Scaffolded Math's Favorite Things


Thanks for stopping by! Through my work at TpT I have met some really great math educators who I am happy to now call friends. We got together this holiday season to bring you a blog hop and giveaway of our favorite math things (kind of like Oprah, only more mathy). 


This giveaway is for a $25 TpT gift card and a copy of the amazing book Mathematical Mindsets. Giveaway details below:)


1: My favorite holiday activity
I love making salt dough ornaments. Squishing the dough is so relaxing - even better than play dough - and the dried ornaments last forever.


Here is a salt dough dog my mom made when I was a little girl. Now it hangs on our Christmas tree. 




And here is a salt dough ornament of our daughter's footprint. The recipe for the dough is simple:

What you need:

2 cups salt (I use sea salt without iodine, but I'm not sure it matters)
4 cups flour
1.5 cups of warm water
water based paint
ribbon

What you do:

Mix together to combine. When the shapes are dry, you can paint them however you'd like. My daughter and I use her washable poster paints.


2: My favorite math activity
This project was one of my favorite projects to do when I taught Algebra because it incorporates so many skills. The project can also easily be adapted to much younger kids.


What you need:
Paper cups (1 per student or small group)
a thumbtack (to pop drainage holes in cup)
A tray to hold the cups
Potting soil
Grass seeds
Graph paper
Rulers

What you do:
Plot the growth of grass seeds over the course of a month. Use the scatter plot to learn about data collection, interpolation, extrapolation, slope, writing linear equations and even piecewise functions. Younger students can focus on the data collection and what it takes to keep a plant alive (older students benefit from this too). You can read more about this project in this post


3: My favorite teacher tool
I am thankful my "Dude, you're an adult and a professional, it's time to start reading again," self talk kept the densely heavy book in my hand and not quickly shoved back into the bookshelf. 


To say this book changed me is an understatement. I hung on every word. It's the best kind of dense. And I want to share it with you.


To enter my giveaway:
For a chance to win a $25 TpT gift card and a copy of the amazing book Mathematical Mindsets:

1) Comment on this post with the title of your favorite book

2) Subscribe* to my blog.


*if you are already subscribed, your comment on this post is your entry:)


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I teach:


(and don't forget to comment on this post:)

I wish you the very happiest of holidays. You are doing an amazing job, especially in our current teaching climate. You are changing kids' lives. This is painfully exhausting (and more rewarding than any other job). You deserve all the rest you get this vacation!

Now it's time to hop over to Math Dyal's blog to enter another giveaway!



Giveaway ends Monday December 18 at 8PM EST when one winner will be chosen randomly!


HAPPY HOLIDAYS to you and your loved ones!


Christmas Math Pennants


The days leading up to Christmas break are crazy. Some kids are excited about Santa, some are excited to be away from school, others are not at all excited about being home. This all leads to a giant soup of emotions that can be really hard to manage.  

I've written a lot about math pennants and how much students enjoying seeing their work displayed. Math pennants also work great for keeping students focused during this time of year. In this post I wanted to highlight some of the holiday math pennants I have made that have a Christmas theme.

You can find all of these holiday math ornaments in the Holiday Math section of my TpT store.


area and perimeter math ornaments

These area and perimeter ornaments ask students to find the area and perimeter of irregular shapes that are measured in unit squares. Students can decorate their pennants with bows and holly.

mixed number improper fraction math pennants

I've done a few sets covering fractions, like this mixed number to improper fractions set that asks students to convert between the two forms. 

fraction math ornaments for Christmas

And the three in this photo come from a set of 60 holiday fraction ornaments covering fraction addition, subtraction and multiplication. These also come in non-holiday form.

graphing linear equations ornaments Christmas Algebra activity

Most of the time when I ask my juniors and seniors if they would rather take their graded papers home or hang them on our classroom "Fridge", they choose to hang them on our fridge. I like this too because we can point to their hard work on harder days as proof that they CAN do it.  

Shown above is a set of graphing linear equations ornaments.



Christmas math solving equations ornaments for Algebra

Here is a newer set of solving equations ornaments. There are 15 for 2-step equation and 15 for multi-step equations. Teachers have mentioned using parts of the set in the different classes they teach. The linear equations ornaments and these solving equations ornaments also come bundled.

I hope you have a wonderfully relaxing break that you enjoy to its fullest. You deserve every minute of it. You are changing lives! That takes a lot of energy!


Holiday math pennants

You can see more math pennants for other holidays, like Pi Day and Valentine's Day, in my Holiday Math Pennants post.




Graphing Grass Linear Equations Project

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. Plotted (0, 0).

graphing grass linear equations project day 0 drainage holes

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. 

graphing grass linear equations project day 0 planting seeds

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. 

graphing grass linear equations project day 0 windowsill

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.


graphing grass linear equations project day 0 graph

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.

graphing grass linear equations project day 2 wax paper covering

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).

graphing grass linear equations project day 4 - seeds have sprouted!

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.

graphing grass linear equations project day 4 first growth

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).

graphing grass linear equations project day 5 graph

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).

graphing grass linear equations project day 6 growth

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.


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

graphing grass linear equations project day 7

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).

linear equations STEM PBL project day 8

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!

linear-equations-project-line-of-fit-week-1

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).

linear equations STEM PBL project day 9

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

graphing grass linear equations project for Algebra day 10

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).

graphing grass linear equations project for Algebra Day 13

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).

linear equations project day 15

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).

graphing grass linear equations algebra project day 16 cutting the grass

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

graphing grass linear equations algebra project day 16 haircut day

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. 

graphing grass linear equations algebra project day 16

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).

graphing grass linear equations algebra project day 17

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! 

graphing grass linear equations algebra project day 17 graph

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

Algebra project for linear functions scatter plots line of fit and slope Day 19

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).

linear equations project

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.

linear equations project

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

My next goal is to learn how to use trend lines in Google Sheets (like teacher Ms. Tannenbaum who commented with a photo of her Google Sheets trend lines on this Facebook post). Pretty cool!



This project is easy to do with materials found at the grocery store and a piece of graph paper. If you'd like a bit more guidance, I have put together a set of materials to go along with this linear equations project in my TpT store. 

(updated 12/12/17)

More to come......

There are more linear equations activities in the post Teaching Linear Equations.


linear equations ornaments






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.


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.