This post is simply a way for me to quickly document/share a few ideas on large whiteboards.
I went to Home Depot and did the following:
Found the large whiteboard sheets:
Had someone make two cuts:
I get one large whiteboard and two smaller boards:
Took home and sanded the corners to get rounded edges:
My classroom desks are in groups of three or four, depending on my furniture, space and mood. Besides using these boards for 3-Act Tasks, here are my favorite everyday activities:
Placemat:
Students are given a question to work on. Each student carves out a section on their whiteboard to solve on their own first. As you can see, there's an open space in the middle.
Once students are done with their individual work, they discuss what their group answer should be and write it in the middle section. This really allows students to compare their work with their peers and give each other support, especially for those who might be stuck or need a nudge. Great everyday use and for review activities like Race Car Math.
I. LOVE. PLACEMAT!
Brain Dump
Brain dump: Project something and have the students write down everything they know about it in their section. Then they compare and contrast as a group before sharing whole group. You could also do a Notice/Wonder (a laThe Math Forum).
Put the timer on and ask students to write as many ways as possible to get to -100 or whatever you fancy. GO!
The Home Depot boards can be a little weighty. If you have the budget, I’d recommend you first look into the large whiteboards from whiteboardsusa.com. They weigh less, have a slightly better writing surface, have rounded corners, and have a carrying handle for kids to easily carry around the classroom. You can get a set of 10 for a little over $100. Top-notch whiteboards.
I use cut-up dark t-shirts and socks as erasers. There are plenty more things you can do with whiteboards and I've documented some of them in a few blog posts. Probably the best investment I've made as a teacher. At teacher trainings, workshops, and conferences, I'm practically begging teachers to get these whiteboards in their classrooms.
Now, I have a blog post in which teachers can refer to. But, here are more awesome additional uses of whiteboards. Nathan Kraft outfitted his entire room with whiteboards, inspired by Alex Overwijk. Don't miss Frank Noschese pioneering all this whiteboard magic. You can see Fawn Nguyen using these on a regular basis too.
Crystal (colleague) and Lynda (fellow) wanted to know more about this. So here's the story:
The previous week, I met with one of my high school fellows who teaches Algebra to freshman. As with all my fellows, it's been an extreme pleasure to work with her because she's hungry for ideas and will take suggestions and run with them. It was so cool to walk into her class this past week and see her running with an idea, again.
She had already taught her students ways to solve linear systems; graphically, substitution, elimination, etc. On this day, she prepared six short videos of her solving linear systems and linear inequalities using Educreations on her iPad. Students were to watch the videos and do error analysis, reporting the following on their handout:
Identify the mistake(s) for each question.
Explain what should have been done.
Fix the mistake and complete the question correctly.
Each video was between 60 and 90 seconds in length. We both discussed what we thought would be most effective for her students and short videos was a must. Have you ever noticed how the majority of Khan videos can be extremely lengthy? Sal Khan usually talks (and repeats himself) while writing things on his digital blackboard. To me, that's a waste of someone's time. It's like you watching me type this blog post while I reread every sentence two or three times, stalling so I can finish typing. Another thing I can't stomach in Khan videos is when he fumbles around searching for colors to write with. Lastly, I find it unfortunate that the videos rarely suggest the viewer to pause and consider what's happening. Here's an example. Sorry, here's a 9+ minute example:
I suggested my fellow pause the recordings often and write the equations "offscreen" when not recording. Then, press record again when she's ready to talk and/or write something important on her screen. She also took advantage of this offscreen time to select different colors in order to emphasize different equations, steps, lines, or shading (linear inequalities).
*See the video structure below with suggested notes and style points.
It took my fellow one prep period on a minimum day to create six videos, a supplemental handout, upload the videos to Educreations, and create hyperlinks on her Haiku page for students to access all the videos. That's super impressive. Talk about an activity with meaningful and HUGE return from an efficient investment in her prep time.
When debriefing with my fellow after class, she was completely ecstatic.
I asked her, "What elements made this awesome?"
She replied:
it was video and new
they liked figuring out someone else's mistake
the videos were short
students could pause, rewind, and start the video over
using Desmos to show a graph of the original equations at the end (comparison)
gave students the idea to use Desmos to check their work/answer
self-pacing
very little hand-raising or students drowning
the videos were easy to make
she passed out the handout and said "go" instead of modeling
the handout had a simple structure
the students did most of work, not the teacher
I love this last element the most. The two of us talked about this specific element the previous week. Now she experienced it first-hand and it's an amazing feeling. As an observer, it was awesome to see the students working hard on a meaningful task and helping each other out so it allows her, the teacher, opportunities to calmly circulate and provide support where necessary.
Student engagement and interest were high. Discussions were plenty and authentic. Students were thriving using thinking skills in the "Analyzing" category of Bloom's Taxonomy or Strategic Thinking category of Webb's Depth of Knowledge. Here's a tip I suggested when I noticed some kids plowing through a video and hadn't caught the mistake: pause and make predictions. The video structure will explain pausing and predicting more.
Video Structure:
Part 1:She takes about 8 seconds to explain her plan
*All of this was written on the screen prior to her pressing record. Style points.
Part 2: Multiply the top equation by (-5) in order to eliminate the x-terms
*Here's where we need to ask students to pause and predict what the top equation will look like after being multiplied by (-5).
Model this for students.
Build "pause and predict" prompts into the video.
Circulate the room and ask students to pause and predict.
SO valuable. Don't skip "pause and predict".
Part 3: Write the new equations "offscreen". Don't record yourself writing these equations.
*Notice the new equation is written in red ink. Style points!
**Pause and predict what it will look like when combining the equations
***Catch the mistake?
Part 4: Combine the two equations.
*Another great use of "offscreen" writing.
Part 5: Find the value of y.
Part 6: Substitute the value of y into one of the original equations.
*Yet, another use of "offscreen" writing here. Part 7: Solve for x this time.
*Ask your students to check for reasonableness.
**Find an alternate way to validate (or invalidate) their conclusion.
Part 8: Insert a screenshot of the system graphed in Desmos.
*Mind grenade: the graph doesn't match the algebraic procedure.
**HUGE style points by inserting a visual representation of the correct answer.
For those of you who don't have 1:1 devices in your schools, no sweat. I still recommend you make a video of some sort. Borrow an iPad from someone. Create an Educreations video for error analysis. Use the tips and techniques mentioned here. Your videos should be less than 90 seconds. Play it to your class. Pause the video to have students make predictions and/or discuss possible errors. I guarantee you, good things will happen.
Tonight, my son wanted me to work with him on his new puzzle.
I don't know your strategy for doing puzzles, but I find all the corners first and then start putting the border together before I start working on the inside. Look at that box again. Would you be able to determine the dimensions (in puzzle pieces) of this puzzle by knowing the total number of pieces?
That was my first question:
A) If you know the total number of puzzle pieces, could you think of the all the possible dimensions (in puzzle pieces) of the puzzle?
Answer:
This puzzle will either be a 1x35 or 5x7.
Then came the next question:
B) Estimate the actual dimensions (in puzzle pieces) given the picture on the box?
Answer:
I'm going to go with 5x7 because five and seven are the only factors of 35 that would reasonably make the rectangular picture on the front of the box. The puzzle should be 5 pieces high and 7 pieces across from left to right.
With a box of 35 pieces, these questions aren't too ridiculously challenging. However, I know there are crazier puzzles out there in the world; puzzle with 500, 750, 1000 pieces, etc. That's where I called on Twitter to help out. Like a champ, the #MTBoS came through and hopefully will continue to come through with #puzzlemath.
Below are some of the tweets I received followed by additional math questions I'm curious about.
