Graphing Grass Linear Equations Project


This linear equations project was one of my favorite things about teaching Algebra. My students would run into the room and right over to the windowsill, excited to see their grass and about taking the day's data. The project is so simple - students plant seeds, grow grass, measure, plot growth, find lines of fit - but the learning opportunities stretch the project so much farther. Students get attached to their little cups of grass. They see slope and line of fit in real life. We learn about interpolation on Mondays by estimating the height our grass was over the weekend and we learn about extrapolation by using our lines of fit. Giving their grass a "haircut" even allows for a real-life first introduction to piecewise functions. I also like to bring Ecology into the discussion by talking about limiting factors on the grass growth.

Entertaining a toddler is tricky business. Since I am not in the classroom this year, my daughter and I will be doing this project together and updating this blog post as we go along (well, I'll be plotting, finding the line of fit and typing since she's only 3:)

Day 0: 
Preparing the cup and planting the seeds


Pop holes in a paper cup. I had this plastic cup lying around, otherwise paper cups work way better. Grass roots don't like standing water, so the cup needs drainage holes. Pop a few holes with a thumbtack in the bottom of one of those waxy paper cups and your grass will be so happy. I had to melt holes in the bottom of this one, which is not the best kid-friendly way to go. 



Soil, seeds, saucer, water. Add soil, place the cup on a tray to catch the runoff water and add about this many seeds. Watch out for the kid who covers the top with seeds an inch deep the second you blink. That kid needs a little extra guidance. I found wheat grass seeds in our house, which is what prompted the project today. In school we always used regular lawn grass seeds. 



Cover the seeds with about 1/8-inch of soil (just so the seeds are covered) and water thoroughly. Place the cup on a windowsill where it'll get sun.



And plot the day's data point. Preparation day is Day 0. 

In my class, grass watering (only if needed, which took a little explaining) and data collection was our warm up for the 20 days of the project. Once the grass started to grow and we could start thinking about slope, equations, line of fit, etc., analysis would stretch a bit farther into each class. The project is ongoing where a little is done each day.

I'll be updating this post as my daughter and I go along. If you want to check out the project, you can find it here.


More to come.....






Solving Equations Activities


When you ask adults what they remember about Geometry, they almost always answer, "A squared plus B squared equals C squared." And when you ask them about Algebra they think of solving equations. Algebra is so much about solving equations and the activities are always good for review, sub days and days before holiday breaks. In this post I round up some solving equations activities that I think are pretty awesome and that work great for any of these times.



Before getting into the roundup, I wanted to show you a set of ornaments I recently made for 2-step and multi-step equations. Students solve equations on each ornament then color and decorate. (There is also a free set of solving 2-step equations pennants on my blog.) Now on to the roundup!
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The Sum-em activities from Karrie at Mrs. E Teaches Math are amazing in how they get students collaborating as a team. Students work in groups of 4, each getting a card. When everyone completes their problem, they sum their answers. If the sum is correct, the group is correct! If not, the group members help each other until all equations have been solved correctly. The cards above are for solving multi-step equations. Mrs. E also has a Sum-em activity for equations requiring distribution.


I love the looks of Karrie's colorful 2-step equations task cards, which can be used as practice or assessment.  
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"You've got math talent!" I love, love, love find the error questions because of the way they foster higher order thinking. Especially with all that can go wrong with solving multi-step equations, finding errors is a super important skill to develop. The solving equations error analysis sheets from Amanda at Free to Discover work great as warm-ups, student practice, stations and homework. 
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When I think of Jennifer from Smith Curriculum and Consulting, I think of her mind-blowing interactive notebooks. She runs workshops all over the country, teaching teachers about INBs. This flippable for solving equations is part of a mini-unit that also includes task cards and practice. 


Here is the inside of the flippable.


Jennifer has also been making these Spin to Win games that are pretty cool. Here is a photo of one in her 8th grade set for solving equations.
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Kara from Learning Made Radical's no solution, infinite solutions and no solution cut and paste activity is a perfect way to hit 8.EE.C.7. It also requires the students to pause, think and really analyze the equations they are given.


Every activity in Kara's store is fun, including this scavenger hunt and a set of Google slides for solving equations with variables on both sides. 
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My favorite thing about Alex from Middle School Math Man's math games is that the student who solves the fastest doesn't automatically win, helping all students feel included and like they have a chance. This is one of his newer games that covers multi-step equations
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Mandy from Math Dyal has created a bunch of self-checking solving equations activities, which is important as students learn to solve (and super time-saving for us). This puzzle asks kids to distribute and combine like terms.


Mandy also made this beautiful coloring activity for 2-step equations that is also self-checking. Best yet, kids can choose their own colors, upping the buy-in.
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And what could be more fun than this battleship activity partner game from Tyra at Algebra and Beyond? The most determined multi-step equation solver (with a sprinkle of luck) wins. Students love this game. 
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solving equations coloring activities math pennants task cards spin to win games puzzles sum em cut and paste

How do you like to practice solving equations? I'd love to hear your ideas!



Tips for Creating Written Material that Supports Visual Learners

Tips for Creating Written Material that Supports Visual Learners

Before our daughter was born, the TV was always on. For me, it was a way to get information and relax. My husband would much rather read. Yet we get along! And since it isn't always possible to watch a video, we all have to access written information at least sometimes. Before becoming a special ed teacher I didn't think much about formatting. Now, I know that there are ways to make written material more accessible to students who have reading difficulties, which in turn lowers their anxiety. In this post I highlight 4 ways to make written information more accessible to visual learners.

As an aside, the only thing ever on our TV now is My Little Pony. Is Season 8 out yet?? 



Tip 1: Font choice: sans serif is best
We all love to rag on Comic Sans. I mean what a comical little font. The thing is, sans serif fonts are easier for kids to read than fonts with serifs. I'm not pushing CS here, it's just that I feel it's gotten a bit of a bad wrap. I like using Century Gothic because it has a lot of the good traits of CS without all the silliness and ridicule. But I'd be amiss to forget this one important point. Take this logarithmic function:



Now in Comic Sans:



I mean, it looks way easier. I think this is the reason our school's math department uses Comic Sans almost exclusively. I also once asked a student with dyslexia which she preferred - the OpenDyslexic we had started using in class or Comic Sans. She chose Comic Sans. The study liked above showed better readability results for Verdana and Helvetica over OpenDyslexic and also recommended Courier, Arial and Computer Modern. Here in Massachusetts our state test - the MCAS - is written in a font with serifs and italicized variables. Here is an example:



Someday I hope this will change. Why should a simple thing like a font change possibly mean the difference between a student graduating or not? There are more tips for ways to make reading materials more accessible for students with reading difficulties in this article from ux movement, including using just one space after a period (a habit I finally made stick), not using justified text or italics and printing on colored paper.



2: Color-coding instructional materials
I love color for no other reason than it's just awesome. But there are some real benefits to color coding when students are first introduced to a new concept. Here is an excerpt of an article titled The Instructional Effect of Coding (Color and Black and White) on Information Acquisition and Retrieval written by Rickard J. Lamberski and Francis M. Dwyer (linked above):


"...That is, students who received color-coded instructional materials and black and white test materials had the potential to utilize the color code in retrieval; however, its absence [in test materials] had no significant effect on achievement compared to students who received color-coded test materials."


(a color-coded Algebra 2 word wall reference)

Using color to make connections really works, even when the color is later taken away. And being really deliberate about color - using the same color each time a term is used, only coloring select terms so that they stand out, not overusing color (something I am working on) especially the first time kids are introduced to a new topic - makes color really meaningful. In that quadratic word wall example above, the equation's shifts are color coordinated to the x and y axis. Even students not yet in Algebra 2 can pick up the pattern.

The article goes on to state:

"...students who received black and white instructional materials and color-coded or black an white test materials achieved significantly less than did students who received color-coded instructional materials."



3: Chunking material
If you're a special education teacher, you know about this. Chunking supports working memory (super short-term memory) that we use to remember 2-step authentication codes or phone numbers from voice messages. It also helps students remember the subject of a long sentence when finally getting to the period (I'm looking at you, Henry David Thoreau). Chunking makes things more visually appealing in my opinion, and this makes kids less intimidated to get started. I use chunking in all of my math materials. Why should formatting be a roadblock to the information?

Here is the Times New Roman, justified, 2-spaces-after-a-period abstract of my graduate thesis. (There were very specific formatting guidelines):



Here's the same passage chunked, not justified, with a sans-serif font:



The box around that now third paragraph isn't needed, but I do like using boxes to highlight certain things or even just to give the eyes a break. Task cards also utilize chunking, which is why they work better to engage students than it seems they should ("aren't task cards just cut up worksheets?" Nope, they're superchunked!)



4: Silly pictures 
I maybe should have stopped at 3. But I really wanted to get this one in here because it works so well. Coloring lowers anxiety, which helps students better absorb information. Whereas using color in instructional materials is deliberate and used sparingly, color on practice materials is full steam ahead. 

Spongebob, Dora, Smurfs, the Simpsons--whatever cartoons students used to watch on TV as younger kids. Slapping a silly picture or something to color on a boring practice sheet has worked wonders for me to motivate students to do work. I mean, how hard could this math be if Spongebob is on it? 


(Coloring the Pythagorean Theorem)

Other than making the math feel lighter, coloring is just plain fun. With teen mental health deteriorating, they need screen-free, relaxed downtime in order to process all the information coming at them from all directions. 

Silly pictures paired with chunking, good spacing, sans serif fonts and deliberate use of color helps visual learners access information. What other tips do you have?  I'd love to read your comments or hear from you! 





Long Division Cheat Sheet

how to do long division cheat cheet

I once joked to another teacher that I'd be happy sitting around making math cheat sheets all day. It was June, the building was probably 150 degrees and we were in the middle of a rational functions unit, which, ironically, is related to long division. Later when I thought about it, I realized that maybe I wasn't totally joking. It's not so much making the sheets themselves (though formatting is strangely addictive), it's making something that a kid can use to help lower stress and build math confidence. No cheat sheet ever takes the place of a teacher, but sometimes every little bit helps when a kid is frustrated and on the verge of giving up.


Integer Operations Graphic Organizer


With integer multiplication and division, the rules are clean and concrete. A negative times a negative is literally the "opposite of a negative" and the rules are pretty simple to remember. With addition and subtraction the rules are a whole lot looser. For students who like things nice and clear, integers can be a real sticking point.