Integrating Depth of Complexity Gate Frames in Math

As December is upon us, so are these three words: deadlines, drowsiness, and decisions. One thing that probably does not change is the running to-do list that seems to pop into your head as your in bed. Don't forget tomorrow you have yard duty. I have to get to work early to make copies of my math assignment. Jacob, Darren, and Julie were absent, so I need to make sure they make up their test. Remember to switch my ELA and math times because students need to leave for band practice during my regular ELA block.  With extra holiday activities and chronic absenteeism, where do you find time to teach and make sure that everyone is on the same page? How do you alter your instruction to present the material in a way so they won't forget it in over the break and without coming up with something new every single time? Little did I know that the solution was one frame, a soft whiteboard, a dry erase marker, and a dry eraser. Yes! That's pretty much it. Embedding Depth of Complexity frames during my math instruction provides a solid structure for students to further their understanding of a math concept and manipulate it in many different ways. It also offers an opportunity to review previous lessons quickly. The best way for students to find the value in these frames is by using them consistently. 

1 DOK frame, 5 skills captured, ALL minds learning

"Remember, yesterday, we learned about inequalities with rational numbers and how to order them, right?" A sea of wide eyes stare back at me, a few nods, and some furrowed eyebrows expressing confusion look back at me. Alright, let me do a quick 5-minute review, and then we will be good to go. I glance at the clock, and somehow 5 minutes turned into 10 minutes, and part of me questions how valuable it was that time and if I will be able to reach today's learning target because of it. Instead of thinking of what I covered, I think about what didn't I cover! I gave simple problems that I could create on the top of my head within a quick second. I didn't check to make sure they could explain and reason their answer using vocabulary, make them represent with a number line, or have them create a situation. To top it all off, the students who didn't need the review are now bored and off task. Its times like these when I wonder how can I be prepared for these hiccups without taking time out of my day to create a review I may or may not need. That's when I realized I needed something that I could have them take out on the spot to review. Something that required students to enhance their ability to follow written directions and me to pinpoint skills for one given math concept-a depth of complexity gate frame with a few icons did the trick. I didn't realize how much one little paper could allow me to focus on the problematic math skills but also be able to walk around and pinpoint the areas of weakness of strength within a second. With embedding these frames, I could complete

maybe three problems. Now, this may not sound like a lot. Still, within these three problems, students created a real-word problem, used and internalized academic vocabulary, explained the reasoning of their answer, provided their solution in an equation, and, last but not least, provided a drawing. Now I am not saying that the second I introduce them to a new gate frame, they will meet my expectations, so when I provide them with a new one, we complete one together on the smartboard. I then give an example they can complete on their own. I've learned that sometimes, students need to feel as if they can do it. It doesn't matter that they have seen the directions one hundred times; the fear of not visually seeing your expectations can hinder them more than anything. The way I see it, if a student is willing to use my example to benefit their own understanding, then we are all winning and the ability to understand another's thinking has been internalized.  

The begining .. but definitely not the end
So as all great things, the start of something new starts with the creativity of the teacher, however once you have created it, it can be used for years to come.

1. Pinpoint what math concepts students struggle retaining or are vital in knowing throughout the movule. Ex. Double digit multiplication
2. On a document edit the gate frame using icons and list components that are necessary for that skill. For example, in fourth grade for multiplication the strategies would be place value chart, area model, partial products, and algorithm form so those would complete your gate frame. **Lets say there are different components of one skill-integers/rational numbers then create multiple frames for that skill in scaffolds as seen in the photos. 
3. Print a copy for each student on cardstock and pass them out to place in a soft whiteboard (White cardstock on one side and red cardstock on the other). Students will slip the frame on the top. When it is time for a new one they will leave the previous ones and add to it. This helps review any strategies on a drop of a hat. 
4. Use as a quick warmup (fluency) for a lesson or to introduce a topic or to review a series of strategies within a topic/Module. 
5. Provide an example for students if necessary for the first time. Then only circle one or two portions of the gate frame. Continue adding portions until students understand or have been taught all portions of the frame.  
6. Put on a timer and allow students to complete independently while walking around the room and monitoring and assisting where needed
7. Pull students together and review their soft whiteboards visually and continue with following problems.

Taking it further

Accoutability: 

• Check one student's board if everything is correct and have them check their tables to determine their answers. Have them explain to a student if they do not understand. 
• Count it as an exit ticket
• If a student is really struggling with a portion of the frame, check the students by staying "yes" provide another problem for them to do, but doon't allow the struggling students to move on. Allow them more time to continue with the problem they are on. 
• Let students know that they will share their answer to a class under the document camera and another student will be referring to the frame as they are talking about it. 

Collaboration/: 

• In pairs, divide the portions of the gate frame between the two-meaning each student has to complete two portions and then when they come together they will have to determine if their answer is correct and if they can support it with numerous methods. 
• Allow students to complete one whole gate frame as a team switching up the portion of they gate frame. 

Kagan:

• After completion of the gate frame allow students to discuss their answer with others, especially if a challeging problem or a skill students struggle with. Students can complete with a mix pair share, complete as a team almost as a jigsaw rotation

Regardless of when you decide to implement gate frames within the school year, the impact they can make is tremendous. Remember there is no right or wrong way to create a frame. I encourage you to create one for an upcoming module or even a past one that you feel students may forget.  

Lively Teaching,

Miss Magana