An Interesting Blog of Math Illustrations --- Picasso Math

Picasso Math is an interesting blog containing illustrations of math topics. These can be used in many ways. I think students would enjoy them. This would also be a great way to bring Novelty to the classroom.

Here are a few ideas:

• Use them as writing/journal prompts. Students could describe the math topic being illustrated or describe what the illustration means.

• Show one to students and have them create their own for a different math concept/topic. For example: Show this one about dividing fractions (see below) and have students create their own about multiplying fractions.

• Have students critique the image. Do they thing it best represents the math topic? If so, why. If not, why?

Happy Illustrating! Hope you enjoy this great resource!

via picassomath.blogspot.com

Excellent Resources from RealWorldMath.org

via realworldmath.org

Here's an example of a Line Graph that was created using Google Earth. This image is courtesy of Real World Math. This site is definitely worth checking out!

About Mirror Neurons

via publicwords.typepad.com

Learn a little about mirror neurons in 51 secs.

Sixty Symbols - Physics and Astronomy videos

via sixtysymbols.com

Very cool site. Check out the Pi symbol and video!

Collaborize Classroom - Online Education Technology for Teachers and Students

via collaborizeclassroom.com

Collaborize Classroom is an easy to use online discussion forum. I especially like the various ways you can post questions for class discussions.
This is an excellent tool for posting multiple choice questions and having students choose answers that do not make sense. You can also have them explain their choices in the Comments section which appears below the Posted Question.
I'll share more ways to use this tool with math students in future posts.

Connect a Million Minds - Videos

via connectamillionminds.com

This is a great video from Connect a Million Minds that demonstrates the type of things are possible because of Math and Science. If you have students who are not interested in math, start showing them videos like this. After seeing what's possible because of math, students who don't like math might just change their minds!!!

Technology Tip: Glogster

A New Way to Create Posters!
Glogster is an interactive poster maker.  You can upload documents and videos into your posters.  You can also create links within the poster.  This is a fantastic way for students to create and share posters about math concepts!!!

Ideas for Using Live Binders with Math Students:

• Alternative Assessments                                                                                                                                                                                                                                                                                                             Have students create a Glog at the end of a unit and use it as an Alternative Assessment.  Ex.  Students could create a Glog about Proportions.  You could give them a rubric of things that must be included in the Glog.  For example:  1 example of a proportion, 1 example of how to solve a proportion, the definition of a proportion, a video of them explaining how to solve a proportion, etc.

• Showing Multiple Representations                                                                                                                                                                                                                                                                                                    Have students create a Glog to show Multiple Representations of a particular problem.  For example:  Create a Glog showing Multiple Representations of how to solve an equation, or create a Glog showing Multiple Representations of how to add fractions (estimate, draw a picture, work the algorithm, justify your answer).

These are just a few of the ways you can use Glogs with your students.  Look for more ways to use Glogster with your math students on our Love of Learning Blog.

Technology Tip: Live Binders

Live Binders is an easy to use online bookmarking site.  You can organize websites by tabs and subtabs.  When you select a tab or subtab, the website or document you have loaded into the binder opens. 

Live Binders Features:

• navigate websites from within the binder
• share binders or keep them private
• allow collaboration on binders
• add notes to binders
• upload images, documents, or videos into binder

Ideas for Using Live Binders with Math Students:

• Create binders with interactive math sites for students to access.                                                                                                                                                          Ex.  A binder could contain sites like  visual fractions, IXL, cool math, funbrain, etc.

• Create binders based on a particular topic and share with students.                                                                                                                                                         Ex.  Create a binder with websites, documents, images, and videos about topics like Pythagorean Theorem, Adding Fractions, Proportions, Angles, etc.)

• Have students create online portfolios with their work.                                                                                                                                                                         When students create products online, they can save them into a Live Binder as an online portfolio.  They can also upload written documents into the binder.  This would be a great way for students to be able to share their work with their parents.

• Create shared portfolios of student's work on a particular topic.                                                                                                                                                                                                                                           Ex.  You could have students create a Glog about angles.  Then you could have the entire class share their Glogs in a Live Binder.  This is a great way to share work and to have it available for students to view any time.

These are just a few of the ways Live Binders can be used with math students.  Creating online Portfolios is also a great way to keep parents involved.  If your school has Student Led Conferences, this would be a new way for students to share their work with parents.

Differentiation Tip: Questioning Strategies

Varying your questioning and targeting specific questions to specific students is a great way to differentiate instruction.  During the course of a class, you can ask higher level or more open questions to students are at a higher level of readiness.  You can direct lower level or more closed questions to students who have a lower level of readiness for the skill or concept being taught.

If you're doing a lesson that involves manipulatives or problem solving, you can provide more or less scaffolding depending on the needs of the student.  Many times opening (providing few parameters) or closing tasks (providing more parameters) can be an easy way to differentiate.

Example of Differentiating by Opening or Closing a Task:

Lesson:  Exploring Fractions with Multilink Cubes

Students are shown an example of a fraction tower made with multilink cubes.  They are then given tasks to create their own fraction towers.

This is a fraction tower that has one-half red cubes.

Task A:  Build a fraction tower that is made up of two-thirds red cubes. 

(This task is completely open.  The only parameter is that is must have two-thirds red cubes.  Students have to decide how many total cubes to use.  Some students might use 2 different colors and some students may use more than 2 colors to build their towers.)


Task B:  Build a fraction tower with 9 total cubes and is made up of two-thirds red cubes.

(This task is now somewhat closed because you have stated how many total cubes to use for the tower.  If students were having trouble with the Task A because it was too open, this would be one way to make it easier.  It does still have an open element to it because you haven't stated if the tower has to have exactly 2 colors or more than 2 colors.)


Task C:  Using 3 different colors, build a tower that represents two-thirds.

(This task is mostly open with 2 parameters:  3 colors and represents two-thirds.)


Task D:  Using 3 different colors and 6 total cubes, build a tower that represents two-thirds.

(This task is completely closed.  Since you are using 6 total cubes and representing two-thirds, you would not be able to create a tower with more than 3 colors.  If you had specified a value greater than 6 for the total cubes, there would still be an open element to the task.)

Task E:  Build a tower that is one-half red, one-third green, and one-sixth blue.

(This task has 3 parameters, but is open in respect to the total number of cubes used to build the tower.  If students were struggling with this task, it could be made easier by giving a total number of cubes or by scaling back on the given parameters.  For example, you could just say to build a tower that represents one-sixth.)

Adjusting questions and tasks can be a quick and easy way to differentiate instruction, but it does take some practice.  The great thing about this strategy for differentiation is that you have plenty opportunities to practice and fine tune it!

Brain-Based Learning Teaching Stategy: Respecting Attentional Limitations

Do you often have trouble getting students to pay attention?  There's a very good reason for this!

Our brains have limitations on how long we can maintain focused attention.  The number of minutes a person can maintain focus is usually equivalent to their age in minutes.  So, if you teach 12 year olds, 12 minutes is about how long they can maintain focused attention.  However, this formula does max out at about 15 - 20 minutes. 

So, what can we do about these attentional limitations?

Knowing these natural limitations, there are several things we can do to keep students focused on the task at hand.  Here are a few strategies for helping students focus.

• Always be mindful of the attention limitations and break teaching into smaller segments.  If you have a lesson that you know is going to take longer than 12 - 15 minutes, break it into chunks.  In between chunks of information, have students do a Think-Pair-Share or something similar to give the brain a break and allow time to process new learning.

• Give Cues as a way to let students know that something important is coming.  For example, say things like, "If you don't hear anything else today, make sure you hear this."

• Use physical actions to get student's attention when you are ready to move on to something else.  For example, say to the class, "join me when you can" and start clapping your hands in some type of pattern.  Students would then repeat the pattern of claps.  Keep doing this until everyone has joined in the clapping, and then go right into the next segment of the lesson.

Differentiation Tip: Think-Pair-Share

Think-Pair-Share is a quick and easy way to tap into student's prior knowledge or to allow students time to process information.  Think-Pair-Share can be used at any point during a lesson.  

Think-Pair-Share Procedure:

• Give a question or vocabulary word to think about

• Allow a few moments (usually about 30 sec to a minute or so) for students to think about the question or problem

• Have students share their thoughts with a partner.  They should also come to an agreement about what they want to share with the class

• Have pairs of students share their thoughts on the question or problem

 Using Think-Pair-Share before a lesson:

• allows students to tap into their prior knowledge.

• allows you to gather formative data about what students already know about a topic before starting instruction.  You can adjust instruction based on student responses.  For example, you may discover that students already know a lot about this topic and only need a short review rather than a complete lesson.  Or,  you may notice that students have some misconceptions about the topic that need to be addressed during instruction. 

Using Think-Pair-Share during a lesson:

• allows students time to process their learning.

• allows you to gather formative data about what students are getting from the lesson.  You can then adjust instruction based on what you see.  If students seem to understand what they've just learned, you can move on.  If they seem to have some misconceptions, you can address them when instruction continues.  This could also be a perfect time to break students into groups based on understanding of the concept.

  Using Think-Pair-Share at the end of a lesson:

• allows students time to process and reflect on their learning.

• allows you to gather formative data about what students got from the lesson.  You can then adjust instruction for the next based on what you learn.  You could use this information to assign small groups the next day.  Some groups may be ready to practice the skills being learned and others may need more small group instruction.

Think-Pair-Share Graphic Organizer:

Think-Pair-Share Graphic Organizer  - This graphic organizer will help students keep track of their thoughts during a Think-Pair-Share.  They could keep it in their binders and keep adding to it each time you do Think-Pair-Shares.

Differentiation Tip: Providing Choices

Allowing students to make choices is one of the most effective and easiest ways to differentiate.  There are many ways to provide students with choices.  One way is to give them choice about which problems they want to work.  You could even have the problems marked as easy, medium, and hard.  You can either allow free choice by just saying each student has to work 10 of the given problems, or you could set more parameters.  Such as,  you have to work 4 easy problems, 4 medium problems, and 2 hard problems. 

Unit Rate Stations Activity:

A favorite activity of my students, was when I made problems into stations and let them choose which ones to work.  I might make 20 problems and tape them on the walls around the room.  (Each problem was a station.)  My students would have to work 10 of the 20 problems. 

One year for Halloween we were learning about unit rates.  I went to the Oriental Trading website and downloaded pictures and prices of various items.  I made 25 stations with one picture per page.  My students had to choose 15 items and calculate the unit rate of each.  I had purposely chosen gross items or items that I thought they would like.  They had more fun with this activity than I had even expected.

You could even have students make up their own stations.  Have each student go to a site like Oriental Trading and make and solve 2 problems of their own.  Then combine the problems made and use these as your stations. 

Added Benefit of Using Stations:  Stations get students out of their seats which gets oxygen flowing to the brain.