Category Archives: Math

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

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#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

Not a “Math Person”? Wrong!

When it comes to math and mindset, there are two #eduheroes I refer to on a regular basis:  Dr. Jo Boaler, who is a professor at Stanford and the genius behind the YouCubed website, and Alice Keeler, who many know to be a Google wizard but also has a published book called, Teaching Math with Google Apps: 50 G Suite Activities.  You can imagine my excitement, then, when I learned that they would be presenting a session together at ISTE. (Dr. Boaler joined us through Google Hangouts).

Dr. Boaler wrote the book, Mathematical Mindsets.  Not surprisingly, it includes a foreword by Carol Dweck, the leading expert on growth and fixed mindsets.  Dr. Boaler’s main points are that we need to value the different ways that people see math and have more class discussions about math – rather than repetitive questions on worksheets. According to her research, people become proficient in mathematics when their brains have the opportunity to make connections between visual and numerical representations – not because they are born “math people.”  The least effective way to teach math is through lecture, while the most effective is with Project and Problem Based Learning.

Both Boaler and Keeler agree that we need to dispel the myth that those who can do math quickly are better thinkers than those who reason through problems.  In fact, Boaler says, “I’m unimpressed that you worked through it quickly because that tells me that you are not thinking deeply.”

Another controversial topic we all agree on – homework.  Recent studies have shown that assigning elementary students homework is ineffective.  Boaler and Keeler (and I agree) both believe that this is true for all ages, particularly when the homework is a worksheet of repetitive practice.  A better way to think about math is to do an activity like the one below, where students think about one problem in multiple ways.

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When an audience member asked about the problem of spending time on conversing about math when there is a scope and sequence to follow, both Keeler and Boaler expressed the feeling that it is actually a waste of time to “plow through” topics despite lack of understanding.  In Boaler’s words, “Pacing guides are the worst evil in education.” Amen!

Keeler shared several “Googlized” adaptations of activities from Boaler’s Week of Inspirational Math, including a nice Slides template for the Four 4’s challenge which includes links to individual slides for students to explain their work.  You can find links to more of Keeler’s templates in her presentation here.

Overall, I was so energized by this session that I was tripping over my words when I debriefed with my colleagues that evening.  I had stayed later just to attend this session, and it was definitely worth my time.  Thank you, Alice Keeler and Jo Boaler!

I want to close this post by helping Alice Keeler to honor her book’s co-author, Diana Herrington, a passionate math teacher who recently passed.  You can read more about Diana and her influence on Alice Keeler here.   One of many great quotes from Diana Herrington on Twitter collected by Alice Keeler is, ““I teach students not math.”

Clothesline Math

Chris Shore is quick to note that he did not invent Clothesline Math.  However, he is the author of the Clothesline Math website, and producer of many of the materials on the site, so I think he definitely deserves some credit!

When I first ran across this site, I was a bit dubious of the value of a Clothesline Math activity.  Basically, the teacher gives out a set of number tents to students, who then must hang them on a clothesline (which represents a number line).  However, once I watched Shore’s video explaining how he introduces Clothesline Math, I realized how this seemingly simple activity could really start some incredible math class discussions.  There are many decisions students need to make when they determine what benchmarks to use on the numberline, the order to place their numbers, and the amount of space in between.  Even with a set of 3 fractions (1/2, 1/3, and 1/4), you could take up an entire class period.

Shore provides different sets of printable numbers (from various math disciplines) and an answer document on his site.  Of course you can DIY with your own supplies and number sets based on whatever you are studying in math class at the moment.

I like the idea of students reasoning through this, and having to justify their responses.  It can also be a great visual and kinesthetic activity that will be much more meaningful that choosing from multiple choice answers on a worksheet.

For more intriguing math sites, take a look at 15 Math Sites That Won’t Make You Fall Asleep.  Let’s get our students excited about math!

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image from: MaxPixel