Pre-Lesson Information:
| Teacher figures out what students know about division (basic and long) | Students answer questions or complete assessment |
| This information helps guide future lessons and supports students who are struggling |
Generate:
| Teacher gets students to compare multiplication and division and their relationship | Students create fact families, skip counting sequences, etc. to show relationship
Students create a relationship between the two concepts |
| When do we use multiplication and division? | Division – Used for splitting items among groups, for sharing, for splitting bills at a restaurant, etc.
Multiplication – for purchasing more than one item, etc. Understanding multiplication will create a solid understanding of division |
Evaluate:
| Teachers asks students to think about basic division and try and figure out how to solve more complex problems (long division) | Students explore and evaluate questions. Can they figure out how to solve the questions?
Can students figure out what steps are required to different solve problems? |
Modify:
| Teacher asks students how to figure out problems with remainders.
How can students use their existing knowledge to solve the problems? |
What happens when a number does not divide evenly?
What can be done with the “leftovers?” (decimals, remainders) When would we use decimals vs remainders? |
The concept that I chose to explore is long division. Using the T-Gem method, I’m hoping that integrating technology into the process will help students grasp the concept a little more easily. I will start with a bit of information about my class dynamics and what I have done before re-introducing these students to long division. In my math class, even though, I have a grade 7 class, I have only 8 students who are actually at a grade 7 level. This has caused our school to take a closer look at how we can best support our struggling learners, since the majority of them have not been tested and therefore, are not on an IEP. As teachers, we are not able to modify the curriculum, but rather, we must do our best to adapt it in a way that makes it accessible for these learners. As part of our PLC (professional learning community), we have created small groups that focus on mastering one or two concepts before moving on. Our goal is to try and fill some of the gaps that these students have so that they can feel a sense of success. At the beginning of the year, we administered an assessment to all the grade 7s so that we could see what concepts they had mastered and what concepts they needed to spend more time on. After working with our students and looking at this assessment, we discovered that there are quite a few students who do not understand how to do long division.
I believe the first problem with long division is that many of the students do not have a solid understanding of basic division. With these intervention groups at my school, this is where we began our lessons. We started with having the students use manipulatives and moving (dividing) these manipulatives into groups. The students were shown some videos to help explain the process (BrainPop, Khan Academy). We also related division to multiplication and showed how they are related (fact families, etc.). Phet has a division simulation that helps show this relationship. The students played “games,” worked with partners, and used whiteboards to practice. Throughout the process, the teachers in the room observed the students and created formative assessments to make sure all of the students were grasping the concept successfully.
Once this small group of students had a deeper understanding of what division is, they moved onto long division (this is the stage they are at now). One strategy that was used had the students using post-it notes to show the relationship between the numbers.
http://middleschoolocd.blogspot.ca/2013/09/throwdown-linky-post-it-note-division.html – Sorry, I couldn’t figure out how to get the visual in this document.
This helped students see where the numbers go, the relationship between the numbers and the importance of lining up columns (this was an issue for many of these learners). One colour is used for the divisor and one for the dividend. The quotient and product are the same colour as the divisor so students can see that they are related. The difference is a third colour (yellow). I am trying to figure out how I can make this digital. Does anyone have any suggestions? Once students have mastered the PROCESS of long division (I find this takes longer than expected), there a tons of games, programs, videos and apps that help students practice this skill to create a solid understanding of how to complete long division questions.
Games:
Who Wants to Be a Millionaire: http://www.math-play.com/Division-Millionaire/division-millionaire.html
Snork’s Long Division Game:
http://kidsnumbers.com/long-division/
Math Mountain:
https://www.funbrain.com/games/math-mountain
Drag and Drop math:
http://mrnussbaum.com/drag-and-drop-math/
Long Division with Scratch
https://scratch.mit.edu/projects/1387273/
Programs:
Mathletics
Apps:
Division!! (free)
https://itunes.apple.com/ca/app/division/id492164003?mt=8
Long Division Touch (free)
https://itunes.apple.com/ca/app/long-division-touch/id574226151?mt=8
Videos
Khan Academy
https://www.khanacademy.org/tag/long-division
Brainpop
https://www.brainpop.com/math/numbersandoperations/division/
One app that is great for getting students to show their understanding and thinking is Explain Everything. In the past, I have had students create a “how to” book so that they can teach others how to do long division. I find this to be a very helpful strategy.
What strategies, resources or technology do you use to teach your students long division?
Nicole
On a side note, I absolutely loved the interactive Periodic Table in the Chemland Interactive website and wish I was able to use this during my chemistry course. Even though many of the concepts within this website are beyond what my grade 7 students are learning, some students might like to explore it if they have an interest in this subject area. In grade 7, students are learning a very basic level of chemistry, but this does not mean that some would not like to extend their learning and use Chemland to do that. They can click on any of the elements to learn more (density, boiling point, melting point, etc.). I also like that the descriptions are clear and written in a way that students can understand.
Nicole,
I have to say, when I first saw your posting, my initial reaction was, “What? Long division? NO WAY students are going to come up with how to long divide by themselves.” I remember when I was learning, the entire process and keeping the lines straight and neat was so outside of what I had ever thought of that I initially didn’t’ see how you were going to accomplish this.
However, after reading what you have put together here, it seems quite feasible! I liked how you divided (get it? 😉 ) the process into sections with guiding questions for each section.
Just as an experiment, I wonder what students would actually do to try and figure out how to long divide without these guiding principles in place?
I do wonder, though, in your generate section, if this is pure T-GEM, as from what I understood, they need to generate hypotheses, not simply background knowledge. So, perhaps the generate section would be more of questioning how do you think numbers are divided? Or how is a bill divided evenly?
With that said, I prefer your way and wouldn’t change it just to try and fit it into the GEM process, as the latter parts are very clearly GEM.
Great, thorough work!
-Jonathan-
Hi Jonathan,
Thanks for your feedback. It’s always nice to hear other educator’s perspectives. I wasn’t quite sure if it fit perfectly into the T-GEM model, so I’m glad you noticed that. Do you have any great programs that you’ve used to teach division?
Nicole
Believe it or not, I have never been called on to teach math! But, I do know that there are some apps out there that my nieces have been using. The iReady program has a competitive head to head mode where students “compete” to answer problems. (Granted, this would be more review, than teaching.) Most of the ones that I have seen have been more drill oriented, less exploratory. But, I wonder if you could link it together with media skills and ask students to create manipulatives and record a short “informational video” about how to do long division.
Hi Jonathan,
Thanks for sharing your ideas! I’ll have to look into the iReady program.
Nicole
Hi Nicole
I like the fact that you brought me back to my elementary days of doing long division. I am not sure if I enjoyed it or not. I played around with the Scratch app for a few minutes and found it confusing – I found the Intro slow and I believe students would need some pen and paper practice first.
I wonder if the Scratch app could have used a movie with sound so that users could scrub through.
A good next step might be to rate or list the top three apps teachers should use.
Christopher
Thanks for your feedback Christopher!
Yes, I have been trialing this “unit” with a small group of students. I think rather than having them work through Scratch, I might have them create their own coding video instead.
So far, if I had to rate the apps, I would rate explain everything first because the teacher can give students questions to solve, they can create their own questions and they can also record their steps and thinking so that the teacher can see if they are having difficulty. This is not a division app, but rather, it can be used across the curriculum.
The second app that I would recommend is Math Mountain (this is a program and can be used on any device). This has been a hit with my students and I often hear them saying that “math is fun!”
The third app that I would recommend would be math bingo – which I didn’t even put on this list. This is a game that works on addition, subtraction, multiplication and division. The kids love it and it works well with my struggling learners.
Nicole