Tag Archives: math

3-Acts Math Tasks

I sent this e-mail to our teachers as my weekly GT Tip, and realized that it would work well as a blog post.  So, here you go!

One of my recent discoveries in the Twitterverse has been “3-Acts Math Tasks.”  According to this site, “A Three-Act Task is a whole group mathematics task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.”

To see examples of 3-Acts Tasks, you can check out Dan Myer’s explanation and modeling of each act here.  You can find links that include printable answer documents to 3-Acts Tasks for Kinder-7th grades on the Weekly Tip page here, as well as links to tasks for upper grades.

The tasks that have been provided by teachers all around the world include pictures and/or video of real-life math problems, making them relevant and intriguing to math students.

What struck me when I read about these tasks is the rich conversation involved, as well as the inclusion of students of all levels.  Many thinking skills are practiced in addition to the actual mathematical operations used.  I know this is long, but here is a poignant story from the NCTM site in an article by @DaneEhlert that emphasizes the value of these tasks,

“My favorite reason for using these tasks is the students themselves. I have to mention one individual whose story inspired me to never take these problems out of the curriculum.

I had a junior in my freshman algebra class last year because he had failed the course twice. On the last day of school, the student came to see me.

“Mr. E, I just want to say thank you. I’ve always struggled with math, but this year I finally got it.”

What struck me the most was the student discussing his previous struggles with math. This was surprising because he was brilliant mathematically. Every time we did an open-ended problem in class, I was blown away by his thought process, visuals, and reasoning. It was incredible to witness, and the other students were in awe, as well. We could all see that this student had an amazing ability to reason mathematically.

I told him he was brilliant, and it showed in his work. His response is why I will always use these tasks.

‘Well, yeah, I was good at those problems because they’re real life. They just make sense.'”

These may seem time-consuming, but the conversations and levels of thinking are designed to replace much of the lecture and practice problems that often engage or make sense to only a fraction of the class.  Hopefully, you will try a few and find them to be worthwhile!

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The Magic of Fibonacci Numbers

My 4th grade class studies mathematical masterpieces each year.  They are always fascinated by Pi and Fibonacci numbers.  Even now, this year’s 5th grade class makes connections related to those favorite topics.  I’m surprised that I have just now found this TED Talk from 2013, where Arthur Benjamin speaks about the “Magic of Fibonacci Numbers.”  This link features Benjamin’s video on TEDEd, so there are multiple choice questions and other resources provided as well.

For some of the other blog posts that I’ve done about the Fibonacci sequence, click here.  And for some of my favorite engaging mathematical websites, check out this post. (Currently the most popular post on this site!)

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image from Pixabay

Sumaze

Sumaze and Sumaze 2 are free mathematics apps available in the Google Play Store or for iOs.  The games and the graphics are simple but elegant.  Players start with a number tile, and must move the tile through a maze by flicking the screen in the appropriate direction.  As users ascend levels, other tiles are added to the maze with operations and numbers on them.  It becomes your goal to not only get your tile to the end of the maze, but to make sure it is equivalent to a particular answer before you try to slide it into the final exit space that will trigger the next level.  Mental math and logic are essential to solving the puzzles as multiple operation tiles start sprinkling your screen and you have to choose the operations to use as well as when to use them.

This is not a game with avatars, XP’s, or any other kind of trendy gaming elements, but it is a good game that will challenge math lovers from ages 7 and up.  It reminds me of two other excellent (and free) mathematics apps that I highly recommended awhile ago: MathSquared and MathScaled.  Students with a passion for math enjoy apps like these – and sometimes those who don’t enjoy math finally discover its appeal.

Sumaze

#wgoitgraph

“What’s Going on in this Graph?” is a new feature from the New York Times that will appear on the second Tuesday monthly for the rest of this school year.  Building on the success of a long-running similar activity,  “WGOITPicture,” this version posts a graphic that has appeared recently in the NYT, with much of the information removed.  Students are encouraged to analyze the image by thinking about these three questions:

  • What do you notice?
  • What do you wonder?
  • What’s going on in this graph?

There is a comment section where students over 13 years old, (or teachers) may post their observations, questions, and extrapolations.  A moderator from the American Statistical Association gives online feedback on the day the graphic is posted, and then the actual details are revealed at the end of the week.

The first “What’s Going on in this Graph?” was posted yesterday.  According to the caption, it has some connection to Hurricane Harvey – but what, exactly?  That is for your students to try to discern.  From the comments I have read so far, there are some extremely perceptive students attempting to decipher the graph’s meaning; it will be fun to see the answer on Friday!

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#gmttc

#gmttc is the official hashtag for the Global Math Task Twitter Challenge.  Classrooms around the world are invited to participate by solving the problems that are tweeted and/or tweeting out their own.  You can formally sign on to be a #gmttc tweeter on this spreadsheet, but this is not a requirement.  It is easy enough to find recently tweeted tasks for your grade level by doing a search for #gmttc with your grade level number at the end.  For example, #gmttc4 will provide you with recent 4th grade challenges.

I enjoy seeing the variety of images students use to present the math problems, and your students will begin to make connections between what they are learning compared to students in other parts of the world.  This is a quick, no fuss way to “flatten the classroom.”  As a whole-class, center, or extension activity, #gmttc is a fun idea to help students get excited about math!

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Splat!

Steve Wyborney recently published this article on Edutopia about a series of math problems he has created on Powerpoint called, “Splat!”  The challenges begin at a low enough level that you could use them with Kindergarten, and increase in difficulty to a point that even secondary students will enjoy the intellectual stimulation.  Steve provides all 50 of the downloadable Powerpoint files here, along with a video in which he explains the process.  Basically, students are shown a group of dots, some of which are then covered with one or more “splats.”  They have to deduce how many dots are under the splats.

I love the potential for rich math conversations with this activity and the natural algebraic thinking that will evolve from solving each of these challenges.  Thanks to Steve for providing these great resources free to educators everywhere!

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image from PublicDomainPictures.net

Week of Inspirational Math #3

Earlier this summer I wrote about an inspiring session at ISTE co-presented by Jo Boaler and Alice Keeler. Boaler is dedicated to spreading the word that anyone can be a math person as long as you have a growth mindset and appropriate learning opportunities.  As a Professor of Mathematics Education at Stanford, Jo Boaler co-founded youcubed.org, and has presented a new “Week of Inspirational Math” curriculum on the site annually for free for the last two years.  Week 3 has just been published on the site, and is ready for educators from K-12 to use.  Having used the Week 1 and Week 2 curriculums in the past, I would highly recommend that you begin your school year with one or all three of these sets of math lessons.  The activities are broken down into grade-level strands, so there is no need to fear that your Kindergarten children will be asked to solve high school equations. 🙂

This year’s lesson include videos, PDF’s, and even access to a program called “Polyup,” which you can learn more about here.

I have personally witnessed students who believe they are “bad at math” be successful with these activities and become excited about doing more.  Those who have had negative experiences learning math can turn these around with thoughtful conversation and the passion of a teacher who believes in them.   Put Week 3 of “Week of Inspirational Math” into your beginning of the year lesson plans, and watch as your students learn to love math!

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image from Clement.sim on Flickr