Tag Archives: Math

Math Stories or “There’s More Than One Way to Solve a Problem”

Maybe I have been watching a little too much TV with G,  my 4 year old, but I am absolutely LOVING Peg + Cat on PBS. It is the perfect mix of math concepts, problem solving strategies, songs, stories, and all around silliness. All of this stuffed into a cute little girl named Peg and her “AMAZZZINNNNGGG”, talking pet cat. One of the best parts of the show is when they finish every challenge with this song…

I am so inspired by all that G is learning from Peg and Cat that I thought I might share some Math inspiration for your kiddos in your classrooms. The Three Acts Of A Mathematical Story from Dan Myer is very similar to Peg+Cat in that teachers create a story built around real-life math.

Here’s the idea :

  • Act 1 – “Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.” (check his site for examples)
  • Act 2 – “The protagonist/student overcomes obstacles, looks for resources, and develops new tools.”
  • Act 3 – “Resolve the conflict and set up a sequel/extension.”

Here is an Example – The Slow Forty

(eMINTS teachers….seeing any connections to the Instructional Procedures unit expectation?)

Check out Dan’s Three Act Math Tasks Spreadsheet and his 3-part blog series with videos and instructions.

This blog post is from 2011, but Dan is not a one hit wonder. I encourage you to explore his recent blog posts and see what he’s been up to….hint hint – he is quite an active presenter and does so much more than Three-Act Math Stories.

Brooke Higgins, occasional blogger, is an eIS for the eMINTS National Center working with eMINTS teachers, trainers, and administrators. All of her posts, including this one, can be found at The Higgins Helps blog.

Forgotten Algebra

The above xkcd comic expresses a common sentiment. Adults sometimes look back at things they learned (and forgot) in school that they have never had to use since graduation. There’s almost a pride that goes along with forgetting everything one learned in school. I don’t know whether this is tied into anti-elitism or a sense of self-sufficiency, but we are proud that we forget how to do math (among other things) as adults.

Is it true that the knowledge taught in school has never been utilized since moving into the work force? Maybe. However, the difference might lie in how we use these skills or knowledge in school and how we may use them in the “real world.”

A comic like the one above should remind us just how important it is to make the work and learning students do in our classrooms as authentic as possible. We have to find ways in which to relate curricula so that students either won’t want to forget what is learned in class. Making content authentic does not guarantee better retention, but it will at least make the learning more meaningful and even more memorable than algebra was for the women in the xkcd comic.

Zac Early is an instructional specialist and blogger for the eMINTS National Center.

eMINTS Conference: Session 4 (Thursday)

Return of the Speed Geekers!

eMINTS National Center staff Doug Caldwell, Ruth Henslee, Jen Foster, Amy Blades and Brooke Higgins lead this fast-paced and exciting session. Participants benefit from the knowledge of others in the field and walk away with a plan for incorporating 2.0 tools in meaningful ways. Workshop participants view actual, practical and rich examples of online technology tools and hear about implementation strategies used to enhance communication, collaboration, and cognitive thinking. The workshop’s activities are delivered in a “speed-geeking” format. Five stations are set up and participants rotate through each station in timed intervals.

Beyond Blogs and Wikis: Technology Tools for the Writing Classroom

Kerry Townsend presents how teachers of writing will learn new ways in which the collaborative writing process can be taught in the modern, technology-enhanced classroom. Web-based applications such as Google Tools, Twitter, Evernote, Prezi and Weebly are discussed as well as AV software and tools such as iPads/iPods, webcams, document cameras, Audacity, iMovie, etc.

Student and Class Created e-books

Cathie Loesing of the eMINTS National Center shows participants how easy it is to create ebooks and share ideas for classroom use. Creating books in the classroom to support developing reading skills, to share learning and as a component of writing instruction is not a new idea. However, eBooks make sharing those projects easier and more rewarding than ever. See how you and your students can use a free online program to create and share e-books that may be read on smart phones, iPads and other eReaders.

SMART Notebook Math Tools

Laura Brockman from SMART Technologies helps participants create, explore and evaluate math concepts with SMART Notebook™ Math Tools. This add-on to SMART Notebook collaborative learning software combines all the tools you need to teach math concepts and solve equations in a single application. It keeps everything at your fingertips, so you can easily incorporate shapes, measurement tools, graphs and tables into lesson activities.

Tuesday’s Tool: Seeing Math Interactive Tools

Secondary math teachers often struggle to find ways to make tools in their classrooms such as interactive white boards (IWB’s) useful. This equipment with accompanying software just doesn’t always meet their needs for higher level math. Seeing Math has a solution…well, several solutions, actually.

Seeing Math‘s secondary division provides several cool downloads of applications which can help higher levels of math come alive on your IWB. All of the tools are free and are copyrighted under the GNU Lesser General Public License (LGPL), which means they are available for public use. The tools offered are as follows:

  • Qualitative Grapher – “Highlight the meaning of a function, and see how it can be seen as something changing over time, with this tool that links a motion model to a graph.”
  • Piecewise Linear Grapher – “Highlight the language of domain and range, and the ideas of continuity and discontinuity, with this tool that links symbolic and graphic representations of each interval of a piecewise linear function.
  • Linear Transformer – “Highlight the meaning of each component of a linear function’s symbolic expression with this tool that links symbolic and graphic representations of translating (dragging) a line vertically or horizontally, rotating it around a fixed point, or reflecting it around the x- or y-axis.”
  • Function Analyzer – “Highlight the rationale behind symbolic operations used to solve a linear equation with this tool that displays changes in the graphic and area models of functions as you change the value of each symbolic element.”
  • Quadratic Transformer – “Highlight the meaning of each component of a quadratic function’s symbolic expression with this tool that links symbolic and graphic representations of translating (dragging) a parabola vertically or horizontally, dilating it, or reflecting it around the x- or y-axis.”
  • System Solver – “Highlight how symbolic operations on a system of linear equations do (or do not) change the graphic or tabular representations of the system.”
  • Plop It – “Highlight how changing a data set affects the mean, median, and mode with this tool (created by The Shodor Education Foundation and modified by The Concord Consortium) that allows you to add and delete data graphically.”
  • Proportioner – “Highlight proportion and scale with this tool that allows you to compare image dimensions by using one image to “paint” another.

Seeing Math also includes online versions of these tools as well as sample lessons. For more information on Seeing Math, check out their website.

Have you ever used the interactive tools from Seeing Math? What uses could you see for such tools? How would one use these tools in a constructivist manner?

Zac Early is an instructional specialist with the eMINTS National Center and honestly forgets most of what he learned in his high school math courses.

Friday 4ALL: Get Excited About Math!

I am currently on vacation with my family in beautiful Colorado Springs, CO. I have been spending some time with my awesome niece and nephews (two are in high school, one is in middle school, and the youngest is in elementary school). While I try to turn off the teacher mode around them, it does sometimes comes out. They were talking about school, and the subject of math came up. Disregarding the age differences, each one has different feelings about math. One would rather eat worms than work on math while another enjoys their advanced math class.

It got me thinking about some of my favorite math resources. It’s no secret amongst my team that I love to teach math. I am really passionate about that subject. I really enjoy making it fun for my students! I believe that the more they see the usefulness out of it, the more they will enjoy it. I thought I would share a few of my favorite math websites.

Grand Prix Multiplication – This is one of my favorite games for practicing multiplication. Students in my classroom are able to race their fellow classmates or kids from around the world. They have to quickly answer multiplication facts. There is even a display board that shows top times. For student safety, students do not use any personal information for a screen name. This game is hosted on a site called Arcademic Skill Builders. I really enjoy the entire site. There are math activities for grades K-12, as well as activities that focus on other subject areas as well.

The Factor Game - This game was a huge hit in our classroom this past school year. Students start out by using a grid that displays the numbers 1 – 30. Student A chooses a number that has to have at least one factor available on the board (ex: 27). Student A receives 27 points. Student B gets to choose all of the numbers that are factors of 27 that haven’t been chosen yet (so, Student B would get the numbers 1, 3, and 9. They would not receive 27, because Student A already chose that number). Student B receives those points (9+3+1 = 13 points). Play continues with Student B choosing a number. Once a number has been chosen, you cannot choose that number throughout the rest of the game. You can lose your turn if you choose a number that doesn’t have any available factors. Also, if you forget to choose a factor, you do not get those points.The student with the most points at the end of the game wins. We set up a championship bracket this year where students would play this game, tournament-style. It was a huge success, and a great way to practice looking for factors!

I really enjoy the entire Illuminations website. It is run by the National Council of Teachers of Mathematics. You can search by grade level and find appropriate activities for your students. They also include lesson plan ideas, online activities, and other resources.

Free Rice – This one has gone around our school. Students can practice multiplication or basic math fact problems. For each correct answer, the Free Rice program donates 10 grains of rice to the World Hunger Program. It’s a great way to practice your math and do something good for others! You can also choose from other subject areas as well.

Set – This is a website designed off of a popular card game in my classroom. Students look for three cards that are either all the same or all different. Kids have a great time looking for the patterns and using reasoning to make their choices! I really like giving logic puzzles as an option to students for when they finish their work. I believe they promote critical thinking.

24 – This one is also adapted off of a card game that I play with kids in my classroom. Students get four cards. They can use addition, subtraction, multiplication, or division, or any combination, but the total at the end must equal 24. They also must use each card.

These are a few of my favorite math resources to use in the classroom. I am lucky in the fact that I have a computer for every two students in my classroom, so I know that this may be difficult without these resources. However, many of these games can be adapted or purchased so they can be used without computers. What are some of your favorite math websites?

This post was originally published here and submitted by its author, Kelly Pfadenhauer, a fourth grade teacher.

HD_Links: Making Sense of Measurement

Here are some links to support students of all ages by giving visual references to help make abstract measurements more concrete.

The Learn.Genetics site created by The University of Utah has created a Cell Size and scale visual that allows visitors to view the size of cells from a coffee been down to a carbon atom. Use the slide bar to zoom down from 12 ml (millimeters) all the way down to 340 pm (picometer = a trillionth of a meter).

Let students compare themselves to other animals by measuring their ear, height, and foot length and see where they line up in size to other animals with similar dimensions. The Lawrence Hall of Science has created the Measure Yourself and other measuring activities such as “Jump Start” which has students jump as far as they can then measure the distance they covered to compare it to their friends and other living organisms like a grasshopper or rabbit.

From the BBC’s Math files, Animal Weigh In, has students balance a scale with weights that equal the same amount as the animals sitting on the scale. Student will practice adding and converting weights in pounds, ounces, grams, kilograms, stones, and tons.

eThemes, your source for online resources that are content focused and are safe for students, has 4 “themes” on measurement that might include additional links to help your students learn about this topic. Check out Math: Metric Measurement, Math: Customary or Standard Measurement, Math: Telling Time, or Science: Temperature.  If you are an eMINTS teacher and still can’t seem to find the exact resources you are looking for resources, you can always request a new eTheme and get what you are looking for and save yourself the time searching Google.

Brooke Higgins is an instructional specialist with the eMINTS National Center. You can read more at her blog Higgins Helpful Hints Blog. Diane McCormack, a PD4ETS Graduate and Instructional Technology Facilitator with the Affton Public Schools, shared some of these and other great resources.

HD Links: Math & Constructivism

Finding the natural overlap between Constructivist teaching and mathematics can often times be a challenge for teachers that are departmentalized and are responsible for teaching just one subject. The nature of math encourages educators to often times focus on the skills and can make it hard to blend the skills together to show how they overlap in real life. The following links might help in creating more authentic learning opportunities where students can use the skills of math in real life applications.

Yummy Math – Focus to supply math teachers with relevant, motivating, and timely mathematics to bring to their classrooms.

Real World Math - Lessons that use Google Earth and collaboration to present math topics, such as rates or scientific notation in unique ways.

Project-based Learning Math Projects – information about PBL and Math including links to PBL resources and lesson ideas.

Scholastic Authentic Math Unit Plans – Ideas to bring the real world into the classroom and create opportunities for students to interact with each other and integrate math into authentic learning situations.

Authentic Activities for Connecting Mathematics to the Real World
– presented at NCTM Regional Conference, Richmond, VA, October 12, 2007 by Leah P. McCoy

These are just a few websites teachers might find helpful when planning inquiry, project or problem-based lessons. If you have additional sites please share them by leaving a comment.

Brooke Higgins is an instructional specialist for the eMINTS National Center and writes for her own blog, Higgins Help.

Real World Math is a Plus

Looking for real world, intriguing problems to get your students thinking?  Then you should check out Plus Magazine.

Plus Magazine offers puzzles, articles, podcasts, and reviews from top mathematicians. The puzzles and problems feature real world applications and highlight careers in math, science, and engineering.   You can also subscribe to the Plus Magazine Podcast.  This web resource could be used to offer challenge problems to the whole class or to spark an idea for a more in depth math project!  When students connect math to the real world, it is a Plus!

Carmen Marty is an instructional specialist with the eMINTS National Center.