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### 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. You can grab the project here in my dropbox.

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.

At the end of the project, students have a cup of grass they can take home and take care of or plant in their yard. Teacher Ms. Allen sent this fun photo of her students' projects repurposed as Easter baskets!

### Linear Equations Project - graphing grass

Day 0:
Preparing the cup and planting the seeds. Plotted (0, 0).

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.

Day 1:
No growth. Plotted (1, 0).

Day 2:
Still no growth. Plotted (2, 0).
If a weekend hits and the seeds still haven't sprouted, it's a good idea to place some wax paper loosely over the top of each cup. On Monday, the wax paper can be removed. This keeps the moisture in while the seeds haven't get germinated. Once the grass is sprouted, this step isn't necessary to do for weekends.

Day 3:
Still no growth. Plotted (3, 0).
We always planted our seeds on a Monday. By Friday the seeds would still just be seeds and the kids would start getting a little skeptical.

Then by Monday, all the cups would magically have grass! Some students would ask if I came in over the weekend to put the grass in there. Over the years, I even had students not believe it was grass because it didn't look like the grass in their neighborhoods.

Day 4:
Some seeds have sprouted! Plotted (4, 0.25).

I tell students to gently press their rulers into the soil to get a more accurate measurement. Especially when the grass is so short, that extra blank space on the end of the ruler can throw off the day's measurement.

The project is editable so you can choose to measure in centimeters. I'm measuring in inches and measured this little guy at 1/4-inch.

Day 5:
Lots more sprouts and growth. Plotted (5, 0.75).

So many skills can be woven into this project, like converting the fractions on the ruler to decimals. The project can even be truncated to just the measuring, data collection and plotting for younger students.

Day 6:
So many more sprouts and a lot more growth. Plotted (6, 1.7).

When the grass starts to get taller, we always measure the tallest blade of grass each day. This may or may not be the same blade measured the day before, but it's the best way I've found to keep the data collection consistent.

The kids get a kick out of each blade being a different height. I like spring boarding off this to talk about how awesome it is that we are all different.

Day 7:
Quicker growth. Plotted (7, 3.2).

The grass grew faster since yesterday than it had in past days. It grew 1.5 inches in one day! I like that the growth is not linear. This makes for more interesting data collection and lots of consideration once we start thinking about line of fit. This can even lead into discussions about nonlinear growth and "concave up vs. concave down".

Day 8:
A little watering. Plotted (8, 4.25).

Twice during the project I ask students to find a line of fit for their current data to help make a height prediction for Day 30. Our grass is growing super fast right now so the height predictions are always off the charts for the first week!

I used the data points from Day 4 and Day 8 to find a line of fit. The equation is y = x - 3.75 and our height prediction for Day 30 is 26.25 inches! SPOILER ALERT! The grass growth eventually slows down. This opens a great conversation about the reasons why the grass won't grow as tall as we predict.

Day 9:
Plotted (9, 5.25).

Day 10:
A little more water. Plotted (10, 6.5).

I have to admit that I'm wondering a little about this wheat grass. It seems to be growing a lot faster than the lawn grass I had always grown with students. By the time we went out to get grass seeds this fall, all the gardening shelves were taken over by Christmas stuff. So I'm wondering if my grid's max height of 13 inches will be enough! We'll see!

Day 11:
Plotted (11, 7.2).
Algebra students, we're going to need a bigger ruler.

While updating the project files, I was reminded why we always measured in inches instead of the more accurate and easier to convert centimeters. My school only had those wooden rulers that don't have metric measurements! The files are all editable so you can change the y-axis label to centimeters.

Day 12:
Plotted (12, 7.5).

Growth may finally be slowing down! I've been sweating it. This is a great chance to bring in come cross-curricular discussion about ecological limiting factors.

Why may the grass not get as tall as we predicted on Day 8? Answers will vary, but the cup size, crowding, the amount of water or sunlight and the genetics of the grass are all discussion topics. Would the grass grow taller if the cup was bigger? If the grass got more sun? More water? Would a different species of grass grow taller? It would be fun to test out one of the hypotheses, like planting new seeds in a bigger cup.

Day 13:
A little more water. Plotted (13, 7.6).

Our grass only gained 1/8 of an inch since yesterday! Converting that 5/8 to a decimal or our grid can be a little confusing for even older students. I feel it's OK to estimate, which is a great skill, but this can also be used as a real-life way to practice conversions.

Day 14:
Missed a day of data (we went away for the night). Interpolated (14, 7.65)

Day 15:
Oh no I didn't. Plotted (15, 7.7).

Welp, we had a champion blade of grass who grew above and beyond all other blades. He really put in work to be the best. And then I accidentally ripped him right off.

Before it happened, I measured this little guy around 7.7 inches. But growth had really slowed down. We were away for the night so I missed Day 14's data, so interpolated the height to have been 7.65 inches yesterday. This is also how we'd deal with weekends at school (the interpolation, not the ripping off part).

Tomorrow it's haircut time...

Day 16:
Haircut day. Plotted (16, 5).

Today was haircut day! This is a fun way to get kids thinking about piecewise functions.

Another blade of grass had been almost as tall as the one I accidentally plucked yesterday, but I decided it was better to extrapolate today's height given the last few days' data, plot an open circle at (16, 7.75) and then a closed circle at (16, 5) after the haircut.

When I have done this project with students, there have been times kids have accidentally plucked the blade they had been measuring. I get it now! It's sad! One of the greatest things about this project is how attached kids get to their grass. It's nice to see tough teenagers care for a living thing.

Day 17:
Wow! Growth! Plotted (17, 5.5).

I'm honestly surprised that our grass grew 1/2 inch since yesterday's haircut! In 24 hours the blades already started growing at different rates with the tallest ones now at 5.5 inches!

Day 18:
Faster growth! Plotted (18, 6.25).

It amazes me how the cells in a living organism all communicate and make growth (and healing) happen. I shared an amazing mitosis video on Facebook the other day that if I stop to think about too long makes my brain hurt. How did our grass know to get growing again once it was cut?

This makes for great classroom conversation about grasses being so omnipresent on Earth because they, unlike other plants, grow from their base.

Day 19:
Growth slowing again. Plotted (19, 6.5).

The growth of our grass has again slowed down as we approach the end of our project. I'd usually have my students track their grass for 20 days (including weekends) and then use that data to do their extrapolation checks.

Extrapolation is so much cooler in context. We saw our grass hit a height ceiling, so we can factor this in when extrapolating.

Day 20:
Another extrapolation! Plotted (20, 6.7).

This is the end! This project creates so many tangent learning opportunities. At the end, students get really attached to their little patches of grass. They get to know about scatter plots, about lines of fit, can find slope between two non-integers, can build equations given two points, are able to extrapolate and interpolate, have seen the beginnings of piecewise functions, can convert between fractions of inches and plots on a grid, and can collect data and measure. Phew! That was a lot! And the best part is that students have fun all along the way.

To sum up our project, I completed one more extrapolation check to estimate the height of our grass at Day 30. With a slope of 0.225, our grass would be 8.95 inches at Day 30, which opens up a great discussion about the reality of this prediction based on the trends in the data we've seen.

For good measure, I gave our grass one more haircut and will plant him outside in the spring.

My next goal is to learn how to enter data and create trend lines in Google Sheets (like teacher Ms. Tannenbaum in this Facebook post). Super cool!

This project is easy to do with materials found at the grocery store. If you'd like a bit more structure, I have put together a set of materials to go along with this graphing grass project (zip file) in my dropbox.

If your students have trouble graphing linear equations, there's a free graphing linear equations cheat sheet in this post.

Related:

1. This is great! We're doing linear regressions next week. I think I'm going to do this with my students, plus I have leftover grass seed from a summer project. Thanks for sharing.

1. Awesome! I hope they love it! I’d love to hear how it went!

2. Love it I will try this with my kids ! Thanks

3. I hope your students have fun with it! This project was always a highlight every year when I taught algebra.

2. I look forward to trying this out with my students. Thanks so much!

1. I'd love to hear how it goes!

3. Hi! I am so excited to do this with my kids. How much soil and seeds do you think I would need to buy?? I am trying to get a price approximation :)

1. One small bag of grass seed is way more than you'd need. I have used the same bag 2 years in a row (when I lived in in apartment and didn't have a yard). As for soil, I'd get one of the bigger bags. Soil tends to be less expensive than seed so even a big bag shouldn't be too expensive. Paper cups (the ones with a slight wax on them) work great because they let the roots breathe better than plastic, so there is another place you can cut cost. I hope your kids enjoy it! I'd love to hear an update!

4. Super idea!
Now I have got the clue to go ahead with something amazing in my Mathematics class. Thank you and expect similar sharing in future too.
In my case, I had tried to do something like Geometric City, Math Quiz/Riddle and some practices from Geogebra.

1. Those are great ideas! I love everything I have seen about Geometric City. I bet the students are very engaged during that project! I hope you have a great year!

5. Awesome project. I'll do this with my students next year. Just wondering if grass seed is available in our town.

1. I’ve had a hard time finding it at certain times of year but people sometimes overseed their lawns in fall so it may still be in stores.

6. I am sending these supplies home with my kiddos when they pick up their textbooks for distance learning in a few weeks. Thanks for giving us a fun project to do together while we are apart.

1. You're pretty awesome for getting supplies to your kiddos even when they are distance learning from home. Thank you for caring so much for your kids. I hope that you have a great year and that your kids enjoy the project.

7. AnonymousJuly 27, 2021

I love this so much! Thank you for sharing this

8. I'm working on a Desmos activity for the kids to use to write their lines of best fit, since we use Desmos, not graphing calculators. Feel free to use, everyone! Currently a work in progress. https://teacher.desmos.com/activitybuilder/custom/61edcd068c4b620a87d47a0c

1. This is GREAT! Thank you so much!