## Math Debates in Elementary Classrooms

Over the past few months I’ve dedicated a good amount of time to to having math conversations. These math conversations occur when the class is unsure of how to solve a problem or when disagreement ensues over what particular strategy should be used to tackle a problem.  The math conversations (or debates) allow students the freedom to openly discuss logical reasoning when solving particular problems.   These conversations can be sparked by the daily math objective or follow another student’s response to a question.  It’s not necessarily planned in my teacher planner as “math conversation” in yellow highlighter, but I do make time for these talks as I feel that they bring value and encourage student ownership.  The conversations also give insight to whether students grasp concepts and are able to articulate their responses accordingly.  Mathematical misconceptions can also be identified during this time.

During these conversations I have manipulatives, chart paper, whiteboards, iPads and computers nearby to assist in the discovery process.  I emphasize that there’s a certain protocol that’s used when we have these discussions.  Students are expected to be respectful and listen to the comments of their classmates.  To make sure the class is on task I decide to have a specific time limit dedicated to these math conversations.  Some days the conversation lasts 5 minutes, other days they may take upwards to 15-20 minutes.  When applicable, I might use an anchor chart to display the progress that we’ve made in answering the questions.  I should also mention that sometimes we don’t find an answer to the question.  Here are a few questions (from students) that have started math conversations this year:

• Why is regrouping necessary? (2nd grade)
• What can’t we divide by zero? (3rd grade)
• Why are parentheses used in math? (3rd grade)
• Why do we need a decimal point? (1st grade)
• When do we need to round numbers? (2nd grade)
• Why is a number to the negative exponent have 1 as the numerator? (5th grade)
• Why do you have to balance an equation? (5th grade)
• How does the partial products multiplication strategy work? (3rd grade)
• Why do you inverse the second fraction when dividing fractions? (5th grade)
• Why is area squared and volume cubed? (4th grade)

Above is just a sampling of a few of the math conversations that we’ve had.  Afterwards, students write in their journals about their experience finding the solution to the problem.

Of course this takes additional time in class, but I believe it’s time well spent.  The Common Core Standards  focus on depth of mathematical understanding, rather than breadth.  This allows opportunities to have these conversations that I feel are beneficial.  They also emphasize the standards of practice below.

• CCSS.Math.Practice.MP1 – Making sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP3 – Construct viable arguments and critique the reasoning of others

Do you have math conversations in your class?

## Equivalent Fractions Tweak

A few days ago I started gathering resources to supplement a math unit on fractions.  The classroom was studying equivalent fractions and I thought there might be a variety of resources available on a few of the blogs that I regularly visit.  I generally follow the #mathchat hashtag  and find/share ideas that relate to mathematics.  While reading a few math blogs on fractions, I came across John Golden’s site that has some amazing ideas that can be used in math classroom.  His triangle pattern template sparked my interest.

John provided a template that’s available on his site.  I printed out the template and began filling out each triangle with fractions.  I ended up with a sheet that looked like this.

So what happened?

First a lot of brainstorming and error checking.  Then I decided to have students cut out the triangles and compile equivalent fractions.  This is what happened …

Students in fourth grade cut out each triangle and combined them to make equivalent fraction squares.  Students worked in collaborative pairs during the project.  I observed students using math vocabulary and having constructive conversations with each other to finish the assignment.

Before giving the assignment to a fifth grade class I decided to eliminate two triangles on the sheet above.  It was the job of the student to find what triangles were missing and create equivalent fractions to complete the squares.  The students were engaged in this activity from start to finish.  Some students even wrote the equivalent decimal next to each square.

Overall this project took approximately 45 minutes to complete and it was worth every minute.  Students used the terms fraction, improper fraction, mixed number, numerator, denominator, multiplication, division, and pattern throughout the project.

Just as I did, feel free to tweak this project to best meet the needs of your students.

## Student Data and Balance

Teachers in K-12 often use student data on a regular basis.  Student achievement data can be used to qualify students for reading, gifted, remedial, enrichment, acceleration, differentiation, and a variety of other services.  Recently, standardized testing data has been the forefront of educational trends and in the news.  Implementing a  balanced approach when looking at student data can keep stakeholders (educators and administrators) grounded in an understanding that the numbers behind the tests may give light to areas of strengths/needs.

Data isn’t evil

Assessing a student’s understanding of a specific concept isn’t necessarily a bad thing.  In fact, over the past few years I’ve grown to appreciate and utilize student achievement data more and more.  Whether the data is from a standardized test or not, the data can be helpful if used correctly. Moving data beyond just a number can benefit teachers and students.  Data can help teachers ask better questions and provide opportunities to reflect on how students learn best. Involving students in analyzing their own data can encourage student goal setting and ownership.

Having conversations with students about their data is powerful.

Have the conversation

I’m definitely not an advocate for having additional standardized tests, although some seem more useful than others.  I find that assessments that give detailed feedback (e.g. areas that need strengthening, %ile compared to the norm, strength areas, next instructional steps, etc.) are more frequently used by teachers, compared to assessments the give little feedback.  Obviously, there isn’t a perfect test available for school purchase.  The assessments that a school uses should give detailed feedback that can be immediately used.

Do you hear a lot of negative talk in regard to standardized assessments?  Having a conversation about an assessment’s effectiveness in informing instruction may be needed. Instead of trash talking the assessments in general, educators and administrators should find assessments that work for them.  PLC teams should emphasize the importance of using formative assessments regularly.  I’ve found that teacher created formative assessments are some of the best ways to find areas that need strengthening and to identify differentiation opportunities.  The purpose of giving the assessments should be communicated to all stakeholders.  When teachers understand why the tests are given, (not just for VAM reasons), they may start to value the benefits of assessing students using a variety of tools (such as Common Core performance assessments).

Balance is needed

With teaching and in life, balance is needed.  Teaching is a profession that can be stressfull.  It has many teachers thinking right now, how many days till Spring Break??   Balancing assessments with instruction takes skill and patience.  Standardized tests are often at the forefront of school administrator’s minds.  One test shouldn’t be used to determine if success, or enough growth has been made to call that school year/class/school successful. Take a breath and look at assessments from a macro lens. A combination of formative, informal, formal, review checkpoints, activators, performance  (insert your assessment here), and even standardized assessments have their place in a school and can be beneficial to a certain extent.  The value of the data often depends on how it’s utilized.

Picture Credit: DigitalArt

“Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won’t come in.” Isaac Asimov

## Measurement and Mini Golf

Approximately a week ago I was paging through my math curriculum. Through a pre-assessment I found that students were in need of a review on angle classification and measuring skills.  The curriculum lessons offered a number of worksheets and angle measuring drills.  Although these lessons seemed beneficial, I felt the need to create a more memorable learning experience for my math students.   At this point, I decided to search for measurement projects. While following #mathchat, I came across this Edgalaxy site.  The project seemed to match many of the objectives that needed strengthening in my class.  I changed up the directions and modified some specifics in order to best meet the needs of my students.

So … a week has passed and almost all of the projects are complete.  I listed the project steps below.  Feel free to use any of the ideas below in your own classroom.

1.  Had out the direction sheet.  Here is a Word template (via Google Docs) for your use.

2.  Review many of the different vocabulary words associated with the project: acute, obtuse, right, parallel, perpendicular, trapezoid, etc.

3.  Show possible examples.  I tend to show just a few examples as I don’t want to give them a mini golf course to copy.

4.  Group the students into pairs.  If you prefer, this project could be implemented as a collaborative group activity.

5.  Students choose their construction paper color (11″ x 20″)

6.  Students draft their course in pencil (on grid paper).  The draft gets approved by the teacher and then is transfered to scale on construction paper.

7.  Students present their final projects to the class.

## iPad Apps for Math Intervention

Over the past few months I’ve been experimenting with guided math strategies in my classroom. One station in my classroom has been dubbed as the technology table. This table has been primarily used to differentiate  instruction to improve students’ understanding of mathematical concepts.  I’ve been using the tech table for the past few months with great success. There are five iPad apps that are used at this table.  Unlike many math apps that offer only demo versions, I’ve found the below apps to be useful in the classroom.

5 Dice

This app is the newest addition to my iPads for intervention list.  This app emphasizes order of operations for upper elementary and middle school students.  The game encourages students to use multiple dice to find the “target” number.  A whiteboard is built into the game for students to work out problem.  Progress reports can be emailed to the teacher for formative assessment data.

This app is used to differentiate math instruction and assigned practice.  What I like so much about this app is the variety of concepts that I’m able to individualize.  For example, if a student needs additional work on the concept of time, then I can setup the app to only give questions related to time. Questions first appear simple, but then become more challenging as questions are answered correctly.  If you prefer, Splash Math will send you a weekly update indicating the progress of each student.

Math Blaster Hyper Blast

This app is used to improve computation fluency.  This interactive app has a quick tutorial to teach students how to move the main character through a variety of mazes.  Students control a space vehicle that inevitably encounters an octopus type of creature.  Students must answer computation (addition, subtraction, multiplication, or division) questions to defeat the boss.

Factor Samurai

Factor Samurai is an app geared towards emphasizing the concepts of prime and composite numbers.  Basically, numbers fly into the air and the student is expected to slice the composite numbers with their fingers.  If it’s a prime number, then the student leaves the number alone.  Some composite numbers can be sliced multiple times.

ScootPad can be used to individualize practice in your classroom.  I’m able to assign specific students certain Common Core objectives to practice. After a student completes an assigned section, they are allowed to see all of the correct answers.  Scootpad will also send the teacher a statistical report of the progress made by individual students.  I’d also like to note that Scootpad can also be used on a PC or MAC.

Honorable Mentions:

#### Rocket Math

update:  02/03/13

I’ve been asked by a number of people what apps I would recommend to an elementary teacher.  I decided to create a quick chart to help.

## Still Exploring Guided Math

I recently participated in an afternoon professional development session led by Laney Sammons.  The session focused on how to implement guided math.  I’m still understanding the guided math process, as you can tell by the picture above.  I wouldn’t consider myself an expert in guided math, but I’m starting to use a few strategies that Laney discussed today.

A few takeaways from today …

• Guided math can be similar to guided reading
• Math games can be used in stations
• Groups should consist of no more than six students
• Groups can be used for informal assessments
• There isn’t a “one size fits all” model for guided math

After the session I decided to explore guided math a bit further.  The links below have been vetted and may help shed additional light on guided math in an elementary setting.

Feel free to share any links or blog posts that you find relevant in the comments section.  Thanks!

* Picture credit to Janoon28

## So You’ve Been to a Common Core Training?

If you are like many educators, then you’ve been trolling to find additional information about the Core and resources that will enhance your instructional practice.  I’ve created a list below that may help us (as we are all in this together) unravel the Common Core and the changes that it will elicit over the next few years.  The links below aren’t listed in any prioritized order, but they are categorized to help you (and me) find and use the information quickly.  I have many of these sites already bookmarked, as I receive questions on the Common Core and it’s far reaching impact.

Blog Posts:

General Info on the Common Core:

Livebinders / Digital Newspapers:

Testing Questions / PAARC / Behind the Scenes:

## “Aligned” to the Common Core

Image by:  Felixico

Now more than ever it seems that educational leaders are being encouraged to align their curriculum to the Common Core. Currently, 45 states and 3 territories have signed the Common Core initiative.  National tests are now being developed to evaluate how well students understand the math and reading Common Core standards.  Seeing that the majority of the United States supports the Core, new “Common Core Aligned” products seem to be popping up everywhere. Workshops, seminars, webinars, and PD sessions are dedicated to communicating how the Common Core standards impact curriculum.  In general, I believe that the workshops mostly benefit teachers. I also believe that the Core will give opportunities for educators to positively change the way that they deliver math and reading instruction. What I’m concerned about though is how the “aligned” resources are being utilized.  I in no way endorse/oppose the products below, but the images & links contribute to the notion of how publishers (McGraw Hill, ASCD, Pearson, etc.) are marketing Common Core resources to educators and administrators.

I’m finding that teachers are being pressured into purchasing these “aligned” materials to prepare their students for the upcoming accountability testing.  I’m not against the Common Core materials being produced or used in the classroom.  I’ve actually read many “aligned” resources and have found them most beneficial.  To be honest, most educators that I know have already viewed a number of the Common Core materials.

Don’t get me wrong, educators should be aware of the new standards and adjust their instruction accordingly.  The over reliance on “aligned” published materials can cause teachers to take less risks as they focus only on items located in specific published books.  In these cases differentiation may occur less as the teacher uses whole group Common Core instructional techniques to cover specific content that’s found on future standardized assessments.  I view the “aligned” resources as important and another tool in an educators tool belt.

“Aligned” materials and other supplemental materials should not be viewed as a magic bullet in raising test scores or in teaching in general.  Instead of impulsively purchasing “aligned” materials, school districts around the country should collaborate with each other to share resources that will benefit all stakeholders involved.  I believe some states are attempting to use this model and I applaud their efforts.

Utilizing teaching strategies that work for educators and their students instill an appreciation for learning and give students an opportunity to show their learning in new settings.  Using solid pedagogy along with supplemental resources allows teachers to differentiate their instruction to meet the needs of all students.