...here's a quick gift from me to you! Merry Christmas!

Let's unwrap how to plot fractions on a number line!

Partial Quotients Part II- Area Models

You may have seen part I (Arrays) for developing representations for division of two-digit by one digit (which can also be used to do three-digit by one digit as well as four-digit by one digit).

In 4.4E, the expectation is also for students to build area models for up to four-digit by one digit problems!

Watch the video below for how to develop this representation with your fourth grade students.

Enjoy and let me know what you think!

Partial Quotients- Part I (Arrays)

Okay, I know nobody likes division! And I'm pretty sure if your students are like mine, they think it's the "hardest thing EVER!".

For this very reason (or reasons), I love the new standards in 3rd and 4th grade that allow students to return to the foundations of math and build models to represent the "long division" beast!

Check out this 4 minute video on 4.4E (fourth grade long division from a concrete and pictorial standpoint).

Tell me what you think!

Digital Science Fair!

Question: Can students create Science Fair projects using digital tools rather than science fair boards?

Hypothesis: Yes, I believe Science Fair projects can be created with digital tools because we can teach students to be more environmentally conscious, students are already acclimated to digital resources and there's an opportunity to share their product, globally!

I saw an amazing display of student work the other day when I was asked to judge the Digital Science Fair at a local school! Students in grades 3-5 had created their science fair project displays in Google Slides and sent them to their Science Specialist. After sorting them into folders in Google drive, we were able to log into google drive and view their displays. 

I was wow'ed even after I watched a Kinder class that had created their display in the Photo Story program and narrated the processes of their science fair class project under the direction and facilitation of their teacher. After scoring and selecting the top 3 winners from each grade level, we were able to walk down to the cafeteria where tables were set up and the 16 finalist were sitting on the left side with their laptops ready to present! 

Shortly thereafter, their student peers from the grade levels poured into the cafeteria and fanned out like crazed fans until they were sitting across from the finalist and viewing their presentations. With star-gazed eyes, 8, 9 and 10 year olds were deep in conversation, heavily engaged with their classmates about the projects that made the final cut! What a sight to behold!

Here's how (through the lens of the Scientific Method):  

Materials: Computers, digital cameras, Excel, iPod touch, iPad, voice recorders, iPhoto, iMovie, HDMI cable, iPhone or Smart phone, Rubric, Google doc (slides), Photostory program, science fair project references, and lab equipment for the experiments.

Sample Rubric

Research: Technology enables our students to assimilate knowledge more readily by employing a wide variety of media addressing all learning styles in our classrooms. We serve urban school children who are are primarily visual/kinesthetic learners who are often intimidated by written instructions. Using a digital camera, a computer, iPod touch, classroom iPads. I will produce school-wide video instructions showing students how they can document, produce and present their science fair project digitally. (source cited: http://www.weareteachers.com/lessons-resources/details/creating-digital-science-fair-projects)

Procedures: 

1. Students are given various research topics to choose from and/or are allowed to pick their own topic (with approval from teacher).

2. Students should be given a rubric and that rubric addressed in a thorough manner from the teacher so students know what the expectations are. 

3. Students do the Science Project either at home or in pairs/groups at school.

4. Students take pictures of their project using a digital camera or phone.

5. Students create their results and analyze their data (then create a graph in Excel or Word).

6. Students draw their conclusion.

7. Students create their project and digitally put it together using iPhoto, iMovie, Power Point (Google Slides) or Photo Story.

8. Students turn in their digital projects (via Google drive) to be scored/judged and finally, to present to their peers.

Data: 

Students hovering around the finalist to view their presentations.

This project had the attention of several students!

Conclusion: 
So, can YOUR school do Digital Science Fairs? Well, I've seen it done and although it may take some tweaking to differentiate it for the needs of YOUR campus, it IS, indeed, possible!

Number lines are strategies too!

I was planning with a 4th grade team the other day and after we discussed what the TEKS meant and what strategies we needewd to use to teach it, we dug into the idea of resources needed.

So the TEK was 4.3CD which states "determine if two given fractions are equivalent using a variety of methods" and "comparing two fractions with different numerators and different denominators and represent the comparison using symbols."

After we discussed using various fraction tiles, towers and circles for students to manipulate to find equivilencies for different fractions such as 1/2, 3/4, and 2/3 to name a few; a teacher brought up the fact that the students needed to also use number lines to identify equivalent fractions (based on the released questions and other resources utilized to unpack the standard).

She was absolutely correct! Students are bringing (or should be) in prior knowledge from Third grade with representing fractions on a number line via 3.3F. Benchmark fractions (0, 1/2 and 1) are a great place to start and utilize as a reference point. Conceptual understanding should include students knowledge of 0 as zero out of the total pieces and 1 whole as the entire number or set of pieces in the fraction (ie: 5/5).

Background knowledge (and pre-teaching or re-teaching) should also include building a number line that emphasizes counting the spaces between notches on a number line. Anyways, back to the thought-provoking idea a teacher came up with. She decided after teaching the initial concepts in her mini-lessons, she would create a station that allowed students to build number lines to compare fractions and/or find equivalent fractions.

So I reached into my stash of number lines and various fraction cards and we created some procedures to implement this activity as a station.

1. Have two students each pull a card.
2. Have both students predict (using benchmark reasoning) which fraction is larger (or smaller).
3. Have both students create/draw a number line (on pre-laminated sentence strips).
4. Use the number line to justify which fraction is largest by describing which benchmark fraction it's closest to.

Possible sentence stems:
"My fraction is __________, because its closer to _______."
"My fraction is closer to _______________, so it is ______________."

Enjoy the opportunity to engage in dynamic coversations with your colleagues (fellow teachers), as many great, simple station ideas can emerge from a clear understanding of the standards.